Generation of internal tides by an oscillating background flow along a corrugated slope

Abstract

The process of internal wave generation by the interaction of an oscillatory background flow (U0 cos (ω0t), V0 sin (ω0t), W0 sin (ω0t)) over a uniform slope is investigated. The stratification is assumed to be uniform and the fluid of infinite depth. Analytical solutions are obtained which give the energy flux in the radiating internal wave field. Since waves are generated not only at the fundamental frequency ω0, but also at all the harmonic frequencies less than the buoyancy frequency, the energy flux for both low and high frequency waves is considered. The acoustic limit approximation (the limiting case in which the tidal excursion, U0/ω0, is much less than the scale of the topography) gives a reasonable approximation to the energy flux.

Conservation laws and invariant solutions of the non-linear governing equations associated with a thermodynamic model of a rotating detonation engines with Korobeinikov׳s chemical source term

“…The gas then expands azimuthally and axially, and is either subsonic or supersonic (or both), depending on the back pressure at the outlet plane. Similarly to our previous studies in [5] and [9], where the dynamics of small perturbations of a certain class of stationary exact solutions to the nonlinear governing equations of geophysical stratified fluid motion in a cylindrical wave field was investigated, the flow in RDE has a very strong circumferential aspect [23]. However, unlike in [5], where a such flow was in virtue of stratification and the effects of rotation due to Coriolis force, for RDE, a such circumferential aspect is due to detonation wave propagation ( [25] ).…”

“…Similar to our approach in [5], since for RDE, the radial dimension is typically small compared to the azimuthal and axial dimension, we shall neglect the radial dependence in our modeling, which allows the RDE to be unrolled into two dimensional flow. Another similar approach for describing the dynamics of weakly nonlinear waves for compressible inviscous flows rotating in an annular ring has been developed in [9] and [8] for stratified and homogeneous fluids (see [7]; [6]; [10] ).…”

Symmetries and Conservation Laws of a Spectral Nonlinear Model for Atmospheric Baroclinic Jets

“…Similar undulations are also found in the ocean on eastward currents such as the Gulf Stream in the north Atlantic ( [4], [5], [6]). A typical wavelength of these disturbances is observed to be of the order of the internal Rossby radius, that is about 4000 km in the atmosphere and 100 km in the ocean.…”

Internal gravity wave beams as invariant solutions of Boussinesq equations in geophysical fluid dynamics

“…Another example is an oscillatory flow over topography. In particular, time-harmonic wave beams radiating outwards from the topography with frequencies equal to that of background flow have been studied in Bell [1], Khatiwala [20] and Ibragimov [15] under different flow and boundary conditions and the topographic geometry. Within the framework of linear theory, the pressure field associated with the internal wave solution of Eqs.…”