FLOW paper selected as Focus on Fluids article (Jan. 2013)

Abstract

We investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb–Chaplygin dipole in a stratified fluid for a high Reynolds number and a wide range of horizontal Froude number and buoyancy Reynolds number . The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale, where is the characteristic horizontal velocity of the dipole and the Brunt–Väisälä frequency; second, the destabilization of the Kelvin–Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits a power law (where is the horizontal wavenumber and is the dissipation rate of kinetic energy) from to the dissipative scales, with an energy deficit between the integral scale and and an excess around . The vertical spectrum of kinetic energy can be expressed as where and are two constants of order unity and is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an shape and approaches the spectrum for , being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the spectrum is associated with large horizontal scales and the spectrum with the scales.

"Spectral analysis of the transition to turbulence from a dipole in stratified fluid"

"The vortex instability pathway in stratified turbulence"