Mixed Rossby–Gravity Wave–Wave Interactions

AbstractMixed triad wave–wave interactions between Rossby and gravity waves are analytically derived using the kinetic equation for models of different complexity. Two examples are considered: initially vanishing linear gravity wave energy in the presence of a fully developed Rossby wave field and the reversed case of initially vanishing linear Rossby wave energy in the presence of a realistic gravity wave field. The kinetic equation in both cases is numerically evaluated, for which energy is conserved within numerical precision. The results are validated by a corresponding ensemble of numerical model simulations supporting the validity of the weak-interaction assumption necessary to derive the kinetic equation. Since they are generated by nonresonant interactions only, the energy transfers toward the respective linear wave mode with vanishing energy are small in both cases. The total generation of energy of the linear gravity wave mode in the first case scales to leading order as the square of the Rossby number in agreement with independent estimates from laboratory experiments, although a part of the linear gravity wave mode is slaved to the Rossby wave mode without wavelike temporal behavior.

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Non-linear gravity wave interactions

Journal of Fluid Mechanics ◽

10.1017/s0022112062001469 ◽

1962 ◽

Vol 14 (04) ◽

pp. 577 ◽

Cited By ~ 132

Author(s):

D. J. Benney

Keyword(s):

Gravity Wave ◽

Wave Interactions ◽

Non Linear ◽

Linear Gravity

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Gravity wave focusing on the Antarctic polar vortex using Gaussian-beam approximation in horizontally non-uniform flows

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-21-0066.1 ◽

2021 ◽

Author(s):

Claudio Rodas ◽

Manuel Pulido

Keyword(s):

Gaussian Beam ◽

Wave Field ◽

Gravity Wave ◽

Polar Vortex ◽

Linear Wave ◽

Beam Approximation ◽

Nonuniform Flows ◽

Antarctic Polar Vortex ◽

Ray Path ◽

The Antarctic

AbstractRay path theory is an asymptotic approximation to the wave equations. It represents efficiently gravity wave propagation in non-uniform background flows so that it is useful to develop schemes of gravity wave effects in general circulation models. One of the main limitations of ray path theory to be applied in realistic flows is in caustics where rays intersect and the ray solution has a singularity. Gaussian beam approximation is a higher-order asymptotic ray path approximation which considers neighboring rays to the central one and thus it is free of the singularities produced by caustics. A previous implementation of the Gaussian beam approximation assumes a horizontally uniform flow. In this work, we extend the Gaussian beam approximation to include horizontally nonuniform flows. Under these conditions the wave packet can undergo horizontal wave refraction producing changes in the horizontal wavenumber, which affects the ray path as well as the ray tube cross-sectional area and so the wave amplitude via wave action conservation. As an evaluation of the Gaussian beam approximation in horizontally nonuniform flows a series of proof-of-concept experiments is conducted comparing the approximation with the linear wave solution given by the WRF model. A very good agreement in the wave field is found. An evaluation is conducted with conditions that mimic the Antarctic polar vortex and the orography of the Southern flank of South America. The Gaussian beam approximation nicely reproduces the expected asymmetry of the wave field. A much stronger disturbance propagates towards higher latitudes (polar vortex) compared to lower latitudes.

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The Performance of a Spectral Wave Model at Predicting Wave Farm Impacts

Energies ◽

10.3390/en13215728 ◽

2020 ◽

Vol 13 (21) ◽

pp. 5728

Author(s):

J. Cameron McNatt ◽

Aaron Porter ◽

Christopher Chartrand ◽

Jesse Roberts

Keyword(s):

Wave Field ◽

Wave Energy ◽

Wave Interaction ◽

Wave Model ◽

Skill Score ◽

Coastal Protection ◽

Linear Wave ◽

Ocean Wave Energy ◽

Wave Farm ◽

The Impact

For renewable ocean wave energy to support global energy demands, wave energy converters (WECs) will likely be deployed in large numbers (farms), which will necessarily change the nearshore environment. Wave farm induced changes can be both helpful (e.g., beneficial habitat and coastal protection) and potentially harmful (e.g., degraded habitat, recreational, and commercial use) to existing users of the coastal environment. It is essential to estimate this impact through modeling prior to the development of a farm, and to that end, many researchers have used spectral wave models, such as Simulating WAves Nearshore (SWAN), to assess wave farm impacts. However, the validity of the approaches used within SWAN have not been thoroughly verified or validated. Herein, a version of SWAN, called Sandia National Laboratories (SNL)-SWAN, which has a specialized WEC implementation, is verified by comparing its wave field outputs to those of linear wave interaction theory (LWIT), where LWIT is theoretically more appropriate for modeling wave-body interactions and wave field effects. The focus is on medium-sized arrays of 27 WECs, wave periods, and directional spreading representative of likely conditions, as well as the impact on the nearshore. A quantitative metric, the Mean Squared Skill Score, is used. Results show that the performance of SNL-SWAN as compared to LWIT is “Good” to “Excellent”.

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Observed Eddy–Internal Wave Interactions in the Southern Ocean

Journal of Physical Oceanography ◽

10.1175/jpo-d-20-0001.1 ◽

2020 ◽

Vol 50 (10) ◽

pp. 3043-3062

Author(s):

Jesse M. Cusack ◽

J. Alexander Brearley ◽

Alberto C. Naveira Garabato ◽

David A. Smeed ◽

Kurt L. Polzin ◽

...

