The viscous lee wave problem and its implications for ocean modelling

Abstract

Ocean circulation models employ horizontal viscosity and diffusivity to represent unresolved sub-gridscale processes such as breaking internal waves. Computational power has now advanced sufficiently to permit regional ocean circulation models to be run at sufficiently high (100m-1km) horizontal res

Surface reflection of bottom generated oceanic lee waves

“…Parametrisation of dissipation and mixing at the sub-grid scale in models is generally implemented through Laplacian (or higher-order) viscous and diffusive terms in the momentum and buoyancy equations – as shown in (2.1)–(2.2). Shakespeare & Hogg (2017) provide a comprehensive overview of the role of Laplacian viscosity and diffusivity in the linear lee wave problem, with a focus on preventing excessive dissipation in wave resolving models. Here, we do not represent the processes that drain energy from the lee wave field, so aim to model them diffusively with this parametrisation.…”

“…Here, we do not represent the processes that drain energy from the lee wave field, so aim to model them diffusively with this parametrisation. However, unlike Shakespeare & Hogg (2017), we are dealing with background flows that vary in the vertical, and thus including the vertical components and of the Laplacian terms in our study significantly complicates the solution.…”

“…A more realistic simulation capturing the characteristic stratification, wind forcing and topography of the SO (Nikurashin et al. 2012) found that 80 % of the wind power input into geostrophic eddies was converted to smaller scales by topography, of which just 20 % radiated into the interior ocean, with most dissipated in the bottom 100 m. However, this and other wave resolving models may use artificially high diffusivity and viscosity, preventing lee waves from radiating in a physical way (Shakespeare & Hogg 2017).…”

“…Parametrisations for energy loss must therefore be used even when the lee waves are resolved, since capturing the length scales of both lee waves ()) and turbulent length scales ()) in a 3-D direct numerical simulation remains prohibitively expensive. Shakespeare & Hogg (2017) investigated the impact of Laplacian parametrisation of mixing and dissipation in lee wave resolving models, and concluded that care must be taken to avoid artificially high viscosity and diffusivity that is not physically justified. They suggest that high levels of dissipation near the bottom boundary in wave resolving models could be a direct result of the high levels of viscosity and diffusivity used in the sub-grid-scale parametrisation.…”

Boundary streaming by internal waves

“…It is therefore crucial to understand the effect of viscous boundary layers. Viscous internal wave beams generated by boundaries have been extensively studied (Voisin 2003), together with their consequences on the bulk energy budget of numerical ocean models (Shakespeare & Hogg 2017). The role of viscous boundary layers has been addressed by Beckebanze & Maas (2016) to close the energy budget of internal wave attractors; Chini & Leibovich (2003) described the viscous boundary layers in the case of Klemp and Durran boundary conditions; Passaggia et al (2014) studied the structure of a stratified boundary layer over a tilted bottom with a small stream-wise undulation.…”