scholarly journals Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Theory

2010 ◽  
Vol 40 (5) ◽  
pp. 1055-1074 ◽  
Author(s):  
Maxim Nikurashin ◽  
Raffaele Ferrari
Keyword(s):  
Internal Waves ◽  
Bottom Topography ◽  
Drake Passage ◽  
Wave Radiation ◽  
Small Scale ◽  
Ocean Bottom ◽  
Inertial Oscillations ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Internal Wave Generation

Abstract Observations and inverse models suggest that small-scale turbulent mixing is enhanced in the Southern Ocean in regions above rough topography. The enhancement extends O(1) km above the topography, suggesting that mixing is supported by the breaking of gravity waves radiated from the ocean bottom. In this study, it is shown that the observed mixing rates can be sustained by internal waves generated by geostrophic motions flowing over bottom topography. Weakly nonlinear theory is used to describe the internal wave generation and the feedback of the waves on the zonally averaged flow. Vigorous inertial oscillations are driven at the ocean bottom by waves generated at steep topography. The wave radiation and dissipation at equilibrium is therefore the result of both geostrophic flow and inertial oscillations differing substantially from the classical lee-wave problem. The theoretical predictions are tested versus two-dimensional high-resolution numerical simulations with parameters representative of Drake Passage. This work suggests that mixing in Drake Passage can be supported by geostrophic motions impinging on rough topography rather than by barotropic tidal motions, as is commonly assumed.

Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Application to the Southern Ocean

2010 ◽  
Vol 40 (9) ◽  
pp. 2025-2042 ◽  
Author(s):  
Maxim Nikurashin ◽  
Raffaele Ferrari
Keyword(s):  
Southern Ocean ◽  
Internal Wave ◽  
Internal Waves ◽  
Acoustic Doppler Current Profiler ◽  
Drake Passage ◽  
Internal Tides ◽  
Wave Radiation ◽  
Small Scale ◽  
Region Theory ◽  
Abyssal Mixing

Abstract Recent estimates from observations and inverse models indicate that turbulent mixing associated with internal wave breaking is enhanced above rough topography in the Southern Ocean. In most regions of the ocean, abyssal mixing has been primarily associated with radiation and breaking of internal tides. In this study, it is shown that abyssal mixing in the Southern Ocean can be sustained by internal waves generated by geostrophic motions that dominate abyssal flows in this region. Theory and fully nonlinear numerical simulations are used to estimate the internal wave radiation and dissipation from lowered acoustic Doppler current profiler (LADCP), CTD, and topography data from two regions in the Southern Ocean: Drake Passage and the southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation previously inferred from finescale measurements in the region, suggesting that it is one of the primary drivers of abyssal mixing in the Southern Ocean.

Bottom pressure induced by the long nonlinear internal waves

2020 ◽  
Author(s):  
Tatiana Talipova ◽  
Efim Pelinovsky
Keyword(s):  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Pressure Fluctuations ◽  
Pressure Sensors ◽  
Storm Surges ◽  
Andaman Sea ◽  
Bottom Pressure ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

<p>The bottom pressure sensors are widely used for the purpose of registration of the sea surface movement. They are particularly efficient to measure long surface waves like tsunami and storm surges. The bottom pressure gauges can be also used to record internal waves in coastal waters. For instance, the perspective system of the internal wave warning in the Andaman Sea is based on the bottom pressure variation data. Here we investigate theoretically the relation between long internal waves and induced bottom pressure fluctuations. Firstly, the linear relations are derived for the multi-modal internal wave field. Then, the weakly nonlinear theory is developed. Structurally, the obtained formula for the bottom pressure induced by the long internal waves is similar to those known for the surface waves within the Green-Naghdi system framework, but the coefficients are determined through the integrals for the water density stratification and vertical mode wave functions. In particular, the bottom pressure variations are calculated for solitary waves in two- and three-layer flows described by the Gardner equation.<br>The research is supported by RFBR grants No. 19-55-15005 and 19-05-00161.</p>

Weakly nonlinear internal waves in a two-fluid system

1996 ◽  
Vol 313 ◽  
pp. 83-103 ◽  
Author(s):  
Wooyoung Choi ◽  
Roberto Camassa
Keyword(s):  
Internal Waves ◽  
Numerical Solutions ◽  
Lower Layer ◽  
Bottom Topography ◽  
Ocean Dynamics ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Characteristic Wavelength ◽  
Upper Boundary

