scholarly journals Scattering of Low-Mode Internal Waves at Finite Isolated Topography

2014 ◽  
Vol 44 (1) ◽  
pp. 359-383 ◽  
Author(s):  
Sonya Legg
Keyword(s):  
Internal Wave ◽  
Froude Number ◽  
Internal Waves ◽  
Wave Breaking ◽  
Internal Tides ◽  
Relative Height ◽  
Incoming Wave ◽  
Topographic Slope ◽  
Height Increase ◽  
Incoming Energy

Abstract A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h0/H0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h0/H0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h0/H0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefore increases as both incoming wave Froude number and topographic height increase. At critical slopes, the dissipation is enhanced along the slope facing the incoming wave. In contrast, at subcritical slopes, dissipation is small until the wave amplitude is sufficiently enhanced by the shoaling topography to exceed the critical Froude number; then large dissipation extends all the way to the surface. The results are shown to generalize to variable stratification and different topographies, including axisymmetric seamounts. The regimes for low-mode internal wave breaking at isolated critical and subcritical topography identified by these simulations provide guidance for the parameterization of the mixing due to radiated internal tides.

Local versus volume-integrated turbulence and mixing in breaking internal waves on slopes

2017 ◽  
Vol 815 ◽  
pp. 169-198 ◽  
Author(s):  
Robert S. Arthur ◽  
Jeffrey R. Koseff ◽  
Oliver B. Fringer
Keyword(s):  
Froude Number ◽  
Internal Waves ◽  
Turbulent Mixing ◽  
Wave Breaking ◽  
Mixing Efficiency ◽  
Breaking Wave ◽  
Incoming Wave ◽  
Turbulent Dissipation ◽  
Efficiency Measures ◽  
Wave Properties

Using direct numerical simulations (DNS), we explore local and volume-integrated measures of turbulence and mixing in breaking internal waves on slopes. We consider eight breaking wave cases with a range of normalized pycnocline thicknesses $k\unicode[STIX]{x1D6FF}$, where $k$ is the horizontal wavenumber and $\unicode[STIX]{x1D6FF}$ is the pycnocline thickness, but with similar incoming wave properties. The energetics of wave breaking is quantified in terms of local turbulent dissipation and irreversible mixing using the method of Scotti & White (J. Fluid Mech., vol. 740, 2014, pp. 114–135). Local turbulent mixing efficiencies are calculated using the irreversible flux Richardson number $R_{f}^{\ast }$ and are found to be a function of the turbulent Froude number $Fr_{k}$. Volume-integrated measures of the turbulent mixing efficiency during wave breaking are also made, and are found to be functions of $k\unicode[STIX]{x1D6FF}$. The bulk turbulent mixing efficiency ranges from 0.25 to 0.37 and is maximized when $k\unicode[STIX]{x1D6FF}\approx 1$. In order to connect local and bulk mixing efficiency measures, the variation in the bulk turbulent mixing efficiency with $k\unicode[STIX]{x1D6FF}$ is related to the turbulent Froude number at which the maximum total mixing occurs over the course of the breaking event, $Fr_{k}^{max}$. We find that physically, $Fr_{k}^{max}$ is controlled by the vertical length scale of billows at the interface during wave breaking.

scholarly journals On Internal Waves Propagating across a Geostrophic Front

2019 ◽  
Vol 49 (5) ◽  
pp. 1229-1248 ◽  
Author(s):  
Qiang Li ◽  
Xianzhong Mao ◽  
John Huthnance ◽  
Shuqun Cai ◽  
Samuel Kelly
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
Horizontal Shear ◽  
Mixing Rate ◽  
Reflection And Transmission ◽  
Topographic Slope ◽  
Virtual Boundary ◽  
The Impact

