Topographic height dependence of internal wave generation by tidal flow over random topography

Abstract

Internal waves (IWs) generated by tidal flow over the seafloor play a critical role in ocean circulation and climate. We determine the dependence of the radiated IW power on topographic parameters in numerical simulations of tidal flow over two‐dimensional random topographic profiles that have the spectrum of oceanic abyssal hills. The IW power increases as the horizontal spatial resolution scale is decreased, but below a certain spatial scale the power saturates at a level less than the linear theory prediction. For increasing topographic RMS height Hrms the emergent interference of the tide and the IWs from different generation sites leads to a transition in the IW power dependence on Hrms from quadratic to linear. This transition in the scaling of the IW power depends on the slopes of a valley's nearest neighboring peaks. Our results should guide the modeling of IW generation by tidal flow over small‐scale ocean topography.

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

“…Previous studies found that interference suppresses conversion for 2‐D periodic and random ridges [ Khatiwala , ; Nycander , ; Zhang and Swinney , ; Zhao et al ., ]. The interference has been found to be characterized by an elevated “virtual seafloor” [ Zhang and Swinney , ].…”

“…Although there are more than 33,000 seamounts in the oceans, they contribute only about 1% percent of the total oceanic internal wave conversion. An improved estimate of the total energy conversion by seamounts will require further investigation of the dependence on the topographic parameters of the 3‐D seamounts, as done for 2‐D ridges [ Zhao et al ., ], and by taking account of the ocean depth. The topographic height dependence of conversion for steep‐sloped seamounts also depends on horizontal aspect ratios of the seamount [ Munroe and Lamb , ]; the global estimates here use an average height.…”

“…Interference has been studied for internal waves generated in 2‐dimensional (2‐D) topographies including double ridges [ Xing and Davies , ; Boschan et al ., ; Buijsman et al ., ], periodic peaks [ Khatiwala , ; Nycander , ; Balmforth and Peacock , ; Zhang and Swinney , ], and random topographies [ Zhang and Swinney , ; Zhao et al ., ]. Numerical studies for both periodic peaks [ Khatiwala , ] and random topographies [ Zhang and Swinney , ] found that wave interference between neighboring ridges leads to a suppression of the barotropic to baroclinic energy conversion for narrowly spaced topographic peaks that are supercritical ( , where the criticality ϵ is the ratio of topographic slope to beam slope).…”

“…Numerical studies for both periodic peaks [ Khatiwala , ] and random topographies [ Zhang and Swinney , ] found that wave interference between neighboring ridges leads to a suppression of the barotropic to baroclinic energy conversion for narrowly spaced topographic peaks that are supercritical ( , where the criticality ϵ is the ratio of topographic slope to beam slope). Other studies revealed that the suppressed conversion is independent of the topographic height of supercritical periodic peaks [ Nycander , ; Balmforth and Peacock , ] and linearly dependent on the topographic height of random topographies [ Zhao et al ., ], in contrast to the quadratic dependence on topographic height for subcritical topography [ Bell , ; Garrett and Kunze , ]. For supercritical topography linear theory overestimates the conversion because the analysis does not account for wave interference at the topography [ Nycander , ].…”

“…For supercritical topography linear theory overestimates the conversion because the analysis does not account for wave interference at the topography [ Nycander , ]. The saturation needs be considered particularly in estimates of internal wave generation by small abyssal hills [ Melet et al ., ; Zhao et al ., ]. A recent study showed that wave interference in 2‐D topographies leads to an elevated “virtual seafloor,” where local topography below the level of the virtual seafloor does not contribute to the conversion of tidal energy into internal waves [ Zhang and Swinney , ].…”