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

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

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

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.

Stocks drift and vortex instability of the potential surface wave

<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>

Approximate Stokes Drift Profiles in Deep Water

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.

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

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.