Keyword(s):

Energy Transfer ◽

Southern Ocean ◽

Internal Wave ◽

Wave Field ◽

Internal Waves ◽

Temporal Variability ◽

Mesoscale Eddy ◽

Linear Wave ◽

Wave Interactions ◽

Internal Wave Field

AbstractThe physical mechanisms that remove energy from the Southern Ocean’s vigorous mesoscale eddy field are not well understood. One proposed mechanism is direct energy transfer to the internal wave field in the ocean interior, via eddy-induced straining and shearing of preexisting internal waves. The magnitude, vertical structure, and temporal variability of the rate of energy transfer between eddies and internal waves is quantified from a 14-month deployment of a mooring cluster in the Scotia Sea. Velocity and buoyancy observations are decomposed into wave and eddy components, and the energy transfer is estimated using the Reynolds-averaged energy equation. We find that eddies gain energy from the internal wave field at a rate of −2.2 ± 0.6 mW m−2, integrated from the bottom to 566 m below the surface. This result can be decomposed into a positive (eddy to wave) component, equal to 0.2 ± 0.1 mW m−2, driven by horizontal straining of internal waves, and a negative (wave to eddy) component, equal to −2.5 ± 0.6 mW m−2, driven by vertical shearing of the wave spectrum. Temporal variability of the transfer rate is much greater than the mean value. Close to topography, large energy transfers are associated with low-frequency buoyancy fluxes, the underpinning physics of which do not conform to linear wave dynamics and are thereby in need of further research. Our work suggests that eddy–internal wave interactions may play a significant role in the energy balance of the Southern Ocean mesoscale eddy and internal wave fields.

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Towards a Global Spectral Energy Budget for Internal Gravity Waves in the Ocean

Journal of Physical Oceanography ◽

10.1175/jpo-d-19-0022.1 ◽

2020 ◽

Vol 50 (4) ◽

pp. 935-944 ◽

Cited By ~ 1

Author(s):

Carsten Eden ◽

Friederike Pollmann ◽

Dirk Olbers

Keyword(s):

Kinetic Equation ◽

Gravity Waves ◽

Energy Budget ◽

Wave Energy ◽

Internal Gravity Waves ◽

Rate Of Change ◽

Spectral Energy ◽

Spectral Space ◽

Wave Interactions ◽

Energy Transfers

AbstractEnergy transfers by internal gravity wave–wave interactions in spectral space are diagnosed from numerical model simulations initialized with realizations of the Garrett–Munk spectrum in physical space and compared with the predictions of the so-called scattering integral or kinetic equation. Averaging the random phase of the initialization, the energy transfers by wave–wave interactions in the model agree well with the predictions of the kinetic equation for certain ranges of frequency and wavenumbers. This validation allows now, in principle, the use of the energy transfers predicted by the kinetic equation to design a global spectral energy budget for internal gravity waves in the ocean where divergences of energy transports in physical and spectral space balance forcing, dissipation, the energy transfers by the wave–wave interactions, or the rate of change of the spectral wave energy. First global estimates show indeed accumulation of the wave energy in a range of latitude ϕ consistent with tidal waves at frequency ωT propagating toward the latitudinal window where 2 < ωT/f(ϕ) < 3, as predicted by the kinetic equation.

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Comparison of Numerical Methods for Modeling the Wave Field Effects Generated by Individual Wave Energy Converters and Multiple Converter Wave Farms

Journal of Marine Science and Engineering ◽

10.3390/jmse8030168 ◽

2020 ◽

Vol 8 (3) ◽

pp. 168 ◽

Cited By ~ 1

Author(s):

J. Cameron McNatt ◽

Aaron Porter ◽

Kelley Ruehl

Keyword(s):

Wave Field ◽

Wave Energy ◽

Numerical Study ◽

Near Field ◽

Linear Wave ◽

Power Curve ◽

Field Effects ◽

Wave Energy Converters ◽

Individual Wave ◽

Energy Converters

This numerical study compares the wave field generated by the spectral wave action balance code, SNL-SWAN, to the linear-wave boundary-element method (BEM) code, WAMIT. The objective of this study is to assess the performance of SNL-SWAN for modeling wave field effects produced by individual wave energy converters (WECs) and wave farms comprising multiple WECs by comparing results from SNL-SWAN with those produced by the BEM code WAMIT. BEM codes better model the physics of wave-body interactions and thus simulate a more accurate near-field wave field than spectral codes. In SNL-SWAN, the wave field’s energy extraction is modeled parametrically based on the WEC’s power curve. The comparison between SNL-SWAN and WAMIT is made over a range of incident wave conditions, including short-, medium-, and long-wavelength waves with various amounts of directional spreading, and for three WEC archetypes: a point absorber (PA), a pitching flap (PF) terminator, and a hinged raft (HR) attenuator. Individual WECs and wave farms of five WECs in various configuration were studied with qualitative comparisons made of wave height and spectra at specific locations, and quantitative comparisons of the wave fields over circular arcs around the WECs as a function of radial distance. Results from this numerical study demonstrate that in the near-field, the difference between SNL-SWAN and WAMIT is relatively large (between 20% and 50%), but in the far-field from the array the differences are minimal (between 1% and 5%). The resultant wave field generated by the two different numerical approaches is highly dependent on parameters such as: directional wave spreading, wave reflection or scattering, and the WEC’s power curve.

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