Bottom topography and internal tide

Three-dimensional direct numerical simulations are performed to examine nonlinear processes during the generation of internal tides on a model continental slope. The remarkably complex wave pattern, shown in Fig. (a), includes energetic internal wave beams coincident with the slope angle, beams at steeper angles, and internal waves generated by boundary-layer turbulence that have a wide range of phase lines. The internal wave field is assessed by a power spectrum analysis of the baroclinic velocity field given by u_bar(x; y; z; t)= u(x; y; z; t)- u_baro(x; z; t), where the barotropic component is the free-stream value of the velocity. Figure (b) shows the power spectra at two locations A and B at different heights. The spectra show several temporal harmonics (nΩ, n ∈ N),, subharmonics ω ∈ [0,Ω), and interharmonics (ωα + nΩ, ωα ∈ [0,Ω)). having significant energy. The discrete spectral peak at the barotropic tidal frequency, ., in Fig. 1(b), corresponds to an energetic linear response which, in physical space, corresponds to the strong beams (upward propagation in black and downward in white) shown in Fig. 1(a). The spectrum at point A shows discrete peaks at the second and third harmonics as well as a significant band of waves with ω>N. These super-N waves are generated by high-frequency turbulence inside the boundary layer as. The spectrum at point B, further away from the slope, has the same energy at the fundamental and second harmonic observed at point A, as well as an additional discrete peak at the first subharmonic. The range of super-N waves in the spectrum is much smaller at point B relative to that at A, since the background does not support freely propagating waves with ω>N.

Ref. B. Gayen and S. Sarkar (2010) Turbulence during the generation of internal tide on a critical slope. Phys.  Rev. Lett., 104, p. 218502