scholarly journals Vertical Transfer of Momentum by Inertia-Gravity Internal Waves on a Two-Dimensional Shear Flow

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
A. A. Slepyshev ◽  
Keyword(s):  
Internal Waves ◽  
Drift Velocity ◽  
Vertical Component ◽  
Wave Frequency ◽  
Stokes Drift ◽  
Wave Propagation Direction ◽  
Vertical Coordinate ◽  
The Mean ◽  
Mean Current ◽  
Stokes Drift Velocity

Purpose. The paper is aimed at investigating the momentum vertical transfer by inertia-gravity internal waves on a two-dimensional flow with a vertical shear of velocity, and also at studying the Stokes drift of liquid particles and the mean current effect on it. Methods and Results. Free internal waves in an infinite basin of constant depth are considered in the Boussinesq approximation with the regard for the Earth rotation. Two components of the mean current velocity depend on the vertical coordinate. The equation for the vertical velocity amplitude has complex coefficients; therefore the eigenfunction and the wave frequency are complex. The corresponding boundary value problem is solved numerically by the implicit Adams scheme of the third order of accuracy. The wave frequency at a fixed wavenumber was found by the shooting method. It was determined that the frequency imaginary part was small and could be either negative or positive depending on a wave number and a mode number. Thus, both weak attenuation and weak amplification of an internal wave are possible. The vertical wave momentum fluxes are nonzero and can exceed the corresponding turbulent fluxes. The Stokes drift velocity, transverse to the wave direction, is nonzero and less than the longitudinal velocity. The vertical component of the Stokes drift velocity is also nonzero and four orders of magnitude less than the longitudinal component. The signs of the vertical component of the Stokes drift velocity for the waves with the frequencies 10 and 16 cph are opposite, since the signs of their frequency imaginary parts are different; and the vertical component of the Stokes drift velocity is proportional to the wave frequency imaginary part. Conclusions. The vertical momentum wave flux of inertia-gravity internal waves differs from zero in the presence of the current whose velocity component, transverse to the wave propagation direction, depends on the vertical coordinate. The component of the Stokes drift velocity, transverse to the wave propagation direction, is nonzero and less than the longitudinal one. The vertical component of the Stokes drift velocity is also nonzero and can contribute to formation of the vertical fine structure.

scholarly journals Vertical Transfer of Momentum by Inertia-Gravity Internal Waves on a Two-Dimensional Shear Flow

2021 ◽  
Vol 37 (4) ◽  
Author(s):  
A. A. Slepyshev ◽  
Keyword(s):  
Internal Waves ◽  
Drift Velocity ◽  
Vertical Component ◽  
Wave Frequency ◽  
Stokes Drift ◽  
Wave Propagation Direction ◽  
Vertical Coordinate ◽  
The Mean ◽  
Mean Current ◽  
Stokes Drift Velocity

Purpose. The paper is aimed at investigating the momentum vertical transfer by inertia-gravity internal waves on a two-dimensional flow with a vertical shear of velocity, and also at studying the Stokes drift of liquid particles and the mean current effect on it. Methods and Results. Free internal waves in an infinite basin of constant depth are considered in the Boussinesq approximation with the regard for the Earth rotation. Two components of the mean current velocity depend on the vertical coordinate. The equation for the vertical velocity amplitude has complex coefficients; therefore the eigenfunction and the wave frequency are complex. The corresponding boundary value problem is solved numerically by the implicit Adams scheme of the third order of accuracy. The wave frequency at a fixed wavenumber was found by the shooting method. It was determined that the frequency imaginary part was small and could be either negative or positive depending on a wave number and a mode number. Thus, both weak attenuation and weak amplification of an internal wave are possible. The vertical wave momentum fluxes are nonzero and can exceed the corresponding turbulent fluxes. The Stokes drift velocity, transverse to the wave direction, is nonzero and less than the longitudinal velocity. The vertical component of the Stokes drift velocity is also nonzero and four orders of magnitude less than the longitudinal component. The signs of the vertical component of the Stokes drift velocity for the waves with the frequencies 10 and 16 cycle/h are opposite, since the signs of their frequency imaginary parts are different; and the vertical component of the Stokes drift velocity is proportional to the wave frequency imaginary part. Conclusions. The vertical momentum wave flux of inertia-gravity internal waves differs from zero in the presence of the current whose velocity component, transverse to the wave propagation direction, depends on the vertical coordinate. The component of the Stokes drift velocity, transverse to the wave propagation direction, is nonzero and less than the longitudinal one. The vertical component of the Stokes drift velocity is also nonzero and can contribute to formation of the vertical fine structure

