scholarly journals A Wave-Resolving Simulation of Langmuir Circulations with a Nonhydrostatic Free-Surface Model: Comparison with Craik–Leibovich Theory and an Alternative Eulerian View of the Driving Mechanism

2018 ◽  
Vol 48 (8) ◽  
pp. 1691-1708 ◽  
Author(s):  
Yasushi Fujiwara ◽  
Yutaka Yoshikawa ◽  
Yoshimasa Matsumura
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Phase Speed ◽  
Current Speed ◽  
Surface Model ◽  
Mean Flow ◽  
Langmuir Circulations ◽  
Wave Induced ◽  
The Waves ◽  
Present Simulation

AbstractThe present study performs a wave-resolving simulation of wind-driven currents under monochromatic surface gravity waves using the latest nonhydrostatic free-surface numerical model. Here, phase speed of the waves is set much greater than the current speed. Roll structures very similar to observed Langmuir circulations (LCs) appear in the simulation only when both waves and down-wave surface currents are present, demonstrating that the rolls are driven by the wave–current interaction. A vorticity analysis of simulated mean flow reveals that the rolls are driven by the torque associated with wave motion, which arises from a correlation between wave-induced vorticity fluctuation and the wave motion itself. Furthermore, it is confirmed that the wave-induced torque is very well represented by the curl of the vortex force (VF), that is, the vector product of mean vorticity and Stokes drift velocity. Therefore, it is concluded that the simulated rolls are LCs and that the wave effects are well represented by the VF expression in the present simulation. The present study further revisits the scaling assumptions made by previous studies that derived VF formulation and shows that there is disagreement among the previous studies regarding the applicability of VF formulation when the wave orbital velocity (proportional to the amplitude times the frequency) is much smaller than the mean flow velocity. The result from the present simulation shows that the VF expression is still valid even with such small wave amplitudes, as long as phase speed of the waves is much greater than the current speed.

scholarly journals Mutual Interaction between Surface Waves and Langmuir Circulations Observed in Wave-Resolving Numerical Simulations

2020 ◽  
Vol 50 (8) ◽  
pp. 2323-2339
Author(s):  
Yasushi Fujiwara ◽  
Yutaka Yoshikawa
Keyword(s):  
Surface Waves ◽  
Friction Velocity ◽  
Phase Speed ◽  
Mutual Interaction ◽  
Stokes Drift ◽  
Horizontal Shear ◽  
Budget Analysis ◽  
Vorticity Budget ◽  
Langmuir Circulations ◽  
The Waves

AbstractWave-resolving simulations of monochromatic surface waves and Langmuir circulations (LCs) under an idealized condition are performed to investigate the dynamics of wave–current mutual interaction. When the Froude number (the ratio of the friction velocity of wind stress imposed at the surface and wave phase speed) is large, waves become refracted by the downwind jet associated with LCs and become amplitude modulated in the crosswind direction. In such cases, the simulations using the Craik–Leibovich (CL) equation with a prescribed horizontally uniform Stokes drift profile are found to underestimate the intensity of LCs. Vorticity budget analysis reveals that horizontal shear of Stokes drift induced by the wave modulation tilts the wind-driven vorticity to the downwind direction, intensifying the LCs that caused the waves to be modulated. Such an effect is not reproduced in the CL equation unless the Stokes drift of the waves modulated by LCs is prescribed. This intensification mechanism is similar to the CL1 mechanism in that the horizontal shear of the Stokes drift plays a key role, but it is more likely to occur because the shear in this interaction is automatically generated by the LCs whereas the shear in the CL1 mechanism is retained only when a particular phase relation between two crossing waves is kept locked for many periods.