AbstractReflection and transmission of normally incident internal waves propagating across a geostrophic front, like the Kuroshio or Gulf Stream, are investigated using a modified linear internal wave equation. A transformation from depth to buoyancy coordinates converts the equation to a canonical partial differential equation, sharing properties with conventional internal wave theory in the absence of a front. The equation type is determined by a parameter Δ, which is a function of horizontal and vertical gradients of buoyancy, the intrinsic frequency of the wave, and the effective inertial frequency, which incorporates the horizontal shear of background geostrophic flow. In the Northern Hemisphere, positive vorticity of the front may produce Δ ≤ 0, that is, a “forbidden zone,” in which wave solutions are not permitted. Thus, Δ = 0 is a virtual boundary that causes wave reflection and refraction, although waves may tunnel through forbidden zones that are weak or narrow. The slope of the surface and bottom boundaries in buoyancy coordinates (or the slope of the virtual boundary if a forbidden zone is present) determine wave reflection and transmission. The reflection coefficient for normally incident internal waves depends on rotation, isopycnal slope, topographic slope, and incident mode number. The scattering rate to high vertical modes allows a bulk estimate of the mixing rate, although the impact of internal wave-driven mixing on the geostrophic front is neglected.

scholarly journals Modeling and Analysis of Internal-Tide Generation and Beamlike Onshore Propagation in the Vicinity of Shelfbreak Canyons

2014 ◽  
Vol 44 (3) ◽  
pp. 834-849 ◽  
Author(s):  
Weifeng G. Zhang ◽  
Timothy F. Duda ◽  
Ilya A. Udovydchenkov
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Internal Tide ◽  
Propagation Model ◽  
Internal Tides ◽  
Wave Radiation ◽  
Beam Radiation ◽  
Control Simulation ◽  
Conversion Rates ◽  
The Cross

Abstract A hydrostatic numerical model with alongshore-uniform barotropic M2 tidal boundary forcing and idealized shelfbreak canyon bathymetries is used to study internal-tide generation and onshore propagation. A control simulation with Mid-Atlantic Bight representative bathymetry is supported by other simulations that serve to identify specific processes. The canyons and adjacent slopes are transcritical in steepness with respect to M2 internal wave characteristics. Although the various canyons are symmetrical in structure, barotropic-to-baroclinic energy conversion rates Cυ are typically asymmetrical within them. The resulting onshore-propagating internal waves are the strongest along beams in the horizontal plane, with the stronger beam in the control simulation lying on the side with higher Cυ. Analysis of the simulation results suggests that the cross-canyon asymmetrical Cυ distributions are caused by multiple-scattering effects on one canyon side slope, because the phase variation in the spatially distributed internal-tide sources, governed by variations in the orientation of the bathymetry gradient vector, allows resonant internal-tide generation. A less complex, semianalytical, modal internal wave propagation model with sources placed along the critical-slope locus (where the M2 internal wave characteristic is tangent to the seabed) and variable source phasing is used to diagnose the physics of the horizontal beams of onshore internal wave radiation. Model analysis explains how the cross-canyon phase and amplitude variations in the locally generated internal tides affect parameters of the internal-tide beams. Under the assumption that strong internal tides on continental shelves evolve to include nonlinear wave trains, the asymmetrical internal-tide generation and beam radiation effects may lead to nonlinear internal waves and enhanced mixing occurring preferentially on one side of shelfbreak canyons, in the absence of other influencing factors.

scholarly journals Strong Internal Waves Generated by the Interaction of the Kuroshio and Tides over a Shallow Ridge

2019 ◽  
Vol 49 (11) ◽  
pp. 2917-2934 ◽  
Author(s):  
Eiji Masunaga ◽  
Yusuke Uchiyama ◽  
Hidekatsu Yamazaki
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
High Frequency ◽  
Deep Ocean ◽  
Internal Tides ◽  
Navier Stokes ◽  
Wave Energy Flux ◽  
The Kuroshio

