Numerical simulations of the interaction of internal waves with a shelf break

2006 ◽  
Vol 18 (7) ◽  
pp. 076603 ◽  
Author(s):  
S. K. Venayagamoorthy ◽  
O. B. Fringer
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Shelf Break

Dissipating and reflecting internal waves

2021 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg
Keyword(s):  
Numerical Simulations ◽  
Linear Theory ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Linear Wave ◽  
Lee Waves ◽  
Lee Wave ◽  
Upper Boundary

AbstractInternal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially-averaged kinetic energy and dissipation of even highly non-linear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes.

Finite-amplitude internal wavepacket dispersion and breaking

2001 ◽  
Vol 429 ◽  
pp. 343-380 ◽  
Author(s):  
BRUCE R. SUTHERLAND
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Large Amplitude ◽  
Finite Amplitude ◽  
Critical Amplitude ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Stability ◽  
The Waves ◽  
Horizontal Wavelength

The evolution and stability of two-dimensional, large-amplitude, non-hydrostatic internal wavepackets are examined analytically and by numerical simulations. The weakly nonlinear dispersion relation for horizontally periodic, vertically compact internal waves is derived and the results are applied to assess the stability of weakly nonlinear wavepackets to vertical modulations. In terms of Θ, the angle that lines of constant phase make with the vertical, the wavepackets are predicted to be unstable if [mid ]Θ[mid ] < Θc, where Θc = cos−1 (2/3)1/2 ≃ 35.3° is the angle corresponding to internal waves with the fastest vertical group velocity. Fully nonlinear numerical simulations of finite-amplitude wavepackets confirm this prediction: the amplitude of wavepackets with [mid ]Θ[mid ] > Θc decreases over time; the amplitude of wavepackets with [mid ]Θ[mid ] < Θc increases initially, but then decreases as the wavepacket subdivides into a wave train, following the well-known Fermi–Pasta–Ulam recurrence phenomenon.If the initial wavepacket is of sufficiently large amplitude, it becomes unstable in the sense that eventually it convectively overturns. Two new analytic conditions for the stability of quasi-plane large-amplitude internal waves are proposed. These are qualitatively and quantitatively different from the parametric instability of plane periodic internal waves. The ‘breaking condition’ requires not only that the wave is statically unstable but that the convective instability growth rate is greater than the frequency of the waves. The critical amplitude for breaking to occur is found to be ACV = cot Θ (1 + cos2 Θ)/2π, where ACV is the ratio of the maximum vertical displacement of the wave to its horizontal wavelength. A second instability condition proposes that a statically stable wavepacket may evolve so that it becomes convectively unstable due to resonant interactions between the waves and the wave-induced mean flow. This hypothesis is based on the assumption that the resonant long wave–short wave interaction, which Grimshaw (1977) has shown amplifies the waves linearly in time, continues to amplify the waves in the fully nonlinear regime. Using linear theory estimates, the critical amplitude for instability is ASA = sin 2Θ/(8π2)1/2. The results of numerical simulations of horizontally periodic, vertically compact wavepackets show excellent agreement with this latter stability condition. However, for wavepackets with horizontal extent comparable with the horizontal wavelength, the wavepacket is found to be stable at larger amplitudes than predicted if Θ [lsim ] 45°. It is proposed that these results may explain why internal waves generated by turbulence in laboratory experiments are often observed to be excited within a narrow frequency band corresponding to Θ less than approximately 45°.

scholarly journals The Lifecycle of Nonlinear Internal Waves in the Northwestern South China Sea

2019 ◽  
Vol 49 (8) ◽  
pp. 2133-2145 ◽  
Author(s):  
Jianjun Liang ◽  
Xiao-Ming Li ◽  
Jin Sha ◽  
Tong Jia ◽  
Yongzheng Ren
Keyword(s):  
South China Sea ◽  
Internal Waves ◽  
South China ◽  
Internal Tide ◽  
In Situ Measurements ◽  
Shelf Break ◽  
Undular Bore ◽  
Nonlinear Internal Waves ◽  
Seasonal Thermocline

AbstractThe life cycle of nonlinear internal waves (NIWs) to the southeast of Hainan Island in the northwestern South China Sea is investigated using synergistic satellite observations, in situ measurements, and numerical simulations. A three-dimensional, fully nonlinear and nonhydrostatic model with ultrafine resolution shows that a diurnal internal tide emanates from a sill in the Xisha Islands at approximately 215 km away from the local shelf break. The internal tide transits the deep basin toward the shelf break and reflects at the sea bottom and seasonal thermocline in the form of a wave beam. Arriving at the shelf break, the internal tide undergoes nonlinear transformation and produces an undular bore. Analyses of in situ measurements reveal that the undular bore appears as sharp depressions of the strong near-surface seasonal thermocline. The undular bore gradually evolves into an internal solitary wave train on the midshelf, which was detected by the spaceborne synthetic aperture radar. This finding has great implications for investigating NIWs in other coastal oceans where waves are controlled by remotely generated internal tides.

scholarly journals Brief communication: The occurrence of rogue waves in the interior of the oceans: A modelling and computational study

2018 ◽  
Author(s):  
Kwok Wing Chow ◽  
Hiu Ning Chan ◽  
Roger H. J. Grimshaw
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Deep Water ◽  
Modulation Instability ◽  
Computational Study ◽  
Rogue Waves ◽  
Buoyancy Frequency ◽  
Spontaneous Generation ◽  
Large Displacements ◽  
Analytical Treatment

