Improving Nonlinear and Nonhydrostatic Ocean Lee Wave Drag Parameterizations

Abstract

Ocean lee waves occur on length scales that are smaller than the grid scale of global circulation models (GCMs). Therefore, such models must parameterize the drag associated with launching lee waves. This paper compares the lee wave drag predicted by existing parameterizations with the drag measured in high-resolution nonhydrostatic numerical simulations of a lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spinup process and identify a characteristic time scale to reach steady state. The maximum instantaneous lee wave drag observed during the spinup period is found to be well predicted by linear lee wave theory for all hill heights. In steady state, the simulations demonstrate the applicability of parameterizing the drag based on applying linear theory to the lowest overtopping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of the LOTS, they implicitly assume hydrostatic flow. For hills tall enough to trap water in their valleys, the simulations identify a set of nonhydrostatic processes that can result in a reduction of the lee wave drag from that given by hydrostatic parameterizations. The simulations suggest implementing a time-dependent nonhydrostatic version of the LOTS-based parameterization of lee wave drag and demonstrate the remarkable applicability of linear lee wave theory to oceanic lee waves.

The Impact of Representations of Realistic Topography on Parameterized Oceanic Lee Wave Energy Flux

“…The hydrostaticity of the model is necessary due to limitation of computational resources, and may impact the lee wavefield. Hydrostaticity is a common assumption for lee wave generation (e.g., Klymak, 2018; Trossman et al., 2013) but can affect the wavefield (F. T. Mayer & Fringer, 2020). We investigate the impact of the hydrostatic assumption on the wave parameterizations in Section 4.4.…”

Non‐Local Energy Dissipation of Lee Waves and Turbulence in the South China Sea

“…In this limit, the flow response is characterized by low‐level lee wave breaking, flow blocking, hydraulic jumps, and wakes (e.g., Klymak, 2018; Klymak et al., 2020). Flows over supercritical topography tend to produce a separating layer and significant turbulence in the lee side of the topography (Mayer & Fringer, 2020; Winters, 2016). The steepness parameter estimated for the big bump is ɛ = 5, which corresponds to a strongly nonlinear flow‐topography interaction regime.…”

Internal Lee Waves Generated by Shear Flow Over Small‐Scale Topography

“…It can reduce ocean stratification associated with warming of the abyssal ocean, accelerate global meridional overturning circulation because of its promotion of deep‐water upwelling, and hence facilitating the renewal of deep water (e.g., MacKinnon et al., 2017; Mashayek et al., 2017; Melet et al., 2014; Trossman et al., 2016; Yang et al., 2021). Internal lee waves have received extensive attention in recent years (e.g., Baker & Mashayek, 2021; De Marez et al., 2020; Johnston et al., 2019; Kunze & Lien, 2019; Legg, 2020; Mayer & Fringer, 2020; Shakespeare, 2020; Shakespeare et al., 2021; Shakespeare & Hogg, 2017; Voet et al., 2020; Xie et al., 2017; Xie & Li, 2019; Xie & Vanneste, 2017).…”