Near-inertial waves and turbulence driven by the growth of swell

Abstract

Between 5% and 25% of the total momentum transferred between the atmosphere and ocean is transmitted via the growth of long surface gravity waves called ''swell.'' In this paper, we use large-eddy simulations to show that swelltransmitted momentum excites near-inertial waves and drives turbulent mixing that deepens a rotating, stratified, turbulent ocean surface boundary layer. We find that swell-transmitted currents are less effective at producing turbulence and mixing the boundary layer than currents driven by an effective surface stress. Overall, however, the differences between swelldriven and surface-stress-driven boundary layers are relatively minor. In consequence, our results corroborate assumptions made in Earth system models that neglect the vertical structure of swell-transmitted momentum fluxes and instead parameterize all air-sea momentum transfer processes with an effective surface stress.

Ocean general circulation models simulate total ocean transport averaged over surface waves

“…where the turbulent vertical diffusivity K is a nonlinear function of mean buoyancy b, mean velocity u L , surface boundary conditions, and depth z. We emphasize that the parameterization in equation ( 15) is sensible, as it dissipates mean kinetic energy 1 2 |u L | 2 (Wagner et al, 2021) and is consistent with large eddy simulation results. For example, Reichl et al (2016) find momentum fluxes aligned with ∂ z u L in large eddy simulations of hurricane-forced boundary layer turbulence, and Pearson (2018) observe that turbulent mixing beneath surface waves tends to homogenize u L .…”

“…Note that the same winds -not the same wind stress -force both OM4 and OM4-CL, and that OM4-CL includes the Stokes tendency term ∂ t u S in equation ( 3). As a result, OM4 and OM4-CL have slightly different column-integrated momentum budgets (Fan et al, 2009;Wagner et al, 2021). Nevertheless, figures 1 and 2 show that these discrepancies are not important.…”

“…Equations ( 2)-( 3) are related by (1) and standard vector identities. Physical interpretations for the green surface wave terms in equations ( 2)-( 3) are discussed by Wagner et al (2021) in their section 2.1, Bühler (2014) in their section 11.3.2, and by Suzuki and Fox-Kemper (2016).…”

“…Only the horizontal components of u S are significant (Vanneste & Young, 2022). ∂ t u S is primarily associated with wave growth beneath atmospheric storms and thus effectively represents the small part of the total parameterized air-sea momentum transfer that is depth-distributed rather than fluxed at or just below the surface (Wagner et al, 2021). We could therefore interpret ∂ t u S as accounted for implicitly in wave-agnostic models by bulk formulae for air-sea momentum transfer.…”

Stokes drift and its discontents

“…This raises the issue of whether the CL formulation is incomplete or misleading in situations with temporal modulation of the wave field, e.g. in ocean observations [16] and in modelling the growth of swell [17].…”