Abstract. The occurrence of unexpectedly large displacements in the interior of the oceans is studied through the dynamics of packets of internal waves, where the evolution is governed by the nonlinear Schrödinger equation. The case of constant buoyancy frequency permits analytical treatment. While modulation instability for surface waves only arises for sufficiently deep water, rogue internal waves may occur if the fluid depth is shallow. The dependence on the stratification parameter and choice of internal modes can be demonstrated explicitly. The spontaneous generation of rogue waves is tested by numerical simulations.

scholarly journals Laboratory experiments and simulations for solitary internal waves with trapped cores

2014 ◽  
Vol 757 ◽  
pp. 354-380 ◽  
Author(s):  
Paolo Luzzatto-Fegiz ◽  
Karl R. Helfrich
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Internal Waves ◽  
Number Fields ◽  
Rate Of Change ◽  
Shear Instability ◽  
Homogeneous Layer ◽  
Uniform Density ◽  
The Core ◽  
Solitary Internal Waves

AbstractWe perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15 % of the overall fluid depth) overlaying a deep homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult to avoid at the experimental scale. By contrast, our experiments with a no-slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer virtual tank. Where overlap exists, our experiments and simulations are in good agreement. In order to provide a robust definition of the trapped core, we propose bounding it as a Lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady robust flows that exhibit good collapse in their properties. The core circulation is small (at most, around 10 % of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4 % of the full density range. We also calculate the circulation, kinetic energy and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin–Long theory for waves with a uniform-density irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson-number fields, and performing a temporal stability analysis based on the Taylor–Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature.

Internal wave excitation from stratified flow over a thin barrier

1998 ◽  
Vol 377 ◽  
pp. 223-252 ◽  
Author(s):  
BRUCE R. SUTHERLAND ◽  
PAUL F. LINDEN
Keyword(s):  
Internal Wave ◽  
Numerical Simulations ◽  
Internal Waves ◽  
Wavelet Transforms ◽  
Large Amplitude ◽  
Internal Gravity Waves ◽  
Wave Excitation ◽  
Mean Flow ◽  
Propagating Waves ◽  
The Waves

We perform laboratory experiments in a recirculating shear flow tank of non-uniform salt-stratified water to examine the excitation of internal gravity waves (IGW) in the wake of a tall, thin vertical barrier. The purpose of this study is to characterize and quantify the coupling between coherent structures shed in the wake and internal waves that radiate from the mixing region into the deep, stationary fluid. In agreement with numerical simulations, large-amplitude internal waves are generated when the mixing region is weakly stratified and the deep fluid is sufficiently strongly stratified. If the mixing region is unstratified, weak but continuous internal wave excitation occurs. In all cases, the tilt of the phase lines of propagating waves lies within a narrow range. Assuming the waves are spanwise uniform, their amplitude in space and time is measured non-intrusively using a recently developed ‘synthetic schlieren’ technique. Using wavelet transforms to measure consistently the width and duration of the observed wavepackets, the Reynolds stress is measured and, in particular, we estimate that when large-amplitude internal wave excitation occurs, approximately 7% of the average momentum across the shear depth and over the extent of the wavepacket is lost due to transport away from the mixing region by the waves.We propose that internal waves may act back upon the mean flow modifying it so that the excitation of waves of that frequency is enhanced. A narrow frequency spectrum of large-amplitude waves is observed because the feedback is largest for waves with phase tilt in a range near 45°. Numerical simulations and analytic theories are presented to further quantify this theory.

scholarly journals Internal Wave Reflection on Shelf Slopes with Depth-Varying Stratification

2013 ◽  
Vol 43 (2) ◽  
pp. 248-258 ◽  
Author(s):  
Rob A. Hall ◽  
John M. Huthnance ◽  
Richard G. Williams
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Shelf Break ◽  
Maximum Slope ◽  
Near Surface ◽  
Shelf Slope ◽  
Linear Slope ◽  
Horizontal Wavelength

Abstract Reflection of internal waves from sloping topography is simple to predict for uniform stratification and linear slope gradients. However, depth-varying stratification presents the complication that regions of the slope may be subcritical and other regions supercritical. Here, a numerical model is used to simulate a mode-1, M2 internal tide approaching a shelf slope with both uniform and depth-varying stratifications. The fractions of incident internal wave energy reflected back offshore and transmitted onto the shelf are diagnosed by calculating the energy flux at the base of slope (with and without topography) and at the shelf break. For the stratifications/topographies considered in this study, the fraction of energy reflected for a given slope criticality is similar for both uniform and depth-varying stratifications. This suggests the fraction reflected is dependent only on maximum slope criticality and independent of the depth of the pycnocline. The majority of the reflected energy flux is in mode 1, with only minor contributions from higher modes due to topographic scattering. The fraction of energy transmitted is dependent on the depth-structure of the stratification and cannot be predicted from maximum slope criticality. If near-surface stratification is weak, transmitted internal waves may not reach the shelf break because of decreased horizontal wavelength and group velocity.

scholarly journals Chlorophyll increase due to internal waves in the shelf-break of Gran Canaria Island (Canary Islands)

2001 ◽  
Vol 65 (S1) ◽  
pp. 89-97 ◽  
Author(s):  
Pablo Sangrà ◽  
G. Basterretxea ◽  
J. L. Pelegrí ◽  
J. Arístegui
Keyword(s):  
Internal Waves ◽  
Canary Islands ◽  
Shelf Break ◽  
Gran Canaria
Sign in / Sign up

Export Citation Format

Share Document