We derive general evolution equations for two-dimensional weakly nonlinear waves at the free surface in a system of two fluids of different densities. The thickness of the upper fluid layer is assumed to be small compared with the characteristic wavelength, but no restrictions are imposed on the thickness of the lower layer. We consider the case of a free upper boundary for its relevance in applications to ocean dynamics problems and the case of a non-uniform rigid upper boundary for applications to atmospheric problems. For the special case of shallow water, the new set of equations reduces to the Boussinesq equations for two-dimensional internal waves, whilst, for great and infinite lower-layer depth, we can recover the well-known Intermediate Long Wave and Benjamin–Ono models, respectively, for one-dimensional uni-directional wave propagation. Some numerical solutions of the model for one-dimensional waves in deep water are presented and compared with the known solutions of the uni-directional model. Finally, the effects of finite-amplitude slowly varying bottom topography are included in a model appropriate to the situation when the dependence on one of the horizontal coordinates is weak.

scholarly journals Solitary Waves and Undular Bores in a Mesosphere Duct

2015 ◽  
Vol 72 (11) ◽  
pp. 4412-4422 ◽  
Author(s):  
Roger Grimshaw ◽  
Dave Broutman ◽  
Brian Laughman ◽  
Stephen D. Eckermann
Keyword(s):  
Solitary Waves ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Solitary Wave Solution ◽  
Internal Gravity Wave ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Wave Radiation ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

Abstract Mesospheric bores have been observed and measured in the mesopause region near 100-km altitude, where they propagate horizontally along a duct of relatively strong density stratification. Here, a weakly nonlinear theory is developed for the description of these mesospheric bores. It extends previous theories by allowing internal gravity wave radiation from the duct into the surrounding stratified regions, which are formally assumed to be weakly stratified. The radiation away from the duct is expected to be important for bore energetics. The theory is compared with a numerical simulation of the full Navier–Stokes equations in the Boussinesq approximation. Two initial conditions are considered. The first is a solitary wave solution that would propagate without change of form if the region outside the duct were unstratified. The second is a sinusoid that evolves into an undular bore. The main conclusion is that, while solitary waves and undular bores decay by radiation from the duct, they can survive as significant structures over sufficiently long periods (~100 min) to be observable.

scholarly journals Downstream Propagation and Remote Dissipation of Internal Waves in the Southern Ocean

2019 ◽  
Vol 49 (7) ◽  
pp. 1873-1887 ◽  
Author(s):  
Kaiwen Zheng ◽  
Maxim Nikurashin
Keyword(s):  
Energy Dissipation ◽  
Southern Ocean ◽  
Internal Wave ◽  
Linear Theory ◽  
Internal Waves ◽  
Turbulent Energy ◽  
Wave Radiation ◽  
Small Scale ◽  
Length Scale ◽  
Geostrophic Flows

AbstractRecent microstructure observations in the Southern Ocean report enhanced internal gravity waves and turbulence in the frontal regions of the Antarctic Circumpolar Current extending a kilometer above rough bottom topography. Idealized numerical simulations and linear theory show that geostrophic flows impinging on rough small-scale topography are very effective generators of internal waves and estimate vigorous wave radiation, breaking, and turbulence within a kilometer above bottom. However, both idealized simulations and linear theory assume periodic and spatially uniform topography and tend to overestimate the observed levels of turbulent energy dissipation locally at the generation sites. In this study, we explore the downstream evolution and remote dissipation of internal waves generated by geostrophic flows using a series of numerical, realistic topography simulations and parameters typical of Drake Passage. The results show that significant levels of internal wave kinetic energy and energy dissipation are present downstream of the rough topography, internal wave generation site. About 30%–40% of the energy dissipation occurs locally over the rough topography region, where internal waves are generated. The rest of the energy dissipation takes place remotely and decays downstream of the generation site with an e-folding length scale of up to 20–30 km. The model we use is two-dimensional with enhanced viscosity coefficients, and hence it can result in the underestimation of the remote wave dissipation and its decay length scale. The implications of our results for turbulent energy dissipation observations and mixing parameterizations are discussed.

scholarly journals Deep-sea turbulence evolution observed by multiple closely spaced instruments

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chu-Fang Yang ◽  
Wu-Cheng Chi ◽  
Hans van Haren
Keyword(s):  
Kinetic Energy ◽  
Internal Waves ◽  
Deep Sea ◽  
Large Scale ◽  
Time Derivative ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Ocean Bottom ◽  
Seafloor Topography

