scholarly journals Downscale energy fluxes in scale-invariant oceanic internal wave turbulence

2021 ◽  
Vol 915 ◽  
Author(s):  
Giovanni Dematteis ◽  
Yuri V. Lvov
Keyword(s):  
Internal Wave ◽  
Wave Turbulence ◽  
Energy Fluxes ◽  
Scale Invariant ◽  
Oceanic Internal Wave

Abstract

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.

scholarly journals Vertical mixing and internal wave energy fluxes in a sill fjord

2016 ◽  
Vol 159 ◽  
pp. 15-32 ◽  
Author(s):  
André Staalstrøm ◽  
Lars Petter Røed
Keyword(s):  
Internal Wave ◽  
Wave Energy ◽  
Vertical Mixing ◽  
Energy Fluxes

scholarly journals Internal wave turbulence at a biologically rich Mid-Atlantic seamount

PLoS ONE ◽  
2017 ◽  
Vol 12 (12) ◽  
pp. e0189720 ◽  
Author(s):  
Hans van Haren ◽  
Ulrike Hanz ◽  
Henko de Stigter ◽  
Furu Mienis ◽  
Gerard Duineveld
Keyword(s):  
Internal Wave ◽  
Wave Turbulence

scholarly journals Bispectral Analysis of Energy Transfer within the Two-Dimensional Oceanic Internal Wave Field

2005 ◽  
Vol 35 (11) ◽  
pp. 2104-2109 ◽  
Author(s):  
Naoki Furuichi ◽  
Toshiyuki Hibiya ◽  
Yoshihiro Niwa
Keyword(s):  
Internal Wave ◽  
Wave Field ◽  
Internal Waves ◽  
Internal Tide ◽  
Energy Cascade ◽  
Minor Role ◽  
Two Dimensional ◽  
Bispectral Analysis ◽  
Internal Wave Field ◽  
Oceanic Internal Wave

Abstract Bispectral analysis of the numerically reproduced spectral responses of the two-dimensional oceanic internal wave field to the incidence of the low-mode semidiurnal internal tide is performed. At latitudes just equatorward of 30°, the low-mode semidiurnal internal tide dominantly interacts with two high-vertical-wavenumber diurnal (near inertial) internal waves, forming resonant triads of parametric subharmonic instability (PSI) type. As the high-vertical-wavenumber near-inertial energy level is raised by this interaction, the energy cascade to small horizontal and vertical scales is enhanced. Bispectral analysis thus indicates that energy in the low-mode semidiurnal internal tide is not directly transferred to small scales but via the development of high-vertical-wavenumber near-inertial current shear. In contrast, no noticeable energy cascade to high vertical wavenumbers is recognized in the bispectra poleward of ∼30° as well as equatorward of ∼25°. A new finding is that, although PSI is possible equatorward of ∼30°, the efficiency drops sharply as the latitude falls below ∼25°. At all latitudes, another resonant interaction suggestive of induced diffusion is found to occur between the low-mode semidiurnal internal tide and two high-frequency internal waves, although bispectral analysis shows that this interaction plays only a minor role in cascading the low-mode semidiurnal internal tide energy.

scholarly journals Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

2008 ◽  
Vol 5 (4) ◽  
pp. 545-580
Author(s):  
H. Z. Baumert ◽  
H. Peters
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Tidal Flow ◽  
Wave Turbulence ◽  
Mean Flow ◽  
Turbulent Length Scale ◽  
Turbulent Dissipation ◽  
New Model ◽  
Turbulence Transition ◽  
Ozmidov Scale

Abstract. A new two-equation, closure-like turbulence model for stably stratified flows is introduced which uses the turbulent kinetic energy (K) and the turbulent enstrophy (Ω) as primary variables. It accounts for mean shear – and internal wave-driven mixing in the two limits of mean shear and no waves and waves but no mean shear, respectively. The traditional TKE balance is augmented by an explicit energy transfer from internal waves to turbulence. A modification of the Ω-equation accounts for the effect of the waves on the turbulence time and space scales. The latter is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean-flow shear when turbulence is produced exclusively by internal waves. The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000). At small energy density E of the internal wave field, the turbulent dissipation rate (ε) scales like ε~E2. This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E1. This is observed, for example, in the swift tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.

The temporal variability of near-inertial internal waves in an internal tide beam

2021 ◽  
Author(s):  
Jonas Löb ◽  
Monika Rhein
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Temporal Variability ◽  
Internal Tide ◽  
Internal Tides ◽  
Inertial Waves ◽  
Energy Fluxes ◽  
Wind Event ◽  
Mode 2 ◽  
Inertial Energy

<p>Low mode internal waves in the stratified ocean are generated by the interaction between barotropic tides and seafloor topography and by the wind field in the near-inertial range. They are crucial for interior mixing and for the oceanic energy pathways, since they carry a large portion of the energy of the entire internal wave field. Long-term observations of energy fluxes of internal waves are sparse. The aim of this work is to study the temporal variability of wind generated low mode near-inertial internal waves inside an internal tide beam emanating from seamounts south of the Azores. For this, 20 months of consecutive mooring observations are used to calculate the mode 1 and mode 2 near-inertial energy fluxes as well as kinetic and potential energies. The gathered time series of near-inertial internal wave energy flux is not steady due to its intermittent forcing and is neither dominated by either mode 1 or mode 2. It shows a peak induced by a distinct strong wind event which is directly linked to wind-power input into the mixed layer north-east of the mooring location, and allows a comparison between the wind event and a background state. Furthermore, indications of non-linear interactions of the near-inertial waves with the internal tides in the form of resonant triad interaction and non-linear self-interaction have been found. This study provides new insights on the relative importance of single wind events and reinforces the assumption of a global non-uniform distribution of near-inertial energy with emphasis in regions where these events occur often and regularly. It furthermore displays its importance to be adequately incorporated into ocean general circulation models and in generating ocean mixing estimates by near-inertial waves as a similarly important component next to the internal tides.</p>

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