scholarly journals Impact of Wave-Vortical Interactions on Oceanic Submesoscale Lateral Dispersion

2021 ◽  
Author(s):  
Gerardo Hernández-Dueñas ◽  
M.-Pascale Lelong ◽  
Leslie M. Smith
Keyword(s):  
Internal Wave ◽  
Wave Mode ◽  
Projection Technique ◽  
Lateral Transport ◽  
Transfer Energy ◽  
Shear Dispersion ◽  
Horizontal Flows ◽  
Order Of Magnitude ◽  
The Waves ◽  
Mode Energy

AbstractSubmesoscale lateral transport of Lagrangian particles in pycnocline conditions is investigated by means of idealized numerical simulations with reduced-interaction models. Using a projection technique, the models are formulated in terms of wave-mode and vortical-mode nonlinear interactions, and they range in complexity from full Boussinesq to waves-only and vortical-modes-only (QG) models. We find that, on these scales, most of the dispersion is done by vortical motions, but waves cannot be discounted because they play an important, albeit indirect, role. In particular, we show that waves are instrumental in filling out the spectra of vortical-mode energy at smaller scales through non-resonant vortex-wave-wave triad interactions. We demonstrate that a richer spectrum of vortical modes in the presence of waves enhances the effective lateral diffusivity, compared to QG. Waves also transfer energy upscale to vertically sheared horizontal flows which are a key ingredient for internal-wave shear dispersion. In the waves-only model, the dispersion rate is an order of magnitude smaller and is attributed entirely to internal-wave shear dispersion.

Trapped internal waves over undular topography

1991 ◽  
Vol 226 ◽  
pp. 205-217 ◽  
Author(s):  
C. Kranenburg ◽  
J. D. Pietrzak ◽  
G. Abraham
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Large Amplitude ◽  
Bottom Topography ◽  
Stratified Flow ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Trapped Waves ◽  
Acoustic Images ◽  
The Waves

We describe observations of slowly decelerating stratified flow over undular bottom topography in an estuary. The flow, which initially was supercritical with respect to the first internal wave mode, approached a resonance after it had become subcritical. A series of acoustic images showed large-amplitude first-mode trapped waves during this phase of the tide. We derive a criterion for quasi-steady response, and present an extension of Yih's class II linear finite-amplitude solutions that accounts for the waves observed.

scholarly journals Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling

2020 ◽  
Vol 221 (3) ◽  
pp. 1580-1590 ◽  
Author(s):  
M van Driel ◽  
C Boehm ◽  
L Krischer ◽  
M Afanasiev
Keyword(s):  
Wave Propagation ◽  
Adaptive Mesh Refinement ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Space ◽  
Adaptive Mesh ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Adjoint Modelling ◽  
The Waves

SUMMARY An order of magnitude speed-up in finite-element modelling of wave propagation can be achieved by adapting the mesh to the anticipated space-dependent complexity and smoothness of the waves. This can be achieved by designing the mesh not only to respect the local wavelengths, but also the propagation direction of the waves depending on the source location, hence by anisotropic adaptive mesh refinement. Discrete gradients with respect to material properties as needed in full waveform inversion can still be computed exactly, but at greatly reduced computational cost. In order to do this, we explicitly distinguish the discretization of the model space from the discretization of the wavefield and derive the necessary expressions to map the discrete gradient into the model space. While the idea is applicable to any wave propagation problem that retains predictable smoothness in the solution, we highlight the idea of this approach with instructive 2-D examples of forward as well as inverse elastic wave propagation. Furthermore, we apply the method to 3-D global seismic wave simulations and demonstrate how meshes can be constructed that take advantage of high-order mappings from the reference coordinates of the finite elements to physical coordinates. Error level and speed-ups are estimated based on convergence tests with 1-D and 3-D models.

Stabilizing effect of surrounding gas flow on a plane liquid sheet

2011 ◽  
Vol 672 ◽  
pp. 5-32 ◽  
Author(s):  
OUTI TAMMISOLA ◽  
ATSUSHI SASAKI ◽  
FREDRIK LUNDELL ◽  
MASAHARU MATSUBARA ◽  
L. DANIEL SÖDERBERG
Keyword(s):  
Growth Rate ◽  
Gas Flow ◽  
Liquid Velocity ◽  
Air Flow ◽  
Liquid Sheet ◽  
Mean Velocity ◽  
Order Of Magnitude ◽  
The Stability ◽  
The Waves ◽  
Half Thickness

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Rel = 3000 and Weber number We = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20% of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

scholarly journals Wave resistance : some cases of unsymmetrical forms

1926 ◽  
Vol 110 (754) ◽  
pp. 233-241 ◽  
Keyword(s):  
Mathematical Problem ◽  
Dynamical Theory ◽  
Wave Resistance ◽  
Experimental Results ◽  
General Effect ◽  
Surrounding Water ◽  
Order Of Magnitude ◽  
To Come ◽  
The Waves ◽  
Two Bodies

