Higher-mode Internal Waves Research Articles

Oblique internal-wave chain resonance over seabed corrugations

Here we show that monochromatic long-crested corrugations on an otherwise flat seafloor can coherently scatter the energy of an oblique incident internal wave to multiple multi-directional higher-mode internal waves via a series of resonant interactions. We demonstrate that a resonance between seabed corrugations and a normally or slightly oblique incident internal wave results in a series of follow-up resonant interactions, which take place between the same corrugations and successively resonated shorter waves. A chain resonance of internal waves that carries energy to small scales is thus obtained, and we find that the Richardson number decreases by several orders of magnitude over the corrugated patch. If the incidence angle is large, and the incident wave perfectly satisfies a resonance condition with the topography, it turns out that not many higher-mode resonance or near-resonance conditions can be satisfied, such that energy stays confined within the first few modes. Nevertheless, if the incident waves are sufficiently detuned from satisfying a perfect resonance condition with the seabed corrugations, then we show that this frequency detuning may balance off the large detuning due to oblique incidence, leading to a chain resonance that again carries energy to small scales. The evolution of the incident and resonated wave amplitudes is predicted from the envelope equation for internal waves over resonant seabed topography in a three-dimensional rotating fluid, which we derive considering the Boussinesq and $f$-plane approximations with $f$ the Coriolis frequency, linear density stratification and small-amplitude corrugations. Our results suggest that topographic features on the ocean floor with a well-defined dominant wavenumber vector, through the chain resonance mechanism elucidated here, may play a more important role than previously thought in the enhancement of diapycnal mixing and energy dissipation.

Generation of Internal Waves by Eddies Impinging on the Western Boundary of the North Atlantic

AbstractDespite the major role played by mesoscale eddies in redistributing the energy of the large-scale circulation, our understanding of their dissipation is still incomplete. This study investigates the generation of internal waves by decaying eddies in the North Atlantic western boundary. The eddy presence and decay are measured from the altimetric surface relative vorticity associated with an array of full-depth current meters extending ~100 km offshore at 26.5°N. In addition, internal waves are analyzed over a topographic rise from 2-yr high-frequency measurements of an acoustic Doppler current profiler (ADCP), which is located 13 km offshore in 600-m deep water. Despite an apparent polarity independence of the eddy decay observed from altimetric data, the flow in the deepest 100 m is enhanced for anticyclones (25.2 cm s−1) compared with cyclones (−4.7 cm s−1). Accordingly, the internal wave field is sensitive to this polarity-dependent deep velocity. This is apparent from the eddy-modulated enhanced dissipation rate, which is obtained from a finescale parameterization and exceeds 10−9 W kg−1 for near-bottom flows greater than 8 cm s−1. The present study underlines the importance of oceanic western boundaries for removing the energy of low-mode westward-propagating eddies to higher-mode internal waves.

A multi-layer model for nonlinear internal wave propagation in shallow water

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

Baroclinic Energy Flux at the Hawaiian Ridge: Observations from the R/P FLIP

Abstract Estimates of baroclinic energy flux are made in the immediate “Nearfield” (September–October 2002) and 450 km offshore (“Farfield”; October–November 2001) of the Kaena Ridge, an active barotropic-to-baroclinic conversion site. The flux estimates are based on repeated profiles of velocity and density obtained from the Research Platform Floating Instrument Platform (FLIP) as an aspect of the Hawaii Ocean Mixing Experiment. Energetic beams associated with both semidiurnal and diurnal internal waves are observed in the Kauai Channel. Beam depths and orientations are consistent with generation along the upper flanks of the ridge. At the far-field site, the baroclinic energy flux is borne primarily by first-mode semidiurnal waves. The energy flux associated with the entire spectrum of internal waves is computed by cross-spectral analysis. Significant energy fluxes are found in the inertial, diurnal, semidiurnal, and twice-semidiurnal frequency bands. The semidiurnal energy flux strongly dominates the spectrum at both sites. The flux magnitude follows the spring–neap cycle of the semidiurnal barotropic tide. The averaged depth-integrated mode-1 semidiurnal energy flux (over the entire water column) in the Farfield is found to be 1.7 ± 0.3 kW m−1 away from the ridge, with peak values up to 4 kW m−1. Small fluxes toward the ridge are occasionally seen at neap tide. At both sites, energy fluxes in the diurnal frequency band represent 15%–20% of the semidiurnal energy flux. In the Farfield, the magnitude of the diurnal energy flux varies in accord with the fortnightly cycle of the barotropic semidiurnal tide, rather than with the diurnal forcing, suggesting that energy for those waves is supplied by a cross-frequency transfer from the low-vertical-mode M2 internal tide to higher-mode internal waves at frequencies ½M2. In the Nearfield, the diurnal flux varies with fluctuations in both diurnal and semidiurnal forcing.

