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.

scholarly journals Eikonal Calculations for Energy Transfer in the Deep-Ocean Internal Wave Field near Mixing Hotspots

2017 ◽  
Vol 47 (1) ◽  
pp. 199-210 ◽  
Author(s):  
Takashi Ijichi ◽  
Toshiyuki Hibiya
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Wave Field ◽  
Vertical Velocity ◽  
Deep Ocean ◽  
Wave Spectra ◽  
Scale Separation ◽  
Transfer Rates ◽  
Calculated Energy ◽  
Internal Wave Field

AbstractIn the proximity of mixing hotspots in the deep ocean, the observed internal wave spectra are usually distorted from the Garrett–Munk (GM) spectrum and are characterized by the high energy level E as well as a shear–strain ratio Rω quite different from that of the GM spectrum. On the basis of the eikonal theoretical model, Ijichi and Hibiya (IH) recently proposed the revised finescale parameterization of turbulent dissipation rates in the distorted internal wave field, although the vertical velocity associated with background internal waves and the strict WKB scale separation, for example, were not taken into account. To see the effects of such simplifying assumptions on the revised parameterization, this study carries out a series of eikonal calculations for energy transfer through various internal wave spectra distorted from the GM. Although the background vertical velocity and the strict WKB scale separation somewhat affect the calculated energy transfer rates, their parameter dependence is confirmed as expected; the calculated energy transfer rates ε follow the basic scaling ε ∝ E2N2f with the local buoyancy frequency N and the local inertial frequency f and exhibit strong Rω dependence quite similar to that predicted by IH.

scholarly journals Nonlinear energy transfer to short gravity waves in the presence of long waves

1995 ◽  
Vol 289 ◽  
pp. 199-226 ◽  
Author(s):  
H. S. Ölmez ◽  
J. H. Milgram
Keyword(s):  
Energy Transfer ◽  
Gravity Waves ◽  
Wave Spectrum ◽  
Nonlinear Interactions ◽  
Physical Reason ◽  
Transfer Rates ◽  
Nonlinear Energy Transfer ◽  
Long Wave ◽  
Direct Numerical Method ◽  
Nonlinear Energy

Existing theories for calculating the energy transfer rates to gravity waves due to resonant nonlinear interactions among wave components whose lengths are long in comparison to wave elevations have been verified experimentally and are well accepted. There is uncertainty, however, about prediction of energy transfer rates within a set of waves having short to moderate lengths when these are present simultaneously with a long wave whose amplitude is not small in comparison to the short wavelengths. Here we implement both a direct numerical method that avoids small-amplitude approximations and a spectral method which includes perturbations of high order. These are applied to an interacting set of short- to intermediate-length waves with and without the presence of a large long wave. The same cases are also studied experimentally. Experimentally and numerical results are in reasonable agreement with the finding that the long wave does influence the energy transfer rates. The physical reason for this is identified and the implications for computations of energy transfer to short waves in a wave spectrum are discussed.

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).

scholarly journals Estimates of wind power and radiative near-inertial internal wave flux

2020 ◽  
Vol 70 (11) ◽  
pp. 1357-1376
Author(s):  
Georg S. Voelker ◽  
Dirk Olbers ◽  
Maren Walter ◽  
Christian Mertens ◽  
Paul G. Myers
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Wind Power ◽  
Mixed Layer ◽  
North Atlantic ◽  
Mixed Layer Depth ◽  
Deep Ocean ◽  
Wave Radiation ◽  
Buoyancy Frequency ◽  
The North

Abstract Energy transfer mechanisms between the atmosphere and the deep ocean have been studied for many years. Their importance to the ocean’s energy balance and possible implications on mixing are widely accepted. The slab model by Pollard (Deep-Sea Res Oceanogr Abstr 17(4):795–812, 1970) is a well-established simulation of near-inertial motion and energy inferred through wind-ocean interaction. Such a model is set up with hourly wind forcing from the NCEP-CFSR reanalysis that allows computations up to high latitudes without loss of resonance. Augmenting the one-dimensional model with the horizontal divergence of the near-inertial current field leads to direct estimates of energy transfer spectra of internal wave radiation from the mixed layer base into the ocean interior. Calculations using this hybrid model are carried out for the North Atlantic during the years 1989 and 1996, which are associated with positive and negative North Atlantic Oscillation index, respectively. Results indicate a range of meridional regimes with distinct energy transfer ratios. These are interpreted in terms of the mixed layer depth, the buoyancy frequency at the mixed layer base, and the wind field structure. The average ratio of radiated energy fluxes from the mixed layer to near-inertial wind power for both years is approximately 12%. The dependence on the wind structure is supported by simulations of idealized wind stress fronts with variable width and translation speeds.

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