scholarly journals Energy Transfer within the Small-Scale Oceanic Internal Wave Spectrum

2003 ◽  
Vol 33 (1) ◽  
pp. 267-282 ◽  
Author(s):  
Ryo Furue
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Wave Spectrum ◽  
Small Scale ◽  
Oceanic Internal Wave

Parametric instability of internal gravity waves

1975 ◽  
Vol 67 (4) ◽  
pp. 667-687 ◽  
Author(s):  
A. D. McEwan ◽  
R. M. Robinson
Keyword(s):  
Internal Wave ◽  
Large Scale ◽  
Wave Spectrum ◽  
Parametric Instability ◽  
Mathieu Equation ◽  
Internal Gravity Waves ◽  
Small Scale ◽  
Preliminary Calculation ◽  
Theoretical Predictions ◽  
Oceanic Internal Wave

A continuously stratified fluid, when subjected to a weak periodic horizontal acceleration, is shown to be susceptible to a form of parametric instability whose time dependence is described, in its simplest form, by the Mathieu equation. Such an acceleration could be imposed by a large-scale internal wave field. The growth rates of small-scale unstable modes may readily be determined as functions of the forcing-acceleration amplitude and frequency. If any such mode has a natural frequency near to half the forcing frequency, the forcing amplitude required for instability may be limited in smallness only by internal viscous dissipation. Greater amplitudes are required when boundaries constrain the form of the modes, but for a given bounding geometry the most unstable mode and its critical forcing amplitude can be defined.An experiment designed to isolate the instability precisely confirms theoretical predictions, and evidence is given from previous experiments which suggest that its appearance can be the penultimate stage before the traumatic distortion of continuous stratifications under internal wave action.A preliminary calculation, using the Garrett & Munk (197%) oceanic internal wave spectrum, indicates that parametric instability could occur in the ocean at scales down to that of the finest observed microstructure, and may therefore have a significant role to play in its formation.

Upscale Energy Transfer by the Vortical Mode and Internal Waves

2014 ◽  
Vol 44 (9) ◽  
pp. 2446-2469 ◽  
Author(s):  
Anne-Marie E. G. Brunner-Suzuki ◽  
Miles A. Sundermeyer ◽  
M.-Pascale Lelong
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Internal Waves ◽  
Numerical Experiments ◽  
Large Scale ◽  
Vertical Shear ◽  
Small Scale ◽  
Driving Mechanism ◽  
Vortex Interaction ◽  
Vertical Scale

Abstract Diapycnal mixing in the ocean is sporadic yet ubiquitous, leading to patches of mixing on a variety of scales. The adjustment of such mixed patches can lead to the formation of vortices and other small-scale geostrophic motions, which are thought to enhance lateral diffusivity. If vortices are densely populated, they can interact and merge, and upscale energy transfer can occur. Vortex interaction can also be modified by internal waves, thus impacting upscale transfer. Numerical experiments were used to study the effect of a large-scale near-inertial internal wave on a field of submesoscale vortices. While one might expect a vertical shear to limit the vertical scale of merging vortices, it was found that internal wave shear did not disrupt upscale energy transfer. Rather, under certain conditions, it enhanced upscale transfer by enhancing vortex–vortex interaction. If vortices were so densely populated that they interacted even in the absence of a wave, adding a forced large-scale wave enhanced the existing upscale transfer. Results further suggest that continuous forcing by the main driving mechanism (either vortices or internal waves) is necessary to maintain such upscale transfer. These findings could help to improve understanding of the direction of energy transfer in submesoscale oceanic processes.

scholarly journals Global Characterization of the Ocean’s Internal Wave Spectrum

2020 ◽  
Vol 50 (7) ◽  
pp. 1871-1891 ◽  
Author(s):  
Friederike Pollmann
Keyword(s):  
Internal Wave ◽  
Gravity Wave ◽  
Spectral Characteristics ◽  
Wave Spectrum ◽  
Internal Gravity Wave ◽  
Ocean Dynamics ◽  
Small Scale ◽  
Northwest Pacific ◽  
Spatial And Temporal Variability ◽  
Spectral Parameters

