Internal tide generation in nonuniformly stratified deep oceans

Abstract

We present numerical and experimental studies of the conversion of tidal motions of an exponentially stratified fluid over two-dimensional knife edge, Gaussian, and complex bottom topography to radiated internal waves in a model of the deep ocean. We compare the radiated internal wave power for cases of strong stratification, where the buoyancy frequency profile N(z) (proportional to the square root of the density gradient) is much larger than the tidal frequency x, to the power radiated for weak stratifications. We consider particularly internal wave generation for topography below a turning depth z td , where Nðz td Þ5x; for z < z td , internal waves are evanescent. We find that topography below a turning depth does generate internal waves that propagate for z > z td , although the radiated power in these waves is much weaker than in cases without turning depths. The radiated power is predicted well by prior analytical theory if the nonuniform stratification is averaged over depths spanning from the bottom boundary up to an effective height z eff . In the absence of a turning depth, we find z eff is approximately equal to the height of the topography, indicating that only the stratification for depths spanned by the topography is relevant. However, in the presence of a turning depth, the vertical scale of the internal tide becomes larger, and z eff increases approximately linearly with the turning depth height toward values comparable to the total fluid depth.

Internal wave pressure, velocity, and energy flux from density perturbations

“…the middle of the domain. The boundary conditions at the top and bottom (17) are physically more important than those at the sides (15) because a no-flux condition is applied at the top and bottom for the Green's function (26). If the beam passes through the top and/or bottom boundary, then the no-flux condition is violated and error is introduced in the Green's function.…”

Internal wave boluses as coherent structures in a continuously stratified fluid

“…All subgrid-scale modellings are turned off, and the code is modified to include the buoyancy term in (2.3) and solve (2.4) along with (2.1)-(2.3). This code has previously been used to simulate internal waves and has been validated with experiments (King, Zhang & Swinney 2009;Dettner, Paoletti & Swinney 2013;Lee et al 2014;Paoletti, Drake & Swinney 2014;Zhang & Swinney 2014;Allshouse et al 2016;Lee et al 2018).…”

Internal wave generation by tidal flow over periodically and randomly distributed seamounts

“…[] and Paoletti et al . [] investigated internal wave conversion for tidal flow over 2‐D topography with N ( z ) decreasing nonlinearly with depth. Future work should examine further how nonuniform N ( z ) affects the barotropic to baroclinic energy conversion by periodically and randomly distributed seamounts, as has been considered in Holloway and Merrifield [] and Llewellyn Smith and Young [] for individual seamounts without wave interference effects.…”

“…Another source of uncertainty in estimates of the internal wave conversion by seamounts, knolls, and ridges is the variation of the buoyancy frequency N(z) with depth; N(z) varies from $10 24 s -1 in the deep ocean to $10 22 s -1 near the ocean surface, as illustrated by Gerkema and van Haren [2007, Figure 2c] and King et al [2012, Figure 5]. Qian et al [2010] and Paoletti et al [2014] investigated internal wave conversion for tidal flow over 2-D topography with N(z) decreasing nonlinearly with depth. Future work should examine further how nonuniform N(z) affects the barotropic to baroclinic energy conversion by periodically and randomly distributed seamounts, as has been considered in Holloway and Merrifield [1999] and Llewellyn Smith and Young [2002] for individual seamounts without wave interference effects.…”