Wave turbulence: A solvable problem applied to Navier-Stokes
arxiv(2024)
摘要
Wave turbulence and eddy turbulence are the two regimes that we may encounter
in nature. The attention of fluid mechanics being mainly focused on
incompressible hydrodynamics, it is usually the second regime that is treated
in books, whereas waves are often present in geophysics and astrophysics. In
these lecture notes, I present the theory of wave turbulence which is free from
the closure problem encountered in eddy turbulence. Basically, the wave
amplitude is introduced in a multiple time scale method as a small parameter to
derive the so-called kinetic equations from which exact results can be obtained
(power-law spectra, direction of the cascade, Kolmogorov's constant) and
compared with the data. Two hydrodynamic applications are considered with
capillary waves and inertial waves, the first leading to isotropic turbulence
and the second to anisotropic turbulence.
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