Gravity Wave Turbulence Research Articles

Surface gravity wave turbulence: three wave interaction?

We consider the turbulence of potential deep-water surface gravity waves, which have dispersion law Ω k = gk (g is the gravity constant, k=| k | ). It is well known that there are no three wave resonance interaction for such waves, and the lowest-order resonance involves four waves. We show the importance of almost resonance three wave interactions; in particular, they determine the life-span of these waves, provided the range of scales is large enough.

Weak turbulence of gravity waves

For the first time weak turbulent theory was demonstrated for surface gravity waves. Direct numerical simulation of the dynamical equations shows Kolmogorov turbulent spectra as predicted by analytical analysis [1] from kinetic equation.

On the Hasselmann and Zakharov Approaches to the Kinetic Equations for Gravity Waves

Abstract It is shown for the first time analytically that two different approaches describing gravity wave turbulence introduced by Hasselmann in 1962 and Zakharov in 1968 result in the same kinetic equation for the second-order correlator.

A simple theory of capillary–gravity wave turbulence

Employing a recently proposed ‘multi-wave interaction’ theory (Glazman 1992), inertial spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g. nonlinear inertia-gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

Kolmogorov-type spectrum for the turbulence of acoustic waves in two dimensions

We find a Kolmogorov-type spectrum for the 2D turbulence of waves with the “sound-like” dispersion law Ω k=u|k| . The spectrum is proportional to P 3 5 , where P is the flux of energy through the scales. This provides an example of turbulence which is weaker than strong hydrodynamic turbulence, but stronger than the weak turbulence of dispersive waves. To analyze the localness of the turbulence we use the simplest closure (the so-called one-loop approximation). We apply the results to the turbulence of shallow water gravity waves, two-dimensional acoustic turbulence.

Gravity Wave Turbulence Interaction in the Presence of a Critical Level

Abstract The analysis of an earlier work on the interaction between an internal gravity wave and the wave-induced turbulence is extended here to the case where the wave is generated by vertical wind shear. The initial system is described by a background wind and a temperature distribution such that the Richardson number is less than ¼. A gravity wave is generated by such a dynamically unstable system and grows exponentially in time. The wave modifies the Richardson number and lowers it, particularly in the neighborhood of the critical level. When the generalized Richardson number falls below an assumed critical level, turbulence is assumed to develop and is described by a “1½th order” scheme. A diffusion coefficient can then be calculated which has a mean and a fluctuating part. It is the latter which turns out to be responsible for the positive feedback between the wave and the wave-induced turbulence resulting in the wave growing at a faster rate than the one predicted by linear theory.

A numerical model of gravity wave breaking and stress in the mesosphere

The stresses generated by breaking gravity waves in the mesosphere are calculated with a numerical model of steady vertically propagating gravity waves that includes wavelength dependent radiative dissipation and turbulent viscosity and conduction. The principal findings are (1) waves do not break for |ū ‐ c| values ≲20 m s−1 as radiative damping prevents wave amplitude growth with altitude for short vertical wavelengths; (2) the downward heat flux due to turbulence of breaking waves and turbulent heating through loss of wave energy could severely affect the global radiative energy balance; and (3) predicted zonal deceleration for steady breaking waves is stronger than required by Apruzese et al. (1982) for the mean circulation. Gravity wave breaking may be an intermittent process; otherwise, gravity wave stresses would produce an adiabatic mesosphere with a zonal mean velocity close to the phase speed of the breaking wave. Diffusive transport of constituents and potential temperature by breaking gravity wave turbulence is shown to be important. In the cases of nitric oxide and atomic oxygen the vertical eddy diffusion coefficients are shown to be sensitive functions of their respective chemical loss rates in the mesosphere and lower thermosphere.