AbstractA key ingredient of energetically consistent ocean models is the parameterized link between small-scale turbulent mixing, an important energy source of large-scale ocean dynamics, and internal gravity wave energetics. Theory suggests that this link depends on the wave field’s spectral characteristics, but because of the paucity of suitable observations, its parameterization typically relies on a model spectrum [Garrett–Munk (GM)] with constant parameters. Building on the so-called “finestructure method,” internal gravity wave spectra are derived from vertical strain profiles obtained from Argo floats to provide a global estimate of the spatial and temporal variability of the GM model’s spectral parameters. For spectral slopes and wavenumber scales, the highest variability and the strongest deviation from the model’s canonical parameters are observed in the North Atlantic, the northwest Pacific, and the Southern Ocean. Internal wave energy levels in the upper ocean are well represented by the GM model value equatorward of approximately 50°, while they are up to two orders of magnitude lower poleward of this latitude. The use of variable spectral parameters in the energy level calculation hides the seasonal cycle in the northwest Pacific that was previously observed for constant parameters. The global estimates of how the GM model’s spectral parameters vary in space and time are hence expected to add relevant detail to various studies on oceanic internal gravity waves, deepening the understanding of their energetics and improving parameterizations of the mixing they induce.

Coupling of surface and internal gravity waves: a mode coupling model

1976 ◽  
Vol 77 (1) ◽  
pp. 185-208 ◽  
Author(s):  
Kenneth M. Watson ◽  
Bruce J. West ◽  
Bruce I. Cohen
Keyword(s):  
Energy Transfer ◽  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Wave Field ◽  
Internal Waves ◽  
Wave Spectrum ◽  
Coupled Model ◽  
Internal Gravity Waves ◽  
Growth Time

A surface-wave/internal-wave mode coupled model is constructed to describe the energy transfer from a linear surface wave field on the ocean to a linear internal wave field. Expressed in terms of action-angle variables the dynamic equations have a particularly useful form and are solved both numerically and in some analytic approximations. The growth time for internal waves generated by the resonant interaction of surface waves is calculated for an equilibrium spectrum of surface waves and for both the Garrett-Munk and two-layer models of the undersea environment. We find energy transfer rates as a function of undersea parameters which are much faster than those based on the constant Brunt-ViiisSila model used by Kenyon (1968) and which are consistent with the experiments of Joyce (1974). The modulation of the surface-wave spectrum by internal waves is also calculated, yielding a ‘mottled’ appearance of the ocean surface similar to that observed in photographs taken from an ERTS1 satellite (Ape1 et al. 1975b).

Global Abyssal Mixing Inferred from Lowered ADCP Shear and CTD Strain Profiles

2006 ◽  
Vol 36 (8) ◽  
pp. 1553-1576 ◽  
Author(s):  
Eric Kunze ◽  
Eric Firing ◽  
Julia M. Hummon ◽  
Teresa K. Chereskin ◽  
Andreas M. Thurnherr
Keyword(s):  
Internal Wave ◽  
Wave Spectrum ◽  
Wave Interaction ◽  
Deep Ocean ◽  
Eddy Diffusivity ◽  
Small Scale ◽  
Tidal Dissipation ◽  
Turbulent Dissipation ◽  
Active Turbulence ◽  
Parametric Subharmonic Instability

