Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model

Abstract

The impact of parameterized topographic internal lee wave drag on the input and output terms in the total mechanical energy budget of a hybrid coordinate high-resolution global ocean general circulation model forced by winds and air-sea buoyancy fluxes is examined here. Wave drag, which parameterizes the generation of internal lee waves arising from geostrophic flow impinging upon rough topography, is included in the prognostic model, ensuring that abyssal currents and stratification in the model are affected by the wave drag. An inline mechanical (kinetic plus gravitational potential) energy budget including four dissipative terms (parameterized topographic internal lee wave drag, quadratic bottom boundary layer drag, vertical eddy viscosity, and horizontal eddy viscosity) demonstrates that wave drag dissipates less energy in the model than a diagnostic (offline) estimate would suggest, due to reductions in both the abyssal currents and stratification. The equator experiences the largest reduction in energy dissipation associated with wave drag in inline versus offline estimates. Quadratic bottom drag is the energy sink most affected globally by the presence of wave drag in the model; other energy sinks are substantially affected locally, but not in their global integrals. It is suggested that wave drag cannot be mimicked by artificially increasing the quadratic bottom drag because the energy dissipation rates associated with bottom drag are not spatially correlated with those associated with wave drag where the latter are small. Additionally, in contrast to bottom drag, wave drag is a non-local energy sink. All four aforementioned dissipative terms contribute substantially to the total energy dissipation rate of about one terawatt. The partial time derivative of potential energy (non-zero since the isopycnal depths have a long adjustment time), the surface advective fluxes of potential energy, the rate of change of potential energy due to diffusive mass fluxes, and the conversion between internal energy and potential energy also play a non-negligible role in the total mechanical energy budget. Reasons for the <10% total mechanical energy budget imbalance are discussed.

Climate Process Team on Internal Wave–Driven Ocean Mixing

“…Using a hydrographic climatology and a similar parameterization for lee wave-driven mixing, Nikurashin and Ferrari (2013) and De Lavergne et al (2016) also show substantial water mass transformation in the Southern Ocean due to internal lee wave-driven mixing. Trossman et al (2013Trossman et al ( , 2016 implemented an inline wave drag parameterization (for both propagating and nonpropagating lee waves) from the atmospheric community (Garner 2005) into a high-resolution ocean general circulation model (Fig. 5d).…”

“…Indeed, Wright et al (2014) found that the use of different stratification products yields a difference of up to 0.25 TW in the global conversion rate into lee waves. Conversion rates are even more sensitive to the near-bottom velocity field (Trossman et al 2013;Melet et al 2015), which can vary drastically with model resolution (Thoppil et al 2011) and should take into account mesoscale eddy velocities. Topographic blocking accounts for most of the predicted dissipation by the Garner (2005) scheme in the bottom 1000 m of two Southern Ocean domains (Trossman et al 2015).…”

“…As parameterized lee-wave drag makes a significant impact on the ocean state (Trossman et al 2013(Trossman et al , 2016, it should be included inline within climate models in a dynamically accurate manner to ensure credible ocean representation in a changing climate. Using linear theory and modeled resolved and parameterized bottom velocities and stratification, Melet et al (2015) showed that the energy flux into lee waves exhibits a clear annual cycle in the Southern Ocean and that the global energy flux is projected to decrease by ~20% from preindustrial to future climate conditions under the representative concentration pathway 8.5 (RCP8.5) scenario.…”

Energy Flux into Internal Lee Waves: Sensitivity to Future Climate Changes Using Linear Theory and a Climate Model

“…How far from their generation site and how high in the water column lee waves dissipate their energy is largely unknown (e.g., Melet et al 2014). Over recent years, the potentially pivotal role of lee waves for the energy budget and dynamical balance of the Southern Ocean has been highlighted in several studies (e.g., Kunze et al 2006;Nikurashin and Ferrari 2010a;Trossman et al 2013;. Over recent years, the potentially pivotal role of lee waves for the energy budget and dynamical balance of the Southern Ocean has been highlighted in several studies (e.g., Kunze et al 2006;Nikurashin and Ferrari 2010a;Trossman et al 2013;.…”

“…Over the last decade, efforts have been focused on parameterizations of the generation and dissipation of internal tides (e.g., Jayne and St. Laurent 2001;Polzin 2009;Decloedt and Luther 2010;Melet et al 2013), which are the most energetic class of internal waves [with O(1) TW of energy being dissipated in the deep ocean]. As it has recently been shown that lee-wavedriven mixing has the potential to impact the ocean state in a climate model (Melet et al 2014), the energy budget of the ocean eddies, and the large-scale circulation (Trossman et al 2013), as well as the deep ocean turbulent mixing (Gille et al 2000;Ito and Marshall 2008;Saenko et al 2012;Nikurashin and Ferrari 2013), parameterizing lee-wave-driven mixing in climate models warrants serious consideration (MacKinnon 2013). As it has recently been shown that lee-wavedriven mixing has the potential to impact the ocean state in a climate model (Melet et al 2014), the energy budget of the ocean eddies, and the large-scale circulation (Trossman et al 2013), as well as the deep ocean turbulent mixing (Gille et al 2000;Ito and Marshall 2008;Saenko et al 2012;Nikurashin and Ferrari 2013), parameterizing lee-wave-driven mixing in climate models warrants serious consideration (MacKinnon 2013).…”