Internal gravity waves: Analysis using the periodic, inverse scattering transform

The discrete periodic inverse scattering transform (DPIST) has been shown t o provide the salient features of nonlinear I;burier analysis for surface s hallow water waves whose dynamics are governed by the Korteweg-de Vries (Kd V) equation - (1) linear superposition of components with power spectra tha t are invariants of the motion of nonlinear dispersive waves and (2) nonlin ear filtering. As it is well known that internal gravity waves also approxi mately satisfy the KdV equation in shallow stratified layers, this paper in vestigates the degree to which DPIST provides a useful nonlinear spectral a nalysis of internal waves by application to simulations and wave tank exper iments of internal wave propagation from localized dense disturbances. It i s found that DPIST analysis is sensitive to the quantity lambda = r/6s epsi lon/mu(2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the d imensionless squared wavenumber. Each separate wave component of the decomp osition of the initial disturbance can have a different lambda value, and t hus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accid ental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.