The internal gravity wave field emitted by a stably stratified turbulent wake

Abstract

AbstractThe internal gravity wave (IGW) field emitted by a stably stratified, initially turbulent, wake of a towed sphere in a linearly stratified fluid is studied using fully nonlinear numerical simulations. A wide range of Reynolds numbers,$\mathit{Re}= UD/ \nu \in [5\times 1{0}^{3} , 1{0}^{5} ] $and internal Froude numbers,$\mathit{Fr}= 2U/ (ND)\in [4, 16, 64] $($U$,$D$are characteristic body velocity and length scales, and$N$is the buoyancy frequency) is examined. At the higher$\mathit{Re}$examined, secondary Kelvin–Helmholtz instabilities and the resulting turbulent events, directly linked to a prolonged non-equilibrium (NEQ) regime in wake evolution, are responsible for IGW emission that persists up to$Nt\approx 100$. In contrast, IGW emission at the lower$\mathit{Re}$investigated does not continue beyond$Nt\approx 50$for the three$\mathit{Fr}$values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with$\mathit{Fr}$and appear to be smaller at the higher$\mathit{Re}$, especially at late times. The initial value of these wavelengths is set by the wake height at the beginning of the NEQ regime. At the lower$\mathit{Re}$, consistent with a recently proposed model, the waves propagate over a narrow range of angles that minimize viscous decay along their path. At the higher$\mathit{Re}$, wave motion is much less affected by viscosity, at least initially, and early-time wave propagation angles extend over a broader range of values which are linked to increased efficiency in momentum extraction from the turbulent wake source.