The trapping and vertical focusing of internal waves in a pycnocline due to the horizontal inhomogeneities of density and currents

1985 ◽  
Vol 158 ◽  
pp. 199-218 ◽  
Author(s):  
S. I. Badulin ◽  
V. I. Shrira ◽  
L. Sh. Tsimring
Keyword(s):  
Wave Packet ◽  
Viscous Dissipation ◽  
Internal Waves ◽  
Equations Of Motion ◽  
Local Maximum ◽  
Velocity Shear ◽  
Vertical Shear ◽  
Small Scale ◽  
The Mean ◽  
Mean Current

This paper studies the propagation of a wave packet in regions where the central packet frequency ω is close to the local maximum of the effective Väisälä frequency Nf(z) = N(z)/[1 − k·U(z)/ω], where k is the central wavevector of the packet and U is the mean current with a vertical velocity shear. The wave approaches the layer ω = Nfm asymptotically, i.e. trapping of the wave takes place. The trapping of guided internal waves is investigated within the framework of the linearized equations of motion of an incompressible stratified fluid in the WKB approximation, with viscosity, spectral bandwidth of the packet, vertical shear of the mean current and non-stationarity of the environment taken into account. As the packet approaches the layer of trapping, the growth of the wavenumber k is restricted only by possible wave-breaking and viscous dissipation. The growth of k is accompanied by the transformation of the vertical structure of internal-wave modes. The wave motion focuses at a certain depth determined by the maximum effective Väisälä frequency Nfm. The trapping of the wave packet results in power growth of the wave amplitude and steepness. At larger times the viscous dissipation becomes a dominating factor of evolution as a result of strong slowing down of the packet motion.The role of trapping in the energy exchange of internal waves, currents and small-scale turbulence is discussed.

scholarly journals Internal tides in the strait of Denmark

2019 ◽  
Vol 55 (3) ◽  
pp. 78-84
Author(s):  
Е. G. Morozov ◽  
D. I. Frey ◽  
S. V. Gladyshev ◽  
А. А. Klyuvitkin ◽  
А. N. Novigatsky
Keyword(s):  
Numerical Model ◽  
Internal Waves ◽  
Field Measurements ◽  
Internal Tides ◽  
Denmark Strait ◽  
Vertical Displacements ◽  
The Mean ◽  
Temperature Records ◽  
The Waves ◽  
Mean Current

Six day temperature records carried out at the three mooring levels revealed isotherm fluctuations in the Denmark Strait sill in July 2018 caused by internal waves. In addition to the field measurements, fluctuations of isopycnals were estimated on the basis of a numerical model. It was shown that the vertical displacements of water particles caused by semidiurnal internal tides are approximately 50 m in the region of the sill crossing the strait. The displacements decrease to 30 m over a distance of 100 km from the sill. The internal waves in the northern part of the strait are more intense than in the southern part because the wave propagates in the opposite direction to the mean current. In the southern part the waves and the current propagate to the south, which increases the wavelength and decreases their amplitudes.

