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

The 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, Re= UD/ ν ∈ [5× 10³ , 10⁵ ] and internal Froude numbers, Fr= 2U/ (ND)∈ [4, 16, 64] ( U , D are characteristic body velocity and length scales, and N is the buoyancy frequency) is examined. At the higher 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≈ 100 . In contrast, IGW emission at the lower Re investigated does not continue beyond Nt≈ 50 for the three Fr values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with Fr and appear to be smaller at the higher 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 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 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.