AbstractThe Kuroshio and tides significantly influence the oceanic environment off the Japanese mainland and promote mass/heat transport. However, the interaction between the Kuroshio and tides/internal waves has not been examined in previous works. To investigate this phenomenon, the two-dimensional high-resolution nonhydrostatic oceanic Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) model was employed. The results show that strong internal tides propagating upstream in the Kuroshio are generated at a near-critical internal Froude number (Fri = 0.91). The upstream internal wave energy flux reaches a magnitude of 12 kW m−1, which is approximately 3 times higher than that of internal waves without the Kuroshio. On the other hand, under supercritical conditions, the Kuroshio suppresses the internal wave energy flux. The interaction of internal tides and the Kuroshio also generates upstream propagating high-frequency internal waves and solitary wave packets. The high-frequency internal waves contribute to the increase in the total internal wave energy flux up to 40% at the near-critical Fri value. The results of this study suggest that the interaction of internal tides and the Kuroshio enhances the upstream propagating internal tides under the specified conditions (Fri ~ 1), which may lead to deep ocean mixing and transport at significant distances from the internal wave generation sites.

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>

PSI in the case of internal wave beam reflection at a uniform slope

2016 ◽  
Vol 789 ◽  
pp. 347-367 ◽  
Author(s):  
Vamsi K. Chalamalla ◽  
Sutanu Sarkar
Keyword(s):  
Internal Wave ◽  
Froude Number ◽  
Growth Rates ◽  
Wave Amplitude ◽  
Wave Beam ◽  
Small Scale ◽  
Finite Width ◽  
Incoming Wave ◽  
Weakly Nonlinear ◽  
Reflected Wave

Two-dimensional numerical simulations are performed to examine internal wave reflection at a sloping boundary. Owing to reflection, the reflected wave amplitude and wavenumber increase. At low values of the incoming wave amplitude, the reflected wave beam is linear and its properties agree well with linear inviscid theory. Linear theory overestimates the reflected wave Froude number, $Fr_{r}$, for higher values of incoming wave amplitude. Nonlinearity sets in with increasing value of incoming wave Froude number, $Fr_{i}$, leading to parametric subharmonic instability (PSI) of the reflected wave beam: two subharmonics emerge from the reflection region with frequencies $0.33{\it\Omega}$ and $0.67{\it\Omega}$ and wavenumbers that add up to those of the reflected wave. The amplification of Froude number due to reflection must be sufficiently large for PSI to occur implying that the off-criticality in wave angle cannot be too large. The simulations also show that, all other parameters being fixed, a threshold in beam amplitude is required for the onset of PSI in the reflected beam, consistent with results from a previous weakly-nonlinear asymptotic theory for a freely propagating finite-width beam. Growth rates of subharmonic modes at moderate reflected wave amplitude are in reasonable agreement with that theory. However, for $Fr_{r}>0.5$, small scale fluctuations becomes prominent and the subharmonic energy growth rates saturate in the simulations in contrast to the theoretical prediction. Increasing the incoming beam thickness (number of carrier wavelengths) increases the strength of PSI. Keeping the incoming Froude number constant and increasing the incoming Reynolds number by a factor of 50 does not have an effect on the unequal division of frequencies among the subharmonic modes that is found in the simulations.

Models of energy loss from internal waves breaking in the ocean

2017 ◽  
Vol 836 ◽  
pp. 72-116 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Exact Solution ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Breaking ◽  
Convective Instability ◽  
Helmholtz Instability ◽  
Turbulent Dissipation ◽  
The Waves ◽  
Data Representative ◽  
Made In

The supply of energy to the internal wave field in the ocean is, in total, sufficient to support the mixing required to maintain the stratification of the ocean, but can the required rates of turbulent dissipation in mid-water be sustained by breaking internal waves? It is assumed that turbulence occurs in regions where the field of motion can be represented by an exact solution of the equations that describe waves propagating through a uniformly stratified fluid and becoming unstable. Two instabilities leading to wave breaking are examined, convective instability and shear-induced Kelvin–Helmholtz instability. Models are constrained by data representative of the mid-water ocean. Calculations of turbulent dissipation are first made on the assumption that all the waves representing local breaking have the same steepness, $s$, and frequency, $\unicode[STIX]{x1D70E}$. For some ranges of $s$ and $\unicode[STIX]{x1D70E}$, breaking can support the required transfer of energy to turbulence. For convective instability this proves possible for sufficiently large $s$, typically exceeding 2.0, over a range of $\unicode[STIX]{x1D70E}$, while for shear-induced instability near-inertial waves are required. Relaxation of the constraint that the model waves all have the same $s$ and $\unicode[STIX]{x1D70E}$ requires new assumptions about the nature and consequences of wave breaking. Examples predict an overall dissipation consistent with the observed rates. Further observations are, however, required to test the validity of the assumptions made in the models and, in particular, to determine the nature and frequency of internal wave breaking in the mid-water ocean.