Stocks drift and vortex instability of the potential surface wave

2021 ◽  
Author(s):  
Alexander Benilov
Keyword(s):  
Surface Wave ◽  
Drift Velocity ◽  
Potential Surface ◽  
Rotation Frequency ◽  
Fluid Particle ◽  
Stokes Drift ◽  
Vortex Instability ◽  
Classical Expression ◽  
Ocean Upper Layer ◽  
Stokes Drift Velocity

<p>It is shown that in the case of potential surface wave an exact solution of the equations of the nonlinear Lagragian’s dynamics of the fluid particle has the drift velocity as an eigenvalue. The fluid particle trajectory is a circular rotation around a center point moving with a constant drift velocity. The rotation frequency differs from the wave frequency by the Doppler’s shift caused by the drift velocity. The constant drift velocity, for the surface wave of small amplitude, coincides with the classical expression for the Stokes drift velocity.</p><p>It is also shown that in the cases with absence of the Stokes drift and with presence of the Stokes drift the vortex instability of a potential surface wave has the same futures. But the vortex temporal variability in the case of the Stokes drift is affected by the Doppler’s shift caused by the Stokes drift velocity. Hence it allows a conclusion that the vortex instability of a potential surface wave initiates turbulent mixing and Lengmure circulation in the ocean upper layer.      </p><p> </p>

scholarly journals Mass Transport in the Stokes Edge Wave for Constant Arbitrary Bottom Slope in a Rotating Ocean

2014 ◽  
Vol 44 (4) ◽  
pp. 1161-1174 ◽  
Author(s):  
Peygham Ghaffari ◽  
Jan Erik H. Weber
Keyword(s):  
Mass Transport ◽  
Edge Wave ◽  
Stokes Drift ◽  
Future Application ◽  
Bottom Slope ◽  
The Mean ◽  
The Given ◽  
The Waves ◽  
Mean Current ◽  
Local Depth

Abstract The Lagrangian mass transport in the Stokes surface edge wave is obtained from the vertically integrated equations of momentum and mass in a viscous rotating ocean, correct to the second order in wave steepness. The analysis is valid for bottom slope angles β in the interval 0 < β ≤ π/2. Vertically averaged drift currents are obtained by dividing the fluxes by the local depth. The Lagrangian mean current is composed of a Stokes drift (inherent in the waves) plus a mean Eulerian drift current. The latter arises as a balance between the radiation stresses, the Coriolis force, and bottom friction. Analytical solutions for the mean Eulerian current are obtained in the form of exponential integrals. The relative importance of the Stokes drift to the Eulerian current in their contribution to the Lagrangian drift velocity is investigated in detail. For the given wavelength, the Eulerian current dominates for medium and large values of β, while for moderate and small β, the Stokes drift yields the main contribution to the Lagrangian drift. Because most natural beaches are characterized by moderate or small slopes, one may only calculate the Stokes drift in order to assess the mean drift of pollution and suspended material in the Stokes edge wave. The main future application of the results for large β appears to be for comparison with laboratory experiments in rotating tanks.

scholarly journals Approximate Stokes Drift Profiles in Deep Water

2014 ◽  
Vol 44 (9) ◽  
pp. 2433-2445 ◽  
Author(s):  
Øyvind Breivik ◽  
Peter A. E. M. Janssen ◽  
Jean-Raymond Bidlot
Keyword(s):  
Velocity Profile ◽  
Drift Velocity ◽  
Ocean Circulation ◽  
Deep Water ◽  
Stokes Drift ◽  
Wave Spectra ◽  
Langmuir Turbulence ◽  
Stokes Transport ◽  
Stokes Force ◽  
Stokes Drift Velocity

Abstract A deep-water approximation of the Stokes drift velocity profile is explored as an alternative to the monochromatic profile. The alternative profile investigated relies on the same two quantities required for the monochromatic profile, namely, the Stokes transport and the surface Stokes drift velocity. Comparisons with parametric spectra and profiles under wave spectra from the Interim ECMWF Re-Analysis (ERA-Interim) and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profile gives a closer match and a more correct shear has implications for ocean circulation models since the Coriolis–Stokes force depends on the magnitude and direction of the Stokes drift profile, and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. The alternative profile comes at no added numerical cost compared to the monochromatic profile.

scholarly journals Transient Evolution of Langmuir Turbulence in Ocean Boundary Layers Driven by Hurricane Winds and Waves

