Scattering of internal tides by barotropic quasigeostrophic flows

Abstract

Received xx; revised xx; accepted xx)Oceanic internal tides and other inertia-gravity waves propagate in an energetic turbulent flow whose lengthscales are similar to the wavelengths. Advection and refraction by this flow cause the scattering of the waves, redistributing their energy in wavevector space. As a result, initially plane waves radiated from a source such as a topographic ridge become spatially incoherent away from the source. To examine this process, we derive a kinetic equation which describes the statistics of the scattering under the assumptions that the flow is quasigeostrophic, barotropic, and well represented by a stationary homogeneous random field. Energy transfers are quantified by computing a scattering cross section and shown to be restricted to waves with the same frequency and identical vertical structure, hence the same horizontal wavelength. For isotropic flows, scattering leads to an isotropic wavefield. We estimate the characteristic time and length scales of this isotropisation, and study their dependence on parameters including the energy spectrum of the flow. Simulations of internal tides generated by a planar wavemaker carried out for the linearised shallow-water model confirm the pertinence of these scales. A comparison with the numerical solution of the kinetic equation demonstrates the validity of the latter and illustrates how the interplay between wave scattering and transport shapes the wave statistics.

Diffusion of inertia-gravity waves by geostrophic turbulence

“…A remarkable feature of this regime is the prediction of a k −2 h energy spectrum consistent with observations in both the ocean and atmosphere. When the assumption of small scales is relaxed, the wave energy obeys a kinetic equation generalising the equations obtained by Danioux & Vanneste (2016) and Savva & Vanneste (2018) in the case of inertial waves and IGWs in a barotropic flow. The kinetic equation captures the transfer of energy between upward and downwardpropagating IGWs which is negligible in the diffusive regime.…”

“…In the weakly nonlinear regime, corresponding to small Rossby and/or Froude numbers, the vortical flow has a 'catalytic' role, enabling the scattering of energy between IGWs through resonant triad interactions while remaining unaffected (Lelong & Riley 1991;Bartello 1995;Ward & Dewar 2010). The qualitative impact of this catalytic interaction has been considered: an isotropic turbulent flow causes the isotropisation of the IGW field (Lelong & Riley 1991;Savva & Vanneste 2018) and a cascade of wave energy to small scales (Bartello 1995;Waite & Bartello 2006a).…”

Frequency diffusion of waves by unsteady flows

“…The catalysing effect in transferring energy of waves with the same frequency was also found in the rotating shallow-water system by Ward & Dewar (2010), but, in this two-dimensional space, the frequency constraint prevents redistribution of energy among waves of different length scales. Similarly, Savva & Vanneste (2018) found that a random barotropic quasi-geostrophic flow can redistribute energy amongst internal tides of the same vertical structure and frequency. Understanding the formation of small-scale waves through nonlinear wave–wave interaction or wave–vortex interactions is not only of fundamental interest, but also provides a means by which to estimate the turbulence production rate (or mixing efficiency), since inertia–gravity wave breaking is a major source of diapycnal mixing in the ocean (MacKinnon et al.…”

Internal Tide Cycle and Topographic Scattering Over the North Mid‐Atlantic Ridge

“…It has been shown that numerous mechanisms impact internal tide dynamics. The major mechanisms include (Eden & Olbers, 2014; Müller et al., 1986; Polzin & Lvov, 2011): (1) interaction with (sub)‐mesoscale ocean turbulence (Duda et al., 2018; Dunphy et al., 2017; Kafiabad et al., 2019; Savva & Vanneste, 2018), (2) scattering by topographic corrugations (Baines, 1971a; Kelly et al., 2013; Müller & Xu, 1992), and (3) nonlinear wave‐wave interactions such as Parametric Subharmonic Instability (e.g., McComas & Bretherton, 1977; MacKinnon et al., 2012; D. J. Olbers, 1976; D. Olbers et al., 2020; Onuki & Hibiya, 2018). As low mode internal tides (typically the first and, to a weaker extent, the second baroclinic modes) can propagate long distances, they lose coherence (which is associated with departure from an exactly repeating signal) through the above‐mentioned processes (Buijsman et al., 2017; B. Li et al., 2020; Nelson et al., 2019) and, in addition, they have a remote impact in the ocean.…”