Scattering of Semidiurnal Internal Kelvin Wave at Step Bottom Topography

A three-dimensional, multi-level model was used to study the energy dissipation of semidiurnal internal Kelvin waves due to their interaction with bottom topography. A simplified topography consisting of a channel with an additional shallow bay was used to clarify the wave’s scattering process. When the first mode semidiurnal internal wave given at an open boundary arrives at the bay mouth, higher-mode internal waves are generated at a step bottom of the bay mouth. As a result, the energy of the first mode internal Kelvin wave is effectively decayed. The decay rate of the internal Kelvin wave depends on both the width and length of the additional bay. The maximum decay rate was found when a resonance condition occurs the bay, that is, the bay length is equal to a quarter of wave length of the first mode internal wave on the shallow region. The decay rate in the wide bay cases is higher than that in a narrow case, due to a contribution from the scattering due to the Poincare wave that emanates from the corners of the bay head. The decay rate with the additional bay is 1.1–1.8 times that of the case without the additional bay. The decay rate due to the scattering process is found to be of the same order as that of the internal and bottom friction.

A description of short period temperature fluctuations in the upper ocean

Dynamical properties of short-period temperature fluctuations are studied. Water temperature was measured continuously at several depths at the following stations: at 38°29.5′N, 141°35.8′E (100 m depth) on the continental shelf off Miyagi Prefecture in the summer of 1967, at 35°01.8′N, 139°0.8.5′E (100 m depth) in Sagami Bay in the summer of 1968, and at 32°32.2′N, 129°53.7′E (74 m depth) in Tachibana Bay in the summer of 1970. These measurements were made with a thermistor array laid down from the R. V.Tanseimaru (Ocean Research Institute, University of Tokyo) which was fixed with bow and stern anchors. Significant temperature fluctuations found at the first and the third stations are thought to be due to first mode internal waves having amplitude 3 to 5 m and period 5 to 20 minutes. The wave length of the waves is estimated to be 25 m to 400 m from the observed density structure. At the second station, we found second-mode internal waves. The period, amplitude and wave length of the waves are about 30 minutes, 1.3 m and 600 m, respectively. In all cases, the spectral density of the temperature fluctuations decreases with increase in frequency. However, the decrease obey neither the −3 power law nor the −5/3 power law. Coherences in the temperature fluctuations between two depths of measurement in the seasonal thermocline are significantly high in the range of frequencies lower than the local Brunt-Vaisala frequency, but are low in the higher frequency range. At the first and the third stations, the difference in the level of coherences between the lower frequencies and the higher frequencies are large. Phase differences between two depths in the thermocline are small in the lower frequency range. This suggests that the first-mode internal waves are predominant over higher-mode internal waves and over other disturbances.

M2 tidal currents in the western North Atlantic

A number of current meter records collected by the Woods Hole Oceanographic Institution have been examined to determine the structure of M 2 tides in the western North Atlantic. Though the signal to noise ratio is low, a simple picture emerges when sufficiently many records are averaged. At a site north of the Gulf Stream, the tidal current is baroclinic, and concentrated near the surface. The result is consistent with generation of internal tides along the continental slope just to the north. At positions south of the Gulf Stream, the records are too few to conclude more than that the tidal velocities are consistent with high mode internal waves.