Engineering Tripos Part IIB, 4A15: Aeroacoustics, 2018-19
Module Leader
Lecturers
Dr Agarwal, Professor Ann Dowling and Professor Nigel Peake
Timing and Structure
16 lectures + 2 examples classes; Assessment: 100% exam
Prerequisites
3A1 assumed
Aims
The aims of the course are to:
- analyse and solve a range of practical engineering problems associated with acoustics.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand how sound is generated.
- understand how sound propagates in free space and within ducts.
- understand shielding and scattering of sound.
- model sound sources for various aeroacoustic problems and design for low noise.
Content
The students are expected to analyse and solve a range of practical engineering problems associated with acoustics. Examples include modelling of noise sources from jets, fans, wind turbines, vacuum cleaners, etc. and exploring ways to reduce noise either at the source or through acoustic damping. Upon completion of this module, the students would be well placed to pursue research in the area of acoustics and related fields. Students would also be more employable (the topics covered in the course is of interest to GE, Rolls-Royce, Dyson, Mitsubishi Heavy Industries, automobile companies and acoustic consultancies)
Classical Acoustics (5L) (Dr A Agarwal)
- The wave equation and simple solutions
- Impedance
- Energy
- Generalised functions and Green’s function
- Sound from simple sources (monopoles, dipole, compact sources)
Jet noise (3L) (Dr A Agarwal)
- Compact quadrupole
- Sound from a single eddy
- Sound from a random distribution of eddies
- Lighthill’s eighth-power law
- Convection and refraction effects
Sound propagation (2L) (Prof. N. Peake)
- Ray theory
- Snell’s law
- Refraction by temperature gradients
Trailing edge noise (2L) (Prof. N. Peake)
- Scattering and shielding
- Scattering from a source near a sharp edge
- Example: Wind turbine noise and the aeroacoustics of the owl
Duct acoustics (2L) (Prof. A P Dowling)
- Normal modes
- Concept of cut-off modes
- Damping/liner
- Helmholtz resonator
- Example: Thermoacoustic instability
Rotor/Fan Noise (2L) (Prof. A P Dowling)
- Rotor alone noise
- Rotor/Stator interaction noise
- Examples: Aircraft noise, fan and turbine noise
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 01/06/2018 12:07
Engineering Tripos Part IIB, 4A15: Aeroacoustics, 2020-21
Module Leader
Lecturers
Dr A. Agarwal and Dr A. Gregory
Timing and Structure
Lent term: 16 lectures + 2 examples classes; Assessment: 100% exam
Prerequisites
3A1 useful, 3C6 useful
Aims
The aims of the course are to:
- analyse and solve a range of practical engineering problems associated with acoustics.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand what sound is and how we perceive it
- understand how sound is generated and propagated
- understand the acoustics of a wide range of music and noise production
Content
We will analyse and solve a range of practical engineering problems associated with acoustics. Examples include modelling of noise sources from jets, fans, musical instruments, human voice, kettles, dripping taps, whistling mice, singing flames, etc. We will also study ways to reduce noise either at the source or through acoustic damping. Upon completion of this module, the students would be well placed to pursue academic research in the area of acoustics and related fields or to work in industry (the topics covered in the course is of interest to GE, Rolls-Royce, Airbus, Dyson, Mitsubishi Heavy Industries, automotive companies, music industry, and acoustic consultancies).
What is sound and how does it propagate? (5L) (Dr A Gregoryl)
- Introduction
- The wave equation
-
Some simple 3D wave fields (plane waves, surface waves and spherical waves)
- Sound transmission through different media
Simples sounds sources (2L) (Dr A Agarwal)
- Pulsating sphere
- Oscillating sphere
- Example: loudspeaker with and without a cabinet
General solution to wave eqn (2L) (Dr. A Gregory)
- Green's function
- Sound from general mass and force sources (examples, Bliz siren and singing telephone wires)
Jet noise (Dr A Agarwal) (1 L)
- Scaling of jet noise. How much does jet noise increase by if we double the jet's velocity?
- What do jets and tuning forks have in common?
- Lighthill's acoustic analogy
- Sound of aircraft jets and handdriers
Duct acoustics (2 L) (Dr A Agarwal)
- Rectangular ducts (example, sound box)
- Low-frequency sound in ducts
- Circular ducts
- Acoustic liners (Helmholtz resonator, blowing over a beer bottle)
Musical acoustics & everyday things (3L) (Drs A Agarwal and A Gregory)
- String instruments
- Wind instruments
- Brass instruments
- Whistling of steam kettles and Rayleigh's Bird Call
- Acoustics of dripping taps
Vocalisation (0.5 L) (Dr A Gregory)
- Human speech, singing and overtone singing
- Mice mating calls
Fan noise (1L) (Dr A Agarwal)
- Rotor alone noise
- Rotor-stator interaction noise
Thermoacoustics instability (0.5 L) (Dr A Agarwal)
- Rijke tube experiment (singing flames)
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 01/09/2020 10:25
Engineering Tripos Part IIB, 4A15: Aeroacoustics, 2021-22
Module Leader
Lecturers
Dr A. Agarwal
Timing and Structure
Lent term: 16 lectures + 2 examples classes; Assessment: 100% exam
Prerequisites
No prerequisites. The module would be of interest to students with Aero, Mechnical, Bio or Civil Engineering background.
