Internal Tide Nonstationarity and Wave–Mesoscale Interactions in the Tasman Sea

Abstract

Internal tides, generated by barotropic tides flowing over rough topography, are a primary source of energy into the internal wavefield. As internal tides propagate away from generation sites, they can dephase from the equilibrium tide, becoming nonstationary. Here, we examine how low-frequency quasigeostrophic background flows scatter and dephase internal tides in the Tasman Sea. We demonstrate that a semi-idealized internal-tide model (the Coupled-mode Shallow Water Model; CSW) must include two background-flow effects to replicate the in-situ internal-tide energy fluxes observed during the Tasmanian Internal-Tide Beam Experiment (TBeam). The first effect is internal-tide advection by the background flow, which strongly depends on the spatial scale of the background flow, and is largest at the smaller scales resolved in the background-flow model (i.e., 50-400 km). Internal-tide advection is also shown to scatter internal-tides from vertical mode-1 to mode-2 at a rate of about 1 mW m−2. The second effect is internal-tide refraction due to background-flow perturbations to the mode-1 eigenspeed. This effect primarily dephases the internal-tide, attenuating stationary energy at a rate of up to 5 mW m−2. Detailed analysis of the stationary internal-tide momentum and energy balances indicate that background-flow effects on the stationary internal tide can be accurately parameterized using an eddy diffusivity derived from a 1D random walk model. In summary, the results identify an efficient way to model the stationary internal tide and quantify its loss of stationarity.

Global Dynamics of the Stationary M2Mode‐1 Internal Tide

“…The simulation used satellite‐derived bathymetry (Smith & Sandwell, 1997), World Ocean Atlas (WOA) stratification (Locarnini et al., 2010; Antonov et al., 2010), and TPXO8 M 2 surface tides (Egbert, 1997). The simulation also employed wave drag (Jayne & St. Laurent, 2001) and diffusion due to a turbulent mean flow (Savage et al., 2020) where γ r and γ κ are free parameters, N b is the buoyancy frequency at the bottom, h 2 is the bottom roughness (see Jayne & St. Laurent, 2001, for details), δc 1 is the mean eigenspeed perturbation due to mesoscale variability (in HYCOM during 2015) and l is an estimate of eddy diameter (see Savage et al., 2020, for details). We set γ r = 2 π /(10 km) following Jayne and St. Laurent (2001), and γ κ = 0.25 to maximize agreement with satellite observations in the control run (Savage et al.…”

“…We set γ r = 2 π /(10 km) following Jayne and St. Laurent (2001), and γ κ = 0.25 to maximize agreement with satellite observations in the control run (Savage et al. 2020) used γ κ = 1 in the Tasman Sea). Globally, wave drag is negligible (i.e., it has a decay timescale greater than 32 days) except at abrupt topography (mid‐ocean ridges and continental margins), where it has a decay timescale of 1–2 days (Figure 1d).…”

“…and diffusion due to a turbulent mean flow (Savage et al, 2020)…”

“…Equations describing the evolution of vertical mode amplitudes were first derived and applied by Griffiths and Grimshaw (2007) and Griffiths (2011). Here, we employ the CSW model used by Savage et al (2020), which is asymptotically accurate for small-amplitude internal tides in a small-Rossby-number (Ro ≪ 1) background flow. The model evolves the stationary vertical-mode transports, U n (x, t), and pressures, p n (x, t), using…”

“…As internal tides propagate through mesoscale turbulence they lose coherence with the surface tide (and astronomical tidal potential), becoming nonstationary (e.g., Rainville & Pinkel, 2006; Zaron, 2017; Nelson et al., 2019). Radiating internal tides also dissipate slowly through a combination of topographic scattering (e.g., Müller & Xu, 1992; Bühler & Holmes‐Cerfon, 2011; Mathur et al., 2014), wave‐meanflow interactions (e.g., Dunphy et al., 2017; Savage et al., 2020), and wave‐wave interactions (e.g., MacKinnon et al., 2013; Olbers et al., 2020). Although the relative role of each decay processes is unknown, the geography of internal‐tide dissipation (as it relates to diapycnal mixing) is a key ingredient in climate models (MacKinnon et al., 2017).…”