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Oscar Dementiev
Oscar Dementiev

Lighthill Waves In Fluids Pdf Download

  • OutlineIntroduction and governing equations (August 27, 29)What are fluids? The continuum hypothesis (Batchelor, pp 1-6; Faber 2-4;Heuberger et al., Science, vol. 292, 905-908, 2001;Arfken, pp 10-37; handout -- all these will be made available)

  • Vectors, tensors, stress

  • Conservation equations for mass, momentum, energy (Leal, chapter 2)

  • Boundary conditions

  • Homeworknumber 1 due Wednesday September 5; you can download Wood's editorial here

  • Homeworknumber 2 due Monday September 10

  • Homeworknumber 3 due Monday September 17

  • Supplemental notes onthe conservation equations and some useful vector identities

  • Scaling and unidirectional flows (September 5, 10)Scaling and dimensional analysis (Middleton and Wilcock, chapter 3; Fowler, chapter 1)

  • Homeworknumber 4 due Wednesday September 19

  • Unidirectional flows (Leal, chapter 3)

  • Homeworknumber 5 due Monday September 24

  • Special limits, features of flows (September 17, 19, 24 and 26)Different limits, e.g., Stokes flows, incompressible flow, irrotational flows, etc. (Hinch, Chapter 3 in Disorder and Mixing;Tritton, chapters 8, 10)

  • Check out NASA's airfoil page

  • Vorticity (Tritton, sections 6.4-6.6)

  • Boundary layers

  • Lubrication theory

  • Homeworknumber 6 due Monday October 1

  • Homeworknumber 7 due Monday October 8

  • Waves (October 1, 3)Waves (Lighthill, chapter 3; Cushman-Roisin, appendix A)

  • Lab, time TBD (perhaps October 29 or 31?) -- Kelvin-Helmholtz instabilities Homeworknumber 8 due Monday October 17

  • Turbulence (October 8)Turbulence (Middleton and Wilcock, chapter 11; Tritton, section 20.4)


  • Gravity currents (October 15, 17)Gravity currents (book by Simpson)

  • Rheology of geological materials and fluids

  • Homeworknumber 9 due Wednesday November 7

  • Convection (October 22, 24)Convection, including double-diffusive convection (paper by Kadanoff, Physics Today, 2001; Tritton, chapters 14, 22, 23)

  • Homeworknumber 10 due Wednesday November 14

  • Porous materials (November 5, 7)Flow in porous materials (Turcotte and Schubert, chapter 9)

  • Optional questions

  • Microhydrodynamics (bubbles and crystals in liquids) (November 14, 19, 26)A few other topics (November 26, 28)Effects of rotation (Cushman-Roisin, chapter 1)

  • Life in moving fluids (Vogel, Life in Moving Fluids)

  • Second midterm Dec 5, in classTerm project presentations (time and date TBD)This is obviously a lot of material, and as a result the course will bemore descriptive than most fluid mechanics classes with an emphasis onscaling analysis.Recommended referencesMy favorite general fluid mechanics books:Batchelor, G.K., An introduction to fluid dynamics, Cambridge UniversityPress, 1967.

  • Faber, T.E., Fluid dynamics for physicists, Cambridge UniversityPress, 1995.

  • Van Dyke, M., An album of fluid motion, Parabolic, 1982.

  • Tritton, D.J., Physical fluid dynamics, Oxford University Press,1988.

  • Landau, L.D. and E.M. Lifshitz, Fluid mechanics, Pergamon Press,1987.

  • Some other books that are very useful references:Middleton, G.V. and P.R. Wilcock, Mechanics in the earth and environmentalsciences, Cambridge University Press, 1994.

  • Furbish, D., Geological fluid mechanics, Oxford University Press.

  • Pedlosky, J., Geophysical fluid dynamics, Springer-Verlag, 1987.

  • Phillips, O.M., Flow and reactions in permeable rocks, CambridgeUniversity Press, 1991.

  • Cushman-Roisin, B., Introduction to geophysical fluid dynamics,Prentice Hall, 1994.

  • Lighthill, J., Waves in fluid, Cambridge University Press, 1978.

  • Turcotte, D.L. and G. Schubert, Geodynamics, John Wiley and Sons,1982.

  • Leal, L.G., Laminar flow and convection transport processes, Butterworth-Heineman,1992.

  • Simpson, J.E., Gravity currents, Cambridge University Press, 1997.

  • Turner, J.S., Buoyancy effects in fluids, Cambridge University Press,1973.

  • Guyon, E., et al., Physical hydrodynamics,Oxford Univ Press, 2001.

  • Whitaker, S., Introduction of Fluid Mechanics,Prentice-Hall, 1968 (nice, simple explanations without sacrificingrigour).

Lighthill Waves In Fluids Pdf Download

In nature, it is not unusual to find stably stratified fluid adjacent to convectively unstable fluid. This can occur in the Earth's atmosphere, where the troposphere is convective and the stratosphere is stably stratified; in lakes, where surface solar heating can drive convection above stably stratified fresh water; in the oceans, where geothermal heating can drive convection near the ocean floor, but the water above is stably stratified due to salinity gradients; possible in the Earth's liquid core, where gradients in thermal conductivity and composition diffusivities maybe lead to different layers of stable or unstable liquid metal; and, in stars, as most stars contain at least one convective and at least one radiative (stably stratified) zone. Internal waves propagate in stably stratified fluids. The characterization of the internal waves generated by convection is an open problem in geophysical and astrophysical fluid dynamics.

In the authors words, this book is a comprehensive introductionto the science of wave motions in liquids and gases. There areobvious difficulties in trying to compile an introductory treatisein a single volume on such a broad subject as waves in fluids. Theplan adopted by the author is to analyse in detail fourrepresentative types of waves (in four separate chapters). Withinthis framework, virtually all of the fundamental ideas needed for aproper understanding of waves in fluids are developed. The book istherefore divided into just four long chapters. There is also ashort epilogue outlining briefly some advanced ideas that would notnormally be included in an introductory text.

Each chapter opens with a broad statement of the field to beexplored and the problems to be tackled. Although the generalapproach is theoretical, the book is by no means purelymathematical. The physical meaning of the theory is everywherestressed, usually with practical examples. Readers are expected topossess a knowledge of elementary dynamics of fluids and ofmechanical analysis, including the theory of functions of a complexvariable. At the end of each chapter is a selection of about adozen exercises of varying difficulty. These serve to extend thetreatment given in the text. Anyone who, after reading andunderstanding the text, can work through these problems will thenknow a great deal about waves in fluids. 350c69d7ab


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