Aims
The aims of the course are to:
- analyse and solve a range of practical engineering problems associated with acoustics.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand what sound is and how we perceive it
- understand how sound is generated and propagated
- understand the acoustics of a wide range of music and noise production
Content
We will analyse and solve a range of practical engineering problems associated with acoustics. Examples include modelling of noise sources from jets, fans, musical instruments, human voice, kettles, dripping taps, whistling mice, singing flames, etc. We will also study ways to reduce noise either at the source or through acoustic damping. Upon completion of this module, the students would be well placed to pursue academic research in the area of acoustics and related fields or to work in industry (the topics covered in the course is of interest to GE, Rolls-Royce, Airbus, Dyson, Mitsubishi Heavy Industries, automotive companies, music and biomedical industries, and acoustic consultancies).
What is sound and how does it propagate? (5L) (Dr A Agarwal)
- Introduction
- The wave equation
-
Some simple 3D wave fields (plane waves, surface waves and spherical waves)
- Sound transmission through different media
Simples sounds sources (2L) (Dr A Agarwal)
- Pulsating sphere
- Oscillating sphere
- Example: loudspeaker with and without a cabinet
General solution to wave eqn (2L) (Dr. A Agarwal)
- Green's function
- Sound from general mass and force sources (examples, Bliz siren and singing telephone wires)
Jet noise (Dr A Agarwal) (1 L)
- Scaling of jet noise. How much does jet noise increase by if we double the jet's velocity?
- What do jets and tuning forks have in common?
- Lighthill's acoustic analogy
- Sound of aircraft jets and handdriers
Duct acoustics (2 L) (Dr A Agarwal)
- Rectangular ducts (example, sound box)
- Low-frequency sound in ducts
- Circular ducts
- Acoustic liners (Helmholtz resonator, blowing over a beer bottle)
Musical acoustics & everyday things (3L) (Drs A Agarwal)
- String instruments
- Wind instruments
- Brass instruments
- Whistling of steam kettles and Rayleigh's Bird Call
- Acoustics of dripping taps
Vocalisation (0.5 L) (Dr A Agarwal)
- Human speech, singing and overtone singing
- Mice mating calls
Fan noise (1L) (Dr A Agarwal)
- Rotor alone noise
- Rotor-stator interaction noise
Thermoacoustics instability (0.5 L) (Dr A Agarwal)
- Rijke tube experiment (singing flames)
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 21/05/2021 13:24
Engineering Tripos Part IIB, 4A15: Aeroacoustics, 2017-18
Module Leader
Lecturers
Dr Agarwal, Professor Ann Dowling and Professor Nigel Peake
Timing and Structure
16 lectures + 2 examples classes; Assessment: 100% exam
Prerequisites
3A1 assumed
Aims
The aims of the course are to:
- analyse and solve a range of practical engineering problems associated with acoustics.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand how sound is generated.
- understand how sound propagates in free space and within ducts.
- understand shielding and scattering of sound.
- model sound sources for various aeroacoustic problems and design for low noise.
Content
The students are expected to analyse and solve a range of practical engineering problems associated with acoustics. Examples include modelling of noise sources from jets, fans, wind turbines, vacuum cleaners, etc. and exploring ways to reduce noise either at the source or through acoustic damping. Upon completion of this module, the students would be well placed to pursue research in the area of acoustics and related fields. Students would also be more employable (the topics covered in the course is of interest to GE, Rolls-Royce, Dyson, Mitsubishi Heavy Industries, automobile companies and acoustic consultancies)
Classical Acoustics (5L) (Dr A Agarwal)
- The wave equation and simple solutions
- Impedance
- Energy
- Generalised functions and Green’s function
- Sound from simple sources (monopoles, dipole, compact sources)
Jet noise (3L) (Dr A Agarwal)
- Compact quadrupole
- Sound from a single eddy
- Sound from a random distribution of eddies
- Lighthill’s eighth-power law
- Convection and refraction effects
Sound propagation (2L) (Prof. N. Peake)
- Ray theory
- Snell’s law
- Refraction by temperature gradients
Trailing edge noise (2L) (Prof. N. Peake)
- Scattering and shielding
- Scattering from a source near a sharp edge
- Example: Wind turbine noise and the aeroacoustics of the owl
Duct acoustics (2L) (Prof. A P Dowling)
- Normal modes
- Concept of cut-off modes
- Damping/liner
- Helmholtz resonator
- Example: Thermoacoustic instability
Rotor/Fan Noise (2L) (Prof. A P Dowling)
- Rotor alone noise
- Rotor/Stator interaction noise
- Examples: Aircraft noise, fan and turbine noise
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 01/06/2018 12:07
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2017-18
Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 03/08/2017 16:05
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2023-24
Module Leader
Lecturers
Prof E Mastorakos and Dr J Li
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam.
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 13/11/2023 20:19
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2025-26
Module Leader
Lecturers
Prof E Mastorakos and Dr J Li
Timing and Structure
Michaelmas term. 16 lectures (including examples classes). Assessment: 100% exam.
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 04/06/2025 13:24
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2020-21
Module Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Michaelmas term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 01/09/2020 10:24
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2018-19
Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 17/05/2018 13:27
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2019-20
Module Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 23/05/2019 15:52
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