Wave-Coherent Airflow and Critical Layers over Ocean Waves

2013 ◽  
Vol 43 (10) ◽  
pp. 2156-2172 ◽  
Author(s):  
Laurent Grare ◽  
Luc Lenain ◽  
W. Kendall Melville
Keyword(s):  
Momentum Flux ◽  
Wave Spectrum ◽  
Phase Speed ◽  
Ocean Waves ◽  
Naval Research ◽  
Critical Height ◽  
Office Of Naval Research ◽  
Mean Wind Speed ◽  
Wave Induced ◽  
The Waves

Abstract An analysis of coherent measurements of winds and waves from data collected during the Office of Naval Research (ONR) High-Resolution air–sea interaction (HiRes) program, from the Floating Instrument Platform (R/P FLIP), off the coast of northern California in June 2010 is presented. A suite of wind and wave measuring systems was deployed to resolve the modulation of the marine atmospheric boundary layer by waves. Spectral analysis of the data provided the wave-induced components of the wind velocity for various wind–wave conditions. The power spectral density, the amplitude, and the phase (relative to the waves) of these wave-induced components are computed and bin averaged over spectral wave age c/U(z) or c/u*, where c is the linear phase speed of the waves, U(z) is the mean wind speed measured at the height z of the anemometer, and u* is the friction velocity in the air. Results are qualitatively consistent with the critical layer theory of Miles. Across the critical height zc, defined such that U(zc) = c, the wave-induced vertical and horizontal velocities change significantly in both amplitude and phase. The measured wave-induced momentum flux shows that, for growing waves, less than 10% of the momentum flux at z ≈ 10 m is supported by waves longer than approximately 15 m. For older sea states, these waves are able to generate upward wave-induced momentum flux opposed to the overall downward momentum flux. The measured amplitude of this upward wave-induced momentum flux was up to 20% of the value of the total wind stress when Cp/u* > 60, where Cp is the phase speed at the peak of the wave spectrum.

scholarly journals Incidence and reflection of internal waves and wave-induced currents at a jump in buoyancy frequency

2014 ◽  
Vol 1 (1) ◽  
pp. 269-315
Author(s):  
J. P. McHugh
Keyword(s):  
Wave Packet ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Transmitted Waves ◽  
The Mean ◽  
Induced Currents ◽  
Wave Induced ◽  
The Waves

Abstract. Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyance frequency approximately modelling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equation for the reflected packet, while the equation governing transmitted waves is only coupled at the interface. Solutions are obtained numerically. The results indicate that the waves create a mean flow that is strong near and underneath the interface, and discontinuous at the interface. Furthermore, the mean flow has an oscillatory component with a vertical wavelength that decreases as the wave packet interacts with the interface.

scholarly journals Incidence and reflection of internal waves and wave-induced currents at a jump in buoyancy frequency

2015 ◽  
Vol 22 (3) ◽  
pp. 259-274 ◽  
Author(s):  
J. P. McHugh
Keyword(s):  
Wave Packet ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Transmitted Waves ◽  
The Mean ◽  
Induced Currents ◽  
Wave Induced ◽  
The Waves

Abstract. Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyancy frequency approximately modeling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equation for the reflected packet, while the equation governing transmitted waves is only coupled at the interface. Solutions are obtained numerically. The results indicate that the waves create a mean flow that is strong near and underneath the interface, and discontinuous at the interface. Furthermore, the mean flow has an oscillatory component that can contaminate the wave envelope and has a vertical wavelength that decreases as the wave packet interacts with the interface.

On internal gravity waves in an accelerating shear flow

1978 ◽  
Vol 88 (4) ◽  
pp. 623-639 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Gravity Waves ◽  
Phase Distribution ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Initial Energy ◽  
Constant Density ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Waves

The investigation of the effects which a changing mean flow has on a uniform train of internal gravity waves (Thorpe 1978a) is continued by considering waves in a uniformly accelerating stratified plane Couette flow with constant density gradient. Experiments reveal a change in the mode structure and phase distribution of the waves, and their eventual breaking near the boundary where the mean flow is greatest, the phase speed of the waves being positive. A linear numerical model is devised which accurately describes the waves up to the onset of their breaking, and this is used to investigate their energetics. The working of the Reynolds stress against the mean velocity gradient results in a very rapid transfer of energy from the waves to the mean flow, so that by the time breaking occurs only a small fraction of their initial energy remains for possible transfer into potential energy of the fluid.The consequences have important applications in oceanography and meteorology, to flow stability and flow generation, and explain some earlier laboratory observations.

