General problems of the internal gravity waves linear theory

Details General problems of the internal gravity waves linear theory General problems of the internal gravity waves linear theory

2006-09-26

arxiv.org/abs/physics/0609236v2

Physics

Fluid Dynamics

52 pages

Scientific paper

The internal gravity waves are the oscillations present in the gravitational field of the stratified medium, that is the mediums which density raises with the depth change. If the equilibrium state of the component volume of this medium is disturbed, for example, upward, then it will become more heavy, than the medium surrounding it, and Archimedian forces will cause its motion back to its equilibrium position . The main parameter of any oscillation system is the oscillation frequency, and it is determined by the ratio of two factors - the restoring forces seeking to return the disturbed system to its equilibrium position and the inertial forces. For the internal waves the restoring forces are proportional to the vertical gradient of density of the liquid, and the inertial forces are proportional to the density itself. The oscillating frequency typical for the internal gravitational waves is the value N(z)=({-g/ro(z)}* {d{ro(z)}/d{z}})^{-1/2} called the buoyancy frequency or Brunt-Vaisala frequency. Here ro(z) - the density as the function of the depth z, g - the acceleration of the gravity, the sign "-" originates due to the fact, that the density raises with the increasing depth and consequently {d{ro}/dz}<0. The paper has considered the planar internal gravitational waves in the exponentially stratified medium, that is in the medium with the constant distribution of Brunt-Vaisala frequency in depth, analyzed the problem of the waves reflection from the planar boundaries, defined the Green's function for the equation of the internal gravity waves in the exponentially stratified medium of the of the endless depth, and also outlined the information on the main properties of the internal gravity waves in the stratified layer of the terminated depth and in the stratified mediums with average shift streams.

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