Surface manifestation of internal waves emitted by submerged localized stratified turbulence

The internal waves (IWs) radiated by the turbulent wake of a sphere of diameter D towed at speed U are investigated using three-dimensional fully nonlinear simulations performed in a linearly stratified Boussinesq fluid with buoyancy frequency N. The study focuses on a broad range of wave characteristics in the far field of the turbulent wave source, specifically at the sea surface (as modelled by a free-slip rigid lid) where the IWs reflect. Six simulations are performed at Reynolds number Re UD/v is an element of{5 x 10(3), 10(5)} and Froude number Fr 2U/(ND) is an element of {4, 16, 64}, where v is viscosity. 'The wave-emitting wake is located at a fixed distance of 9D below the surface. As the wake evolves for up to 0(300) units of buoyancy time scale 1/N, 1W characteristics, such as horizontal wavelength A0 and wave period T, are sampled at. the sea surface via wavelet transforms of horizontal divergence signals. The statistics of amplitudes and orientations of 1W-induced surface strains are also reported. The mean dimensionless observable wavelength (lambda) over bar (H)/D at the sea surface decays in time as (Nt)(-1), which is due to the waves' dispersion. rfhis observation is in agreement with a linear propagation model that is independent of the wake Re and Fr. This agreement. further suggests that the most energetic waves impacting the surface originate from the early-time wake that is adjusting to buoyancy. The most energetic dimensionless wavelength (lambda) over bar (H)/D is found to scale as Fr-1/3 and decrease with Re, which causes the arrival time (in Nt units) of the strongest waves at the surface to scale as Fr-1/3 and increase with Re. This wavelength (lambda) over bar (H)/D is also found to correlate with the vertical Taylor scale of the wake turbulence. 1W-driven phenomena at the surface that are of interest to an observer, such as the local enrichment of surfactant and the transport of ocean surface tracers, are also examined. The local enrichment ratio of surface scalar scales linearly with the steepness of IWs that reach the surface, and the ratio often exceeds a possible visibility threshold. The Lagrangian drifts of ocean tracers, which are linked to the nonlinear interaction between incident and reflecting 1W packets, create a local divergence in lateral mass transport right above the wake centreline, an effect that intensifies strongly with increasing Fr. The findings of this study may serve as a platform to investigate the generation and surface manifestation of 1Ws radiated by other canonical submerged stratified turbulent flows.