Interaction of finite-amplitude waves with vertically sheared current fields

2009 ◽  
Vol 627 ◽  
pp. 179-213 ◽  
Author(s):  
OKEY G. NWOGU
Keyword(s):  
Free Surface ◽  
Transport Equation ◽  
Gravity Waves ◽  
Modulational Instability ◽  
Surface Boundary ◽  
Mean Flow ◽  
Vorticity Field ◽  
Time Step ◽  
Vorticity Transport ◽  
Wave Induced

A computationally efficient numerical method is developed to investigate nonlinear interactions between steep surface gravity waves and depth-varying ocean currents. The free-surface boundary conditions are used to derive a coupled set of equations that are integrated in time for the evolution of the free-surface elevation and tangential component of the fluid velocity at the free surface. The vector form of Green's second identity is used to close the system of equations. The closure relationship is consistent with Helmholtz's decomposition of the velocity field into rotational and irrotational components. The rotational component of the flow field is given by the Biot–Savart integral, while the irrotational component is obtained from an integral of a mixed distribution of sources and vortices over the free surface. Wave-induced changes to the vorticity field are modelled using the vorticity transport equation. For weak currents, an explicit expression is derived for the wave-induced vorticity field in Fourier space that negates the need to numerically solve the vorticity transport equation. The computational efficiency of the numerical scheme is further improved by expanding the kernels of the boundary and volume integrals in the closure relationship as a power series in a wave steepness parameter and using the fast Fourier transform method to evaluate the leading-order contribution to the convolution integrals. This reduces the number of operations at each time step from O(N2) to O(NlogN) for the boundary integrals and O[(NM)2] to O(NlogN) for the volume integrals, where N is the number of horizontal grid points and M is the number of vertical layers, making the model an order of magnitude faster than traditional boundary/volume integral methods. The numerical model is used to investigate nonlinear wave–current interaction in depth-uniform current fields and the modulational instability of gravity waves in an exponentially sheared current in deep water. The numerical results demonstrate that the mean flow vorticity can significantly affect the growth rate of extreme waves in narrowband sea states.

scholarly journals Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction

2009 ◽  
Vol 627 ◽  
pp. 161-178 ◽  
Author(s):  
MAURIZIO QUADRIO ◽  
PIERRE RICCO ◽  
CLAUDIO VIOTTI
Keyword(s):  
Drag Reduction ◽  
Travelling Waves ◽  
Phase Speed ◽  
Travelling Wave ◽  
Wall Turbulence ◽  
Energetic Efficiency ◽  
Friction Drag ◽  
Mean Flow ◽  
The Waves ◽  
Spanwise Velocity

Waves of spanwise velocity imposed at the walls of a plane turbulent channel flow are studied by direct numerical simulations. We consider sinusoidal waves of spanwise velocity which vary in time and are modulated in space along the streamwise direction. The phase speed may be null, positive or negative, so that the waves may be either stationary or travelling forward or backward in the direction of the mean flow. Such a forcing includes as particular cases two known techniques for reducing friction drag: the oscillating wall technique (a travelling wave with infinite phase speed) and the recently proposed steady distribution of spanwise velocity (a wave with zero phase speed). The travelling waves alter the friction drag significantly. Waves which slowly travel forward produce a large reduction of drag that can relaminarize the flow at low values of the Reynolds number. Faster waves yield a totally different outcome, i.e. drag increase (DI). Even faster waves produce a drag reduction (DR) effect again. Backward-travelling waves instead lead to DR at any speed. The travelling waves, when they reduce drag, operate in similar fashion to the oscillating wall, with an improved energetic efficiency. DI is observed when the waves travel at a speed comparable with that of the convecting near-wall turbulence structures. A diagram illustrating the different flow behaviours is presented.

Vertical Profiles of the Wave-Induced Airflow above Ocean Surface Waves

2018 ◽  
Vol 48 (12) ◽  
pp. 2901-2922 ◽  
Author(s):  
Laurent Grare ◽  
Luc Lenain ◽  
W. Kendall Melville
Keyword(s):  
Southern California ◽  
Phase Speed ◽  
Critical Layer ◽  
Wave Age ◽  
Ocean Surface Waves ◽  
Sonic Anemometers ◽  
Mean Wind Speed ◽  
The Mean ◽  
Wave Induced ◽  
The Waves