1. One of the chief features of interest in curves showing the variation of wave resistance with velocity is the occurrence of oscillations about a mean curve, which may be regarded as due to interference between the waves produced by the front and rear portions of the model. In various comparisons made between theoretical curves and such suitable experimental results as are available, the greatest divergence is perhaps in the magnitude of these oscillations, the theore­tical curves showing effects many times greater than similar experimental results. There are, no doubt, many approximations in the hydro-dynamical theory which preclude too close a comparison between theoretical and experimental results in any particular case, but it seems fairly certain that the divergence in question must be largely due to neglecting the effects of fluid friction. For several reasons it is useless to attempt at present a direct introduction of vis­cosity into the mathematical problem, but a consideration of its general effect suggests one or two calculations which may be of interest The direct effect of viscosity upon waves already formed may be assumed to be relatively small; the important influence is one which makes the rear portion of the model less effective in generating waves than the front portion. We may imagine this as due to the skin friction decreasing the general relative velocity of model and surrounding water as we pass from the fore end to the aft end ; or we may picture the so-called friction belt surrounding the model, and may consider the general effect as equivalent to a smoothing out of the curve of the rear portion of the model. Without pursuing these speculations further, they suggest calculations which can be made for models in frictionless liquid when the form of the model is unsymmetrical in this manner ; and the particular point to be examined is the effect of such modification upon the magnitude of the inter­ference phenomena. The first sections compare, in this respect, two bodies entirely submerged in the liquid. The form in each case is a surface of revolution ; one is symmetrical fore and aft and has sharp pointed ends, while in the other the rear portion is cut away so as to come to a fine point. By inspection of the expressions for the wave resistance it is seen that the oscillating terms are of a lower order of magnitude in the latter than in the former case.

Secondary flow due to Alfvén waves

1977 ◽  
Vol 80 (1) ◽  
pp. 179-202 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Hyperbolic Equations ◽  
Wave Mode ◽  
Alfven Waves ◽  
Secondary Flows ◽  
Alfvén Waves ◽  
Stored Energy ◽  
Axial Field ◽  
Electromagnetic Characteristics ◽  
The Waves ◽  
Made In

Large (gigajoule) amounts of energy can in principle be stored as kinetic energy in liquid metal circulating round a torus and can be extracted at the gigawatt level by Alfvén waves propagating along an imposed axial field. A major limitation on the energy that may be so stored is the disruption of these primary Alfvén waves by secondary flows in meridional planes, associated with out-of-balance centrifugal forces ahead of and behind the waves and non-uniform magnetic pressures at the wave fronts. Vorticity, created at the wave, itself propagates in secondary Alfvén waves.This paper gives a linearized treatment of these secondary motions and the associated perturbations of the imposed axial field and compares the resulting disruption of the primary wave mode with crude estimates made in an earlier paper. The main case treated is the discharge of the stored energy into a matched resistor by an Alfvén step wave but the secondary consequences of standing primary waves are also explored. The nature of the solutions depends on the electromagnetic characteristics of the walls normal to the imposed field. The problem is mathematically interesting because it involves the joint solving of elliptic and hyperbolic equations that are coupled by the boundary conditions at these walls.

scholarly journals Deep-water sediment wave formation: linear stability analysis of coupled flow/bed interaction

2011 ◽  
Vol 680 ◽  
pp. 435-458 ◽  
Author(s):  
L. LESSHAFFT ◽  
B. HALL ◽  
E. MEIBURG ◽  
B. KNELLER
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Internal Wave ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Wave Mode ◽  
Bottom Current ◽  
Field Observations ◽  
Sediment Bed

A linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier–Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien–Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt–Väisälä frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations.

scholarly journals Seismic imaging of a thermohaline staircase in the western tropical North Atlantic

2010 ◽  
Vol 7 (1) ◽  
pp. 361-389
Author(s):  
I. Fer ◽  
P. Nandi ◽  
W. S. Holbrook ◽  
R. W. Schmitt ◽  
P. Páramo
Keyword(s):  
Internal Wave ◽  
North Atlantic ◽  
Vertical Mixing ◽  
Global Ocean ◽  
Turbulent Dissipation ◽  
Tropical North Atlantic ◽  
Seismic Reflection Method ◽  
Order Of Magnitude ◽  
Salt Fingering ◽  
Wave Induced

Abstract. Multichannel seismic data acquired in the Lesser Antilles in the western tropical North Atlantic indicate that the seismic reflection method has imaged an oceanic thermohaline staircase. Synthetic modeling of observed density and sound speed profiles corroborates inferences from the seismic imagery. Laterally coherent, uniform layers are present at depths ranging from 550–700 m and have a separation of ~20 m, with thicknesses increasing with depth. Reflection coefficient, a measure of the acoustic impedance contrasts, associated with the interfaces is one order of magnitude greater than the background levels. Hydrography sampled in previous surveys puts a constraint on the longevity of these layers in this area to within a maximum of three years. Spectral analysis of layer horizons in the thermohaline staircase indicates that internal wave activity is anomalously low, suggesting weak internal wave-induced turbulence and mixing. Results from two independent measurements, the application of a finescale parameterization to observed high-resolution velocity profiles and direct measurements of turbulent dissipation rate, confirm the low levels of turbulence and mixing. The lack of internal wave-induced mixing allows for the maintenance of the staircase. Our observations show the potential that seismic oceanography can contribute to an improved understanding of temporal occurrence rates, and the geographical distribution of thermohaline staircases and can improve current estimates of vertical mixing rates ascribable to salt fingering in the global ocean.

