Kolmogorov Spectra of Turbulence I

1. Front Matter

   Pages I-XIII

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2. Introduction

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 1-8

3. Equations of Motion and the Hamiltonian Formalism

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 9-62

4. Statistical Description of Weak Wave Turbulence

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 63-82

5. Stationary Spectra of Weak Wave Turbulence

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 83-143

6. The Stability Problem and Kolmogorov Spectra

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 145-206

7. Physical Applications

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 207-244

8. Conclusion

   • Vladimir E. Zakharov, Victor S. L’vov, Gregory Falkovich

   Pages 245-248

9. Back Matter

   Pages 249-265

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Since the human organism is itself an open system, we are naturally curious about the behavior of other open systems with fluxes of matter, energy or information. Of the possible open systems, it is those endowed with many degrees of freedom and strongly deviating from equilibrium that are most challenging. A simple but very significant example of such a system is given by developed turbulence in a continuous medium, where we can discern astonishing features of universality. This two-volume monograph deals with the theory of turbulence viewed as a general physical phenomenon. In addition to vortex hydrodynamic turbulence, it considers various cases of wave turbulence in plasmas, magnets, atmosphere, ocean and space. A sound basis for discussion is provided by the concept of cascade turbulence with relay energy transfer over different scales and modes. We shall show how the initial cascade hypothesis turns into an elegant theory yielding the Kolmogorov spectra of turbulence as exact solutions. We shall describe the further development of the theory discussing stability prob­ lems and modes of Kolmogorov spectra formation, as well as their matching with sources and sinks. This volume is dedicated to developed wave turbulence in different media.

• Damping
• Dissipation
• Kinetische Gleichungen
• Plasma
• Turbulenz
• Wellenspektrum
• atmosphere
• kinetic equations
• spectra
• stability
• turbulence
• wave spectrum
• fluid- and aerodynamics

• Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia

  Vladimir E. Zakharov

• Physics Department, Weizmann Institute of Science, Rehovot, Israel

  Victor S. L’vov, Gregory Falkovich

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