*S. F. Edwards*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper which examines the problem of steady homogeneous isotropic turbulence under idealized conditions, allowing the for the exact form of the correlation functions to be ...
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This chapter presents a paper which examines the problem of steady homogeneous isotropic turbulence under idealized conditions, allowing the for the exact form of the correlation functions to be determined. Liouville's equation, and its generalization when a random input of energy is presented, is a useful starting point for the derivation of the steady distribution function of velocities, but it is inadequate for the study of the correlation functions when the velocities are taken at different points in time and a more general equation is derived to handle this problem. After an intuitive discussion of the problem, a general method is given for solving both Liouville's equation and the new extended equation. The solutions are then discussed in detail and it is shown that for a certain class of input behaviours, exact solutions can be given for the structure of the velocity correlation function. The chapter concludes with a discussion of the validity of the method of solution.Less

This chapter presents a paper which examines the problem of steady homogeneous isotropic turbulence under idealized conditions, allowing the for the exact form of the correlation functions to be determined. Liouville's equation, and its generalization when a random input of energy is presented, is a useful starting point for the derivation of the steady distribution function of velocities, but it is inadequate for the study of the correlation functions when the velocities are taken at different points in time and a more general equation is derived to handle this problem. After an intuitive discussion of the problem, a general method is given for solving both Liouville's equation and the new extended equation. The solutions are then discussed in detail and it is shown that for a certain class of input behaviours, exact solutions can be given for the structure of the velocity correlation function. The chapter concludes with a discussion of the validity of the method of solution.

*Peter Davidson*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198722588
- eISBN:
- 9780191789298
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198722588.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics

This book presents the subject of turbulence. The aim of the book is to bridge the gap between the elementary, heuristic accounts of turbulence and the more rigorous accounts given. Throughout, the ...
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This book presents the subject of turbulence. The aim of the book is to bridge the gap between the elementary, heuristic accounts of turbulence and the more rigorous accounts given. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth.Less

This book presents the subject of turbulence. The aim of the book is to bridge the gap between the elementary, heuristic accounts of turbulence and the more rigorous accounts given. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth.