Abstract
Oceanic internal tides and other inertia–gravity waves propagate in an energetic turbulent flow whose length scales 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 wave field. 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.
Highlights
The propagation of inertia–gravity waves in the ocean has received a great deal of attention, mainly motivated by the role they play in the large- and mesoscale circulation, through wave–mean-flow interaction, mixing and dissipation
The inertia–gravity wave spectrum is dominated by two types of waves: near-inertial oscillations, with frequencies close to the inertial frequency f, which are mainly generated by winds, and internal tides (ITs), primarily at the semi-diurnal lunar frequency, which are generated by the interaction of the barotropic tide with
This paper examines the scattering of oceanic ITs – or of any inertia–gravity wave – caused by the turbulent mesoscale flow in which they propagate
Summary
The propagation of inertia–gravity waves in the ocean has received a great deal of attention, mainly motivated by the role they play in the large- and mesoscale circulation, through wave–mean-flow interaction, mixing and dissipation. The form of the scattering term in the kinetic equation for a(x, k, t) shows that energy transfers are restricted to waves with the same frequency or, equivalently, the same wavenumber |k| These transfers result from interactions within resonant triads consisting of two ITs of equal frequencies with a zero-frequency flow (vortical) mode – the so-called catalytic interactions of Lelong & Riley (1991) and Bartello (1995). We analyse the predictions of the kinetic equation, focusing our attention on parameters representative of the first baroclinic mode of the semidiurnal lunar tide M2 These predictions include a time scale for wave isotropisation applicable to statistically homogeneous wave fields (i.e. such that ∇xa = 0) and in particular to the isotropisation of an initially plane wave examined numerically by Ward & Dewar (2010) in a shallow-water set-up.
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