Directional spectra and eigen-solutions of vertically standing wavemodes of internal waves in shallow seas

Some approximate formulas, based on the internal- wave directional spectral model established by Schott and Willebrand (1973), of vertically standing wavemode eigenfunctions and a dispersion relation of internal waves in shallow seas are presented. An optimization method to estimate internal wave directional spectra is described and the confidence interval expression of the estimates is established. The GM spectral model of oceanic internal waves cannot be used in shallow seas (01 bers, 1983). Internal waves in shallow seas have two origins: oceanic (those generated in and propagating from the deep sea and ocean) and local (Phillips, 1977). As both reveal obvious propagation orientations, it is important to investigate the directional properties of the internal wave field. Though cross correlation function or cross-spectrum analyses can reveal the directional properties in some degree (Fang et al., 1984, and Fang, 1987), internal- wave directional spectrum analysis can further estimate the main propagation directions of wave components with different modenumbers and frequencies. So the latter is a more effective analysis tool. Because internal- wave directional spectrum analysis requires high quality data and long computer time, there are very few study reports so far on this subject. Among them. Schott and Willebrands' (1973) work is noteworthy. On the supposition, of linearization, they derived an internal- wave directional spectrum model. Internal-wave directional-spectra in shallow seas are investigated in the present study with their work as reference. Project supported by the National Natural Science Foundation of China.