AbstractAn analysis of coherent measurements of winds and waves from data collected during the ONR Southern California 2013 (SoCal2013) program from R/P FLIP off the coast of Southern California in November 2013 is presented. An array of ultrasonic anemometers mounted on a telescopic mast was deployed to resolve the vertical profile of the modulation of the marine atmospheric boundary layer by the waves. Spectral analysis of the data provides the wave-induced components of the wind velocity for various wind-wave conditions. Results show that the wave-induced fluctuations depend both on the spectral wave age and the normalized height , where c is the linear phase speed of the waves with wavenumber k and is the mean wind speed measured at the height z. The dependence on the spectral wave age expresses the sensitivity of the wave-induced airflow to the critical layer where . Across the critical layer, there is a significant change of both the amplitude and phase of the wave-induced fluctuations. Below the critical layer, the phase remains constant while the amplitude decays exponentially depending on the normalized height. Accounting for this double dependency, the nondimensionalization of the amplitude of the wave-induced fluctuations by the surface orbital velocity collapses all the data measured by the array of sonic anemometers, where a is the amplitude of the waves.

Drift and deformation of oil slicks due to surface waves

2009 ◽  
Vol 620 ◽  
pp. 313-332 ◽  
Author(s):  
K. H. CHRISTENSEN ◽  
E. TERRILE
Keyword(s):  
Remote Sensing ◽  
Theoretical Model ◽  
Remote Sensing Data ◽  
Mean Flow ◽  
Horizontal Deformation ◽  
Oil Slick ◽  
Damping Rate ◽  
The Mean ◽  
Wave Induced ◽  
The Waves

We present a theoretical model for the wave-induced drift and horizontal deformation of an oil slick. The waves and the mean flow are coupled through the influence of the mean flow on the concentration of slick material, which in turn determines the damping rate of the waves and hence the transfer of momentum from the waves to the mean flow. We also briefly discuss a simplified version of the model that can be used when remote sensing data are available. With this simpler model the wave-induced forcing of the mean flow is obtained directly from observations of the wave field, hence knowledge of any specific slick properties is not required.

scholarly journals Langmuir circulations beneath growing or decaying surface waves

2002 ◽  
Vol 469 ◽  
pp. 317-342 ◽  
Author(s):  
W. R. C. PHILLIPS
Keyword(s):  
Growth Rate ◽  
Free Surface ◽  
Surface Waves ◽  
Wind Wave ◽  
Similarity Solutions ◽  
Base Flow ◽  
Wave Conditions ◽  
Langmuir Circulations ◽  
The Waves ◽  
Base Flows

The instability to longitudinal vortices of two-dimensional density-stratified temporally evolving wavy shear flow is considered. The problem is posited in the context of Langmuir circulations, LCs, beneath wind-driven surface waves and the instability mechanism is generalized Craik–Leibovich, either CLg or CL2. Of interest is the influence of non-stationary base flows on the instability according to linear theory. It is found that the instability is described by a family of similarity solutions and that the growth rate of the instability, in non-stationary base flows, is doubly exponential in time, although the growth rate reduces to exponential when the base flow is stationary. An example is given for weakly sheared wind-driven flow evolving in the presence of growing irrotational surface waves. Waves aligned both with the wind and counter to it are considered, as is the role of stratification. Antecedent to the example is an initial value problem posed by Leibovich & Paolucci (1981) for neutral waves in slowly evolving shear. Here, however, the waves and shear may grow (or decay) at rates comparable with the LCs. Furthermore the current here has two components: a wind-driven portion due to the wind stress applied at the free surface and a second due to the diffusion of momentum due to the wave-amplitude-squared free-surface stress condition. Using the case for neutral waves in non-stratified uniform shear for reference, it is found, in general, that growing waves are stabilizing while decaying waves are destabilizing to the formation of LCs, although the latter applies only for sufficiently large spanwise spacings and is subject to a globally stable lower bound. Decaying waves in the absence of wind can also be destabilizing to LCs. When the wind is counter to the waves, however, only decaying waves are unstable to LCs. Furthermore, while growing waves are stable to the formation of LCs in the presence of stable stratification, decaying waves are unstable in both aligned and opposed wind-wave conditions. Unstable stratification on the other hand, is destabilizing to LCs for all temporal waves in both aligned and opposed wind-wave conditions.

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