Generation of Vertical Fine Structure by Internal Waves in a Shear Flow
Open Journal of Fluid Dynamics
The generation of vertical fine structure by inertia-gravity internal waves in a two-dimensional stratified shear flow is investigated. In the linear approximation, the boundary value problem for the amplitude of the vertical velocity of internal waves has complex coefficients, the imaginary part of which is small. The wave frequency and the eigenfunction of the boundary problem for the internal waves are complex (and we show that a weak damping of the wave occurs). The phase shift between the
... shift between the fluctuations of density and vertical velocity differs from π/2; therefore, the wave-induced vertical mass flux is non-zero. It is shown that dispersion curves are cut off in the low-frequency domain due to the influence of critical layers, where the frequency of the wave with the Doppler shift is equal to the inertial one. The Stokes drift velocity is determined in the weakly nonlinear approximation, on the second order in the amplitude of the wave. The vertical component of the Stokes drift velocity is also non-zero and contributes to wave transfer. The summary wave mass flux exceeds the turbulent one and leads to irreversible deformation of the average density profile which can be interpreted like a fine structure generated by the wave. On the shelf, this deformation is more than in deep-water part of the Black Sea at the same amplitude of а wave. The vertical scale of the fine structure of Brunt-Väisälä frequency, generated by a wave, corresponds to really observed value.