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

We investigate through numerical simulations 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 Re = 28000 and a wide range of horizontal Froude number F_h ∈ [0.0225 0.135] and buoyancy Reynolds number R = ReF_h² ∈ [14 510]. A spectral analysis shows that this transition is dominated by two kinds of transfers: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale L_b = U/N, where U is the characteristic horizontal velocity of the dipole and N the Brunt-Väisälä frequency; second, the destabilization of the Kelvin-Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. We show that the anisotropic spectra at the maximum of dissipation share many characteristics with those obtained from numerical simulations of forced stratified turbulence and from measurements in the atmosphere and in the ocean. The article presenting this study [2] is the subject of a Focus on Fluids article [10].