Abstract Internal wave–wave interaction theories and observations support a parameterization for the turbulent dissipation rate ɛ and eddy diffusivity K that depends on internal wave shear 〈Vz2〉 and strain 〈ξz2〉 variances. Its latest incarnation is applied to about 3500 lowered ADCP/CTD profiles from the Indian, Pacific, North Atlantic, and Southern Oceans. Inferred diffusivities K are functions of latitude and depth, ranging from 0.03 × 10−4 m2 s−1 within 2° of the equator to (0.4–0.5) × 10−4 m2 s−1 at 50°–70°. Diffusivities K also increase with depth in tropical and subtropical waters. Diffusivities below 4500-m depth exhibit a peak of 0.7 × 10−4 m2 s−1 between 20° and 30°, latitudes where semidiurnal parametric subharmonic instability is expected to be active. Turbulence is highly heterogeneous. Though the bulk of the vertically integrated dissipation ∫ɛ is contributed from the main pycnocline, hotspots in ∫ɛ show some correlation with small-scale bottom roughness and near-bottom flow at sites where strong surface tidal dissipation resulting from tide–topography interactions has been implicated. Average vertically integrated dissipation rates are 1.0 mW m−2, lying closer to the 0.8 mW m−2 expected for a canonical (Garrett and Munk) internal wave spectrum than the global-averaged deep-ocean surface tide loss of 3.3 mW m−2.

Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean

1976 ◽  
Vol 74 (2) ◽  
pp. 375-399 ◽  
Author(s):  
Dirk J. Olbers
Keyword(s):  
Energy Transfer ◽  
Energy Balance ◽  
Internal Wave ◽  
Wave Field ◽  
Wave Spectrum ◽  
Fluid Motion ◽  
Deep Ocean ◽  
Nonlinear Interactions ◽  
Nonlinear Energy Transfer ◽  
Spectral Models

The source function describing the energy transfer between the components of the internal wave spectrum due to nonlinear interactions is derived from the Lagrangian of the fluid motion and evaluated numerically for the spectral models of Garrett & Munk (1972a, 1975). The characteristic time scales of the transfer are found to be typically of the order of some days, so that nonlinear interactions will play an important role in the energy balance of the wave field. Thus implications of the nonlinear transfer within the spectrum for generation and dissipation processes are considered.

Internal Wave Generation by a Combination of Tidal and Steady Currents

2021 ◽  
Author(s):  
Xiaolin Bai ◽  
Kevin Lamb ◽  
José da Silva
Keyword(s):  
Internal Wave ◽  
Wave Generation ◽  
Satellite Observations ◽  
Internal Tides ◽  
Small Scale ◽  
Western Boundary ◽  
Boundary Current ◽  
Reanalysis Dataset ◽  
Amazon Shelf ◽  
Internal Wave Generation

<p>In the presence of topography, two main contributors for internal wave energy are tide-topography interaction transferring energy from the barotropic tide to internal tides, and lee wave generation when geostrophic currents or eddying abyssal flows interact with topography. In the past few decades, many studies considered the respective contribution of the oscillating flows or steady background flows, but few investigations have considered both.  </p><p>In this talk, we consider the joint effects of tidal and steady currents to investigate internal wave generation and propagation on the Amazon shelf, a hotspot for internal solitary wave (ISW) generation. The Amazon Shelf is off the mouth of the Amazon River in the southwest tropical Atlantic Ocean, affected by strong tidal constituents over complex bottom bathymetry and a strong western boundary current, the North Brazilian Current (NBC). Both satellite observations and numerical modelling are used in this study. Satellite observations provide a clear visualization of the wave characteristics, such as temporal and spatial distributions, propagating direction and its relation to background currents. Based on parameters from satellite observations and reanalysis dataset, we set up a model to numerically investigate the dynamics of the ISW generation. We demonstrate that the small-scale topography contributes to a rich generation of along-shelf propagating ISW, which significantly contribute to the ocean mixing and potentially cause sediment resuspension. Moreover, the ISW-induced currents also contribute to the sea surface wave breaking as observed by satellite measurements. In addition, statistics based on a decade of satellite images and numerical investigations on seasonal variations of the ISWs and the NBC improve our understanding of the generation and evolution of these nonlinear internal waves in the presence of background currents.</p>

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