AbstractTurbulent mixing in the deep ocean is not well understood. The breaking of internal waves on sloped seafloor topography can generate deep-sea turbulence. However, it is difficult to measure turbulence comprehensively due to its multi-scale processes, in addition to flow–flow and flow–topography interactions. Dense, high-resolution spatiotemporal coverage of observations may help shed light on turbulence evolution. Here, we present turbulence observations from four broadband ocean bottom seismometers (OBSs) and a 200-m vertical thermistor string (T-string) in a footprint of 1 × 1 km to characterize turbulence induced by internal waves at a depth of 3000 m on a Pacific continental slope. Correlating the OBS-calculated time derivative of kinetic energy and the T-string-calculated turbulent kinetic energy dissipation rate, we propose that the OBS-detected signals were induced by near-seafloor turbulence. Strong disturbances were detected during a typhoon period, suggesting large-scale inertial waves breaking with upslope transport speeds of 0.2–0.5 m s−1. Disturbances were mostly excited on the downslope side of the array where the internal waves from the Pacific Ocean broke initially and the turbulence oscillated between < 1 km small-scale ridges. Such small-scale topography caused varying turbulence-induced signals due to localized waves breaking. Arrayed OBSs can provide complementary observations to characterize deep-sea turbulence.

scholarly journals Eddy-Induced Modulation of Turbulent Dissipation over Rough Topography in the Southern Ocean

2013 ◽  
Vol 43 (11) ◽  
pp. 2288-2308 ◽  
Author(s):  
J. Alexander Brearley ◽  
Katy L. Sheen ◽  
Alberto C. Naveira Garabato ◽  
David A. Smeed ◽  
Stephanie Waterman
Keyword(s):  
Southern Ocean ◽  
Internal Wave ◽  
Ocean Circulation ◽  
Wave Energy ◽  
Bottom Topography ◽  
Temporal Correlation ◽  
Drake Passage ◽  
Wave Radiation ◽  
Bottom Current ◽  
Turbulent Dissipation

Abstract Mesoscale eddies are universal features of the ocean circulation, yet the processes by which their energy is dissipated remain poorly understood. One hypothesis argues that the interaction of strong geostrophic flows with rough bottom topography effects an energy transfer between eddies and internal waves, with the breaking of these waves causing locally elevated dissipation focused near the sea floor. This study uses hydrographic and velocity data from a 1-yr mooring cluster deployment in the Southern Ocean to test this hypothesis. The moorings were located over a small (~10 km) topographic obstacle to the east of Drake Passage in a region of high eddy kinetic energy, and one was equipped with an ADCP at 2800-m depth from which internal wave shear variance and dissipation rates were calculated. Examination of the ADCP time series revealed a predominance of upward-propagating internal wave energy and a significant correlation (r = 0.45) between shear variance levels and subinertial near-bottom current speeds. Periods of strong near-bottom flow coincided with increased convergence of eddy-induced interfacial form stress in the bottom 1500 m. Predictions of internal wave energy radiation were made from theory using measured near-bottom current speeds, and the mean value of wave radiation (5.3 mW m−2) was sufficient to support the dissipated power calculated from the ADCP. A significant temporal correlation was also observed between radiated and dissipated power. Given the ubiquity of strong eddy flows and rough topography in the Southern Ocean, the transfer from eddy to internal wave energy is likely to be an important term in closing the ocean energy budget.

scholarly journals Strong Modulation of Short Wind Waves and Ka-Band Radar Return Due to Internal Waves in the Presence of Surface Films. Theory and Experiment

2021 ◽  
Vol 13 (13) ◽  
pp. 2462
Author(s):  
Stanislav A. Ermakov ◽  
Irina A. Sergievskaya ◽  
Ivan A. Kapustin
Keyword(s):  
Phase Velocity ◽  
Internal Waves ◽  
Wind Waves ◽  
Strong Increase ◽  
Small Scale ◽  
Surface Films ◽  
Ka Band ◽  
Steady Current ◽  
Backscatter Modulation ◽  
Resonance Surface

Strong variability of Ka-band radar backscattering from short wind waves on the surface of water covered with surfactant films in the presence of internal waves (IW) was studied in wave tank experiments. It has been demonstrated that modulation of Ka-band radar return due to IW strongly depends on the relationship between the phase velocity of IW and the velocity of drifting surfactant films. An effect of the strong increase in surfactant concentration was revealed in convergent zones, associated with IW orbital velocities in the presence of a “resonance” surface steady current, the velocity of which was close to the IW phase velocity. A phenomenological model of suppression and modulations in the spectrum of small-scale wind waves due to films and IW was elaborated. It has been shown that backscatter modulation could not be explained by the modulation of free (linear) millimeter-scale Bragg waves, but was associated with the modulation of bound (parasitic) capillary ripples generated by longer, cm–dm-scale waves—a “cascade” modulation mechanism. Theoretical analysis based on the developed model was found to be consistent with experiments. Field observations which qualitatively illustrated the effect of strong modulation of Ka-band radar backscatter due to IW in the presence of resonance drift of surfactant films are presented.

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