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33 results

Page 1 of 2

Fluid Mechanics
  • 2nd edition
  • Gregory Falkovich
  • Published online:
    04 August 2018
    Print publication:
    12 April 2018
  • The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. This textbook, fully revised and enlarged for the second edition, presents the minimum of what every physicist, engineer and mathematician needs to know about hydrodynamics. It includes new illustrations throughout, using examples from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, and geophysical and astrophysical phenomena, providing readers with a better understanding of the world around them. Aimed at undergraduate and graduate students as well as researchers, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains forty-one original problems with very detailed solutions, progressing from dimensional estimates and intuitive arguments to detailed computations to help readers understand fluid mechanics.

Fluid Mechanics
  • A Short Course for Physicists
  • Gregory Falkovich
  • Published online:
    05 June 2012
    Print publication:
    14 April 2011
  • The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. In this book, the fundamental ideas of fluid mechanics are presented from a physics perspective. Using examples taken from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, the book provides readers with a better understanding of the world around them. It teaches the art of fluid-mechanical estimates and shows how the ideas and methods developed to study the mechanics of fluids are used to analyze other systems with many degrees of freedom in statistical physics and field theory. Aimed at undergraduate and graduate students, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains 32 exercises of varying difficulties, from simple estimates to elaborate calculations, with detailed solutions to help readers understand fluid mechanics.

Non-equilibrium Statistical Mechanics and Turbulence
  • John Cardy, Gregory Falkovich, Krzysztof Gawedzki
  • Edited by Sergey Nazarenko, Oleg V. Zaboronski
  • Published online:
    05 June 2012
    Print publication:
    11 December 2008
  • Methods of non-equilibrium statistical mechanics play an increasingly important role in modern turbulence research, yet the range of relevant tools and methods is so wide and developing so fast that until now there has not been a single book covering the subject. As an introduction to modern methods of statistical mechanics in turbulence, this volume rectifies that situation. The book comprises three harmonised lecture courses by world class experts in statistical physics and turbulence: John Cardy introduces Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport. To encourage readers to deepen their understanding of the theoretical material, each chapter contains exercises with solutions. Essential reading for students and researchers in the field of theoretical turbulence, this volume will also interest any scientist or engineer who applies knowledge of turbulence and non-equilibrium physics to their work.

  • 6 - The Russian school

  • Edited by Peter A. Davidson, University of Cambridge, Yukio Kaneda, Nagoya University, Japan, Keith Moffatt, University of Cambridge, Katepalli R. Sreenivasan, New York University
  • Book:
    A Voyage Through Turbulence
    Published online:
    07 October 2011
    Print publication:
    08 September 2011, pp 209-237

  • Summary

    The towering figure of Kolmogorov and his very productive school is what was perceived in the twentieth century as the Russian school of turbulence. However, important Russian contributions neither start nor end with that school.

    Physicist and pilot

    … the bombs were falling almost the way the theory predicts. To have conclusive proof of the theory I'm going to fly again in a few days.

    A.A. Friedman, letter to V.A. Steklov, 1915

    What seems to be the first major Russian contribution to the turbulence theory was made by Alexander Alexandrovich Friedman, famous for his work on non-stationary relativistic cosmology, which has revolutionized our view of the Universe. Friedman's biography reads like an adventure novel. Alexander Friedman was born in 1888 to a well-known St. Petersburg artistic family (Frenkel, 1988). His father, a ballet dancer and a composer, descended from a baptized Jew who had been given full civil rights after serving 25 years in the army (a so-called cantonist). His mother, also a conservatory graduate, was a daughter of the conductor of the Royal Mariinsky Theater. His parents divorced in 1897, their son staying with the father and becoming reconciled with his mother only after the 1917 revolution. While attending St. Petersburg's second gymnasium (the oldest in the city) Friedman befriended a fellow student Yakov Tamarkin, who later became a famous American mathematician and with whom he wrote their first scientific works (on number theory, received positively by David Hilbert).

  • Prologue

  • Gregory Falkovich, Weizmann Institute of Science, Israel
  • Book:
    Fluid Mechanics
    Published online:
    05 June 2012
    Print publication:
    14 April 2011, pp xi-xii

  • Summary

    The water's language was a wondrous one, some narrative on a recurrent subject …

    A. Tarkovsky, translated by A. Shafarenko

    There are two protagonists in this story: inertia and friction. One meets them first in the mechanics of particles and solids where their interplay is not very complicated: inertia tries to keep the motion while friction tries to stop it. Going from a finite to an infinite number of degrees of freedom is always a game-changer. We will see in this book how an infinitesimal viscous friction makes fluid motion infinitely more complicated than inertia alone ever could. Without friction, most incompressible flows would stay potential, i.e. essentially trivial. At solid surfaces, friction produces vorticity, which is carried away by inertia and changes the flow in the bulk. Instabilities then bring about turbulence, and statistics emerges from dynamics. Vorticity penetrating the bulk makes life interesting in ideal fluids though in a way different from superfluids and superconductors.

    On the other hand, compressibility makes even potential flows non-trivial as it allows inertia to develop a finite-time singularity (shock), which friction manages to stop. It is only in a wave motion that inertia is able to have an interesting life in the absence of friction, when it is instead partnered with medium anisotropy or inhomogeneity, which cause the dispersion of waves. The soliton is a happy child of that partnership.

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