scholarly journals Нелинейные поверхностные волны в симметричной трехслойной структуре из оптических сред с различными механизмами формирования нелинейного отклика

2020 ◽  
Vol 128 (3) ◽  
pp. 358
Author(s):  
С.Е. Савотченко
Keyword(s):  
Layer Structure ◽  
Propagation Constant ◽  
Diffusion Mechanism ◽  
Analytical Form ◽  
Wave Mode ◽  
Crystal Thickness ◽  
Photorefractive Crystals ◽  
Surface Wave Propagation ◽  
Nonlinear Surface Waves ◽  
The Waves

The propagation of surface TM waves in a three-layer structure, which is a crystal thickness plate with a focusing nonlinearity of a Kerr type, sandwiched between uniaxial photorefractive crystals with a diffusion mechanism for the formation of nonlinearity is considered. Nonlinear surface waves with different attenuation patterns can propagate along the interfaces between the layers. Waves of one type attenuate with distance from the interfaces without oscillations into the depth of the outer layers of photorefractive crystals, and the waves of other type attenuate with oscillations. Wave profiles can have two forms of symmetry about the center of a three-layer structure: symmetric and antisymmetric. The two waves with a symmetric distribution exist with nonperiodic damping and the damping without oscillations. The waves only with antisymmetric distribution exist with nonperiodic damping and the damping without oscillations. The dependences of the propagation constant on the characteristics of the layered structure for the long-wave mode of surface wave propagation are found in an explicit analytical form. The conditions for their existence are indicated.

Spectra and Coherence of Wind-Generated Internal Waves

1976 ◽  
Vol 33 (10) ◽  
pp. 2323-2328 ◽  
Author(s):  
R. H. Käse ◽  
C. L. Tang
Keyword(s):  
Energy Density ◽  
Internal Wave ◽  
Internal Waves ◽  
Wind Stress ◽  
Wave Mode ◽  
Wave Number ◽  
Small Scale ◽  
Two Dimensional ◽  
Scale Turbulence ◽  
Main Thermocline

On the basis of a model for an internal wave field that is generated by a randomly varying isotropic wind stress and in which energy is transferred to small-scale turbulence, we derive the two-dimensional energy density function. The coherence scales are determined by the highest order internal wave mode that is not affected by virtual friction in the main thermocline, provided the curl of the wind stress has a white noise wave number spectrum. In general, this mode number scale is increasing monotonically with frequency. As a result of such a frequency dependent mode bandwidth, the vertical coherence drops with increasing frequency.

scholarly journals Global Patterns of Low-Mode Internal-Wave Propagation. Part I: Energy and Energy Flux

2007 ◽  
Vol 37 (7) ◽  
pp. 1829-1848 ◽  
Author(s):  
Matthew H. Alford ◽  
Zhongxiang Zhao
Keyword(s):  
Internal Wave ◽  
Time Scales ◽  
Energy Flux ◽  
Internal Tide ◽  
Companion Paper ◽  
Internal Tides ◽  
Frequency Bands ◽  
Order Of Magnitude ◽  
Hawaiian Ridge ◽  
Mesoscale Currents

Abstract Extending an earlier attempt to understand long-range propagation of the global internal-wave field, the energy E and horizontal energy flux F are computed for the two gravest baroclinic modes at 80 historical moorings around the globe. With bandpass filtering, the calculation is performed for the semidiurnal band (emphasizing M2 internal tides, generated by flow over sloping topography) and for the near-inertial band (emphasizing wind-generated waves near the Coriolis frequency). The time dependence of semidiurnal E and F is first examined at six locations north of the Hawaiian Ridge; E and F typically rise and fall together and can vary by over an order of magnitude at each site. This variability typically has a strong spring–neap component, in addition to longer time scales. The observed spring tides at sites northwest of the Hawaiian Ridge are coherent with barotropic forcing at the ridge, but lagged by times consistent with travel at the theoretical mode-1 group speed from the ridge. Phase computed from 14-day windows varies by approximately ±45° on monthly time scales, implying refraction by mesoscale currents and stratification. This refraction also causes the bulk of internal-tide energy flux to be undetectable by altimetry and other long-term harmonic-analysis techniques. As found previously, the mean flux in both frequency bands is O(1 kW m−1), sufficient to radiate a substantial fraction of energy far from each source. Tidal flux is generally away from regions of strong topography. Near-inertial flux is overwhelmingly equatorward, as required for waves generated at the inertial frequency on a β plane, and is winter-enhanced, consistent with storm generation. In a companion paper, the group velocity, ĉg ≡ FE−1, is examined for both frequency bands.

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