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Register a new userDownscale energy fluxes in scale invariant oceanic internal wave turbulence
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We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-colinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wave numbers in both the vertical and the horizontal directions. Our results compare favorably with the finescale parametrization of ocean mixing that was proposed in [Polzin et al. (1995)].
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Direct Numerical Simulations of turbulent channel flows at friction Reynolds number 550, 1000, 1500, are used to analyse the turbulent production, transfer and dissipation mechanisms in the compound space of scales and wall-distances by means of the Kolmogorov equation generalized to inhomogeneous anisotropic flows. Two distinct peaks of scale-energy source are identified. The first stronger one belongs to the near-wall cycle. Its location in the space of scales and physical space is found to scale in viscous units while its intensity grows slowly with $Re$, indicating a near-wall modulation. The second source peak is found further away from the wall in the putative overlap layer and it is separated from the near-wall source by a layer of significant scale-energy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scale-by-scale analysis of this source highlights well-defined features that are used to make the properties of the outer turbulent source independent of Reynolds number and wall-distance by rescaling the problem. Overall, the present results suggest a strong connection of the observed outer scale-energy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the near-wall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Inner-outer interactions between the near-wall and outer source region in terms of scale-energy fluxes are also analysed. It is conjectured that the near-wall modulation of the statistics at increasing Reynolds number can be related to a confinement of the near-wall turbulence production due to the presence of increasingly large production scales in the outer scale-energy source region.
We report evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is {em not}, in fact, slow. Instead nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with conventional wisdom that regards the Garrett and Munk spectrum as an approximate stationary state and puts the self-consistency of a resonant kinetic equation at a serious risk. We explore possible reasons for and resolutions of this paradox. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. This leads to improved self-consistency of the kinetic equation.
In the paper taking the assumption of the slowness of the change of the parameters of the vertically stratified medium in the horizontal direction and in time, the evolution of the non-harmonic wave packages of the internal gravity waves has been analyzed. The concrete form of the wave packages can be expressed through some model functions and is defined by the local behavior of the dispersive curves of the separate modes near to the corresponding special points. The solution of this problem is possible with the help of the modified variant of the special-time ray method offered by the authors (the method of geometrical optics), the basic difference of which consists that the asymptotic representation of the solution may be found in the form the series of the non-integer degrees of some small parameter. At that the exponent depends on the concrete form of representation of this package. The obvious kind of the representation is determined from the principle of the localness and the asymptotic behavior of the solution in the stationary and the horizontally-homogeneous case. The phases of the wave packages are determined from the corresponding equations of the eikonal, which can be solved numerically on the characteristics (rays). Amplitudes of the wave packages are determined from the laws of conservation of the some invariants along the characteristics (rays).
Results of direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time simultaneous formation of both direct and inverse cascades was observed in the framework of primordial dynamical equations. At the same time, strong long waves background was developed. It was shown, that obtained Kolmogorov spectra are very sensitive to the presence of this condensate. Such situation has to be typical for experimental wave tanks, flumes, and small lakes.
We present a model describing evolution of the small-scale Navier-Stokes turbulence due to its stochastic distortions by much larger turbulent scales. This study is motivated by numerical findings (laval, 2001) that such interactions of separated scales play important role in turbulence intermittency. We introduce description of turbulence in terms of the moments of the k-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko, 2003). Working with the $k$-space moments allows to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the 2D turbulence shows that the energy cascade is scale invariant and Gaussian whereas the enstrophy cascade is intermittent. In 3D, we show that the statistics of turbulence wavepackets deviates from gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centered at its origin and having one large, one neutral and one small axes with the velocity field pointing parallel to the smallest axis.
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