The fate and impact of internal waves induced by strong shear current over a marginal ridge

2020 ◽  
Author(s):  
Peiwen Zhang ◽  
Wenjia Min
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Vertical Mixing ◽  
Internal Tide ◽  
Stratified Flow ◽  
Internal Tides ◽  
Energy Field ◽  
Nonlinear Internal Waves ◽  
Highly Nonlinear ◽  
Shear Current

<p>Internal waves with strong vertical mixing could be induced by stratified flow over seafloor obstacles. Noted that the stratified flow not only trigger internal tides, but also highly nonlinear internal waves like internal lee waves and internal solitary waves over steep topography features, and the highly nonlinear internal waves are suggested to play an important role in turbulence and mixing. As a typical seafloor obstacle, ridge could significantly modified the propagation of internal tide, internal lee wave and internal solitary wave. We focused on I-Lan ridge with asymmetrical topography feature in Kuroshio region. To the north of the I-Lan ridge, the depth of Philippine basin reached 4000m compared with the depth of 1500m in the south of the ridge, leading to different characteristics of internal wave energy field and ecological characteristics between two sides. Based on numerical simulations, we revealed the generation and propagation of internal waves over marginal ridge, causing by the shear current induced by Kuroshio. We also discussed the turbulence kinetic energy contributed by linear internal waves and nonlinear internal waves, providing the strength of vertical turbulent mixing around the I-Lan ridge. Then we demonstrated the characteristics of complex internal wave field in the strong background shear current over I-Lan ridge.</p>

scholarly journals Intrinsic Nonlinearity and Spectral Structure of Internal Tides at an Idealized Mid-Atlantic Bight Shelf Break

2013 ◽  
Vol 43 (12) ◽  
pp. 2641-2660 ◽  
Author(s):  
Weifeng G. Zhang ◽  
Timothy F. Duda
Keyword(s):  
Internal Wave ◽  
Energy Conversion ◽  
Internal Waves ◽  
Shelf Break ◽  
Internal Tides ◽  
Vertical Shear ◽  
Spectral Structure ◽  
Strong Nonlinearity ◽  
Momentum Exchange ◽  
Baroclinic Energy Conversion

Abstract To quantify dynamical aspects of internal-tide generation at the Mid-Atlantic Bight shelf break, this study employs an idealized ocean model initialized by climatological summertime stratification and forced by monochromatic barotropic tidal currents at the offshore boundary. The Froude number of the scenario is subunity, and the bathymetric slope offshore of the shelf break is supercritical. A barotropic-to-baroclinic energy conversion rate of 335 W m−1 is found, with 14% of the energy locally dissipated through turbulence and bottom friction and 18% radiated onto the shelf. Consistent with prior studies, nonlinear effects result in additional super- and subharmonic internal waves at the shelf break. The subharmonic waves are subinertial, evanescent, and mostly trapped within a narrow beam of internal waves at the forcing frequency. They likely result from nonresonant triad interaction associated with strong nonlinearity. Strong vertical shear associated with the subharmonic waves tends to enhance local energy dissipation and turbulent momentum exchange (TME). A simulation with reduced tidal forcing shows an expected diminished level of harmonic energy. A quasi-linear simulation verifies the role of momentum advection in controlling the relative phases of internal tides and the efficiency of barotropic-to-baroclinic energy conversion. The local TME is tightly coupled with the internal-wave dynamics: for the chosen configuration, neglecting TME causes the internal-wave energy to be overestimated by 12%, and increasing it to high levels damps the waves on the continental shelf. This work implies a necessity to carefully consider nonlinearity and turbulent processes in the calculation of internal tidal waves generated at the shelf break.

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.

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