2012 ◽  
Vol 42 (11) ◽  
pp. 1959-1980 ◽  
Author(s):  
Peter P. Sullivan ◽  
Leonel Romero ◽  
James C. McWilliams ◽  
W. Kendall Melville
Keyword(s):  
Drift Velocity ◽  
Large Scale ◽  
Stokes Drift ◽  
Langmuir Turbulence ◽  
Cell Orientation ◽  
Left Hand ◽  
Right Hand ◽  
The Right ◽  
Ocean Boundary ◽  
Stokes Drift Velocity

Abstract A large-eddy simulation (LES) model, which adopts wave-averaged equations with vortex force, is used to investigate Langmuir turbulence and ocean boundary layer (OBL) dynamics in high-wind hurricane conditions. The temporally evolving spatially asymmetric wind and wave Stokes drift velocity imposed in the LES are generated by a spectral wave prediction model adapted to Hurricane Frances traveling at a speed of 5.5 m s−1. The potency of Langmuir turbulence depends on the turbulent Langmuir number, the wind–Stokes drift alignment, and the depth scale of the Stokes profile Ds relative to the OBL depth h. At the time of maximum winds, large-scale vigorous coherent cells develop on the right-hand side of the storm under the inertially rotating winds; the Stokes drift velocity is well tuned to the surface winds. Much weaker cells develop on the left-hand side of the storm, partly because of reduced Stokes production. With misaligned winds and waves the vertical momentum fluxes can be counter to the gradient of Stokes drift, and the cell orientation tracks the direction of the mean Lagrangian shear. The entrainment flux is increased by 20% and the sea surface temperature is 0.25 K cooler on the right-hand side of the storm in the presence of Langmuir turbulence. Wave effects impact entrainment when the ratio Ds/|h| > 0.75. Because of wind–wave asymmetry Langmuir cells add quantitatively to the left–right asymmetry already understood for hurricanes due to resonance. And the transient evolution of the OBL cannot be understood simply in terms of equilibrium snapshots.

The dominant frequency analysis of interfacial wave in wet-gas pipeline transportation based on NIR absorption

2021 ◽  
pp. 1-10
Author(s):  
Zhiyue Zhao ◽  
Ning Zhao ◽  
Lide Fang ◽  
Xiaoting Li
Keyword(s):  
Liquid Film ◽  
Predictive Accuracy ◽  
Film Surface ◽  
Dominant Frequency ◽  
Wave Frequency ◽  
Interfacial Wave ◽  
Long Distance ◽  
Wet Gas ◽  
The Mean ◽  
Predictive Correlation

During the long-distance transportation of wet-gas, the dominant frequency is of great significance for the study of pipeline fatigue and damage, and the safety production. Therefore, the theoretical and experimental researches for dominant frequency are carried out increasingly. However, most of the current prediction correlation of dominant frequency are mainly applicable to atmospheric pressure conditions (0.1 MPa), and the prediction accuracy is not accurate enough. The paper obtains the time series signal of liquid film thickness by near-infrared (NIR) sensor, and then calculates the wave frequency by the power spectrum density (PSD). The performance of typical predictive correlation is evaluated and analyzed by utilizing the experimental data at different flow and pressure conditions (0.1–0.8) MPa. The structure of Strouhal number and Lockhart-Martinelli (L-M) parameter are optimized reasonably, the mean velocity of the liquid film surface, the density increment of gas core, the gas core mass flow and average liquid film velocity are considered in the L-M parameter, a modified interfacial wave frequency correlation is proposed. The results indicate that the mean absolute error of the predictive correlation is 9.06% (current data) and 25.64% (literature data). The new correlation has a better predictive accuracy.

Axisymmetric internal waves generated by a travelling oscillating body

1969 ◽  
Vol 35 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T. N. Stevenson
Keyword(s):  
Internal Waves ◽  
Salt Solution ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Dispersive Waves ◽  
The Mean ◽  
Oscillating Sphere

Experiments are presented in which axisymmetric internal waves are generated by an oscillating sphere moving vertically in a stably stratified salt solution. The Reynolds numbers for the sphere based on the diameter and the mean velocity are between 10 and 200. Lighthill's theory for dispersive waves is used to calculate the phase configuration of the internal waves. The agreement between experiment and theory is reasonably good.

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