7 - Internal Tides

Summary

The vertical stratification of density in the ocean is illustrated and the key quantity, the buoyancy frequency, is defined. A governing set of linear equations to describe internal tides is derived, followed by an explanation of the two principal ways of solving them: the method of vertical modes and the method of characteristics. The strengths and limitations of both are discussed. Simple examples are provided for constant stratification and a three-layer system. The notions of group velocity of phase speed of internal waves (tides) are introduced. The solutions for reflection from a linearly sloping bottom is derived; an example the distribution of the steepness in ocean bathymetry is shown. Finally, an analytical solution of the generation of internal tides is given for a simple model set-up involving a small-amplitude sill; this is followed by a numerical example in a more realistic setting.