Evanescent to propagating internal waves in experiments, simulations, and linear theory

2020 ◽  
Vol 61 (12) ◽  
Author(s):  
Allison Lee ◽  
Kyle Hakes ◽  
Yuxuan Liu ◽  
Michael R. Allshouse ◽  
Julie Crockett
Keyword(s):  
Linear Theory ◽  
Internal Waves

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.

Estimate of the applicability limits of a linear theory of internal waves

2010 ◽  
Vol 45 (5) ◽  
pp. 787-792 ◽  
Author(s):  
V. V. Bulatov ◽  
Yu. V. Vladimirov
Keyword(s):  
Linear Theory ◽  
Internal Waves

scholarly journals HIGHER ORDER KORTEWEG-DE VRIES MODELS FOR INTERNAL WAVES

2003 ◽  
Vol 2 (2) ◽  
pp. 15
Author(s):  
J. JAHARUDDIN
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Linear Theory ◽  
Internal Waves ◽  
Solvability Condition ◽  
Vries Equation ◽  
Asymptotic Methods ◽  
Higher Order ◽  
De Vries ◽  
Order Extension

By using asymptotic methods, evolution equation is derived for the internal waves in density stratified fluid. This evo- lution equation arise as a solvability condition. A higher-order extension of the familiar Korteweg-de Vries equation is produced for internal waves in a density stratified flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed via integrals of the modal function for the linear theory of long internal waves.

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 Near-inertial dissipation due to stratified flow over abyssal topography

2021 ◽  
Author(s):  
Varvara Zemskova ◽  
Nicolas Grisouard
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Linear Theory ◽  
Internal Waves ◽  
Wave Breaking ◽  
Large Scale ◽  
Stratified Flow ◽  
Dissipation Rates ◽  
Flow Over Topography

<p>Linear theory for steady stratified flow over topography sets the range for topographic wavenumbers over which freely propagating internal waves are generated, whose radiation and breaking contribute to energy dissipation in the interior. Previous work demonstrated that dissipation rates can be enhanced over large-scale topographies with wavenumbers outside of such radiative range. We conduct idealized rotating 3D numerical simulations of steady stratified flow over 1D topography and quantify kinetic energy dissipation. We vary topographic width, which determines whether the obstacle is within the radiative range, and height, which measures the degree of flow non-linearity. Simulations with certain width and height combinations develop periodicity in wave breaking and energy dissipation, which is enhanced in the domain interior. Dissipation rates for tall and wide non-radiative topography are comparable to those of radiative topography, even away from the bottom, which is important for the ocean where wider hills also tend to be taller. </p>

Dynamics of a stratified shear layer above a region of uniform stratification

2009 ◽  
Vol 630 ◽  
pp. 191-223 ◽  
Author(s):  
HIEU T. PHAM ◽  
SUTANU SARKAR ◽  
KYLE A. BRUCKER
Keyword(s):  
Shear Layer ◽  
Wave Field ◽  
Linear Theory ◽  
Internal Waves ◽  
Small Scale ◽  
Turbulent Kinetic Energy Budget ◽  
Turbulent Dissipation ◽  
Deep Region ◽  
Direct Generation ◽  
Scale Turbulence

Direct numerical simulations (DNS) are performed to investigate the behaviour of a weakly stratified shear layer in the presence of a strongly stratified region beneath it. Both, coherent Kelvin–Helmholtz (KH) rollers and small-scale turbulence, are observed during the evolution of the shear layer. The deep stratification measured by the Richardson number Jd is varied to study its effect on the dynamics. In all cases, a pycnocline is found to develop at the edges of the shear layer. The region of maximum shear shifts downward with increasing time. Internal waves are excited, initially by KH rollers, and later by small-scale turbulence. The wave field generated by the KH rollers is narrowband and of stronger amplitude than the broadband wave field generated by turbulence. Linear theory based on Doppler-shifted frequency of the KH mode is able to predict the angle of the internal wave phase lines during the direct generation of internal waves by KH rollers. Waves generated by turbulence are relatively weaker with a broader range of excitation angles which, in the deep region, tend towards a narrower band. The linear theory that works for the internal waves excited by KH rollers does not work for the turbulence generated waves. The momentum transported by the internal waves into the interior can be large, about 10% of the initial momentum in the shear layer, when Jd ≃ 0.25. Integration of the turbulent kinetic energy budget in time and over the shear layer thickness shows that the energy flux can be up to 17% of the turbulent production, 33% of the turbulent dissipation rate and 75% of the buoyancy flux. These numbers quantify the dynamical importance of internal waves. In contrast to linear theory where the effect of deep stratification on the shear layer instabilities has been found to be weak, the present nonlinear simulations show that the evolution of the shear layer is significantly altered because of the significant momentum and energy carried away by the internal waves.

scholarly journals Energetics and mixing of stratified, rotating flow over abyssal hills

2021 ◽  
Author(s):  
Varvara Zemskova ◽  
Nicolas Grisouard
Keyword(s):  
Energy Transfer ◽  
Energy Loss ◽  
Linear Theory ◽  
Internal Waves ◽  
Mixing Efficiency ◽  
Mean Flow ◽  
Diapycnal Mixing ◽  
Transfer Rates ◽  
Non Linear ◽  
Mixing Rates

One of the proposed mechanisms for energy loss in the ocean is through dissipation of internal waves, in particular above rough topography where internal lee waves are generated. Rates of dissipation and diapycnal mixing are often estimated using linear theory and a constant value for mixing efficiency. However, previous oceanographic measurements found that non-linear dynamics may be important close to topography. In order to investigate the role of non-linear interactions, we conduct idealized 3D numerical simulations of steady flow over 1D topography and vary the topographic height, which correlates to the degree of flow non-linearity. We analyze spatial distribution of energy transfer rates between internal waves and the non-geostrophic portion of time-mean flow, and of dissipation and diapycnal mixing rates. In our simulations with taller, more non-linear topographies, energy transfer rates are similar to previously unexplained oceanographic observations near topography: internal waves gain energy from time-mean flow through horizontal straining and lose energy through vertical shearing. In the tall topography simulations, buoyancy fluxes also play a significant role, consistent with observations but contrary to linear wave theory, suggesting that quasigeostrophy-based approximations and linear theory may not hold in some regions above rough topography. Both dissipation and mixing rates increase with topographic height, but their vertical distributions differ between topographic regimes. As such, vertical profile of mixing efficiency is different for linear and non-linear topographic regimes, which may need to be incorporated into parameterizations of small-scale processes in models and estimates of ocean energy loss.

On the linear theory of waves in media with periodic structures

1991 ◽  
Vol 161 (9) ◽  
pp. 201-209 ◽  
Author(s):  
Polina S. Landa ◽  
V.F. Marchenko
Keyword(s):  
Linear Theory ◽  
Periodic Structures
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