Oceanic Internal Tides Research Articles

Enhanced Dissipation of Internal Tides in a Mesoscale Baroclinic Eddy

Abstract The dissipation of low-mode internal tides as they propagate through mesoscale baroclinic eddies is examined using a series of numerical simulations, complemented by three-dimensional ray tracing calculations. The incident mode-1 internal tide is refracted into convergent energy beams, resulting in a zone of reduced energy flux in the lee of the eddy. The dissipation of internal tides is significantly enhanced in the upper water column within strongly baroclinic (anticyclonic) eddies, exhibiting a spatially asymmetric pattern, due to trapped high-mode internal tides. Where the eddy velocity opposes the internal tide propagation velocity, high-mode waves can be trapped within the eddy, whereas high modes can freely propagate away from regions where eddy and internal wave velocities are in the same direction. The trapped high modes with large vertical shear are then dissipated, with the asymmetric distribution of trapping leading to the asymmetric distribution of dissipation. Three-dimensional ray tracing solutions further illustrate the importance of the baroclinic current for wave trapping. Similar enhancement of dissipation is also found for a baroclinic cyclonic eddy. However, a barotropic eddy is incapable of facilitating robust high modes and thus cannot generate significant dissipation of internal tides, despite its strong velocities. Both energy transfer from low to high modes in the baroclinic eddy structure and trapping of those high modes by the eddy velocity field are therefore necessary to produce internal wave dissipation, a conclusion confirmed by examining the sensitivity of the internal tide dissipation to eddy radius, vorticity, and vertical scale. Significance Statement The oceanic tides drive underwater waves at the tidal frequency known as internal tides. When these waves break, or dissipate, they can lead to mixing of oceanic heat and salt which impacts the ocean circulation and climate. Accurate climate predictions require computer models that correctly represent the distribution of this mixing. Here we explore how an oceanic eddy, a swirling vortex of order 100–400 km across, can locally enhance the dissipation of oceanic internal tides. We find that strong ocean eddies can be hotspots for internal tide dissipation, for both clockwise and anticlockwise rotating vortices, and surface-enhanced eddies are most effective at internal tide dissipation. These results can improve climate model representations of tidally driven mixing, leading to more credible future predictions.

Scattering of internal tides by barotropic quasigeostrophic flows

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.

An asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow

We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.

Nonlinear harmonic generation by diurnal tides

Recent observations from the South China Sea have demonstrated that semi-diurnal tides sometimes generate a double-frequency harmonic. Similar harmonic generation has been found in laboratory experiments and numerical simulations of internal wave beams refracting into a pycnocline. Here, a weakly nonlinear theory of internal wave refraction is applied to oceanic internal tides in an idealized stratification profile. The steady state harmonic amplitude is calculated as a function of the tidal frequency and the pycnocline characteristics. The results indicate that harmonic generation by nonlinear refraction of semi-diurnal tides is consistent with the South China Sea observations.

The recent history of our understanding of low-mode internal tides in the ocean

The past decade has seen a renaissance in the interest in oceanic internal tides and their role in mixing the abyssal ocean. One of the sparks of this renaissance was the discovery of the remarkable coherence of low-mode internal tides using an ocean acoustic tomography array deployed in the central North Pacific Ocean in 1987. The result was subsequently confirmed by satellite altimetry. This talk will review these results and related results from the 1991 Acoustic Mid-Ocean Dynamics Experiment (AMODE) in the North Atlantic and the 2001 Hawaiian Ocean Mixing Experiment (HOME) around the Hawaiian Ridge. Internal tides are generated by tidal forces hence they are a means by which the tides dissipate energy. With wavelengths of 150-km, low-mode semidiurnal internal tides appear to propagate 1000’s of kilometers across ocean basins while retaining considerable coherence.

Resonant diurnal internal tides in the North Atlantic

Using an acoustic tomography array located midway between Puerto Rico and Bermuda, enhanced diurnal tidal signals associated with the lowest internal-wave mode have been observed. These signals result from a diurnal internal wave with O(500-km) wavelength that is resonantly trapped between the shelf just north of Puerto Rico and the turning latitude, a distance of about 1100 km. The data obtained using the large acoustical array are consistent with the predicted Airy-function variation with latitude of diurnal internal waves near the turning latitude. The existence of this wave is a striking demonstration of the long spatial and temporal coherence of oceanic internal tides.

Resonant diurnal internal tides in the North Atlantic

Using a large acoustical array located midway between Puerto Rico and Bermuda, we have observed enhanced diurnal tidal signals associated with the lowest internal‐wave mode. These signals result from a diurnal internal wave resonantly trapped between the shelf just north of Puerto Rico and the turning latitude, a distance of about 1100 km. The data obtained using the large acoustical array are consistent with the predicted Airy‐function variation with latitude of diurnal internal waves near the turning latitude. The existence of this wave is a striking demonstration of the long spatial and temporal coherence of oceanic internal tides. In general, the energy radiated by such waves is a loss of energy from the earth‐moon system and a source of energy for mixing in the deep ocean.

The generation of internal tides by flat-bump topography

A general procedure for the calculation of the oceanic internal tides generated by the interaction of the surface tide with bottom topography is derived, and applied to typical cases. The formalism is restricted here to essentially two-dimensional topography whose surface is never tangential to the local direction of internal tidal energy propagation, but has otherwise arbitrary shape. The theory is applicable to a wide range of density stratifications which permits a two-parameter fit to any oceanic case. Results have been calculated for certain representative topographic shapes, most notably continental slopes, and these indicate that the rate of conversion of surface tide energy into internal tide energy generally increases rapidly with topographic height, but also depends strongly on the geometry. For instance, for this model, continental slopes are far more effective internal tide generators than, say, the Mid-Atlantic Ridge. For a model ocean with constant Brunt-Väisälä frequency, N, the internal wave energy fluxes on each side of a continental slope (satisfying the above criteria) are approximately equal, but for an ocean with a realistic density profile the energy flux and energy density are larger on the shallow continental shelf than in the deep ocean.