FY 1975

Multimode long wave transport in irregular basins

González, F.I.

Hawaii Institute of Geophysics, HIG-75-9, 201 pp (1975)

A generalized separation of variables technique known as multimoding is used to treat the partial differential equations governing time-harmonic, long wave oscillations in two-port basins. First, biorthogonal eigenfunction expansions are used to represent the surface elevation at each cross section of the basin (each eigenfunction in the expansion is interpreted as a spatial mode of the oscillation). Then the mode-amplitude coefficients of the expansion are found to be governed by a vector differential equation which evolves along the basin axis. The multimode approach thus reduces the original two-dimensional problem into a series of one-dimensional problems in the transverse and longitudinal directions, respectively. The second order multimode equations are next decomposed into a set of coupled first order equations for the left- and right-moving components of each mode (the two-flow decomposition). To accomplish the decomposition, it is necessary to take the square root of the wave-number matrix. This problem is resolved by introducing the notions of eigenfunction matrices (their special properties are developed and exploited in order to render the matrix diagonal). With the decomposition completed, Riccatian differential equations for the reflectance and transmittance scattering matrices are forthcoming, and transport techniques may therefore be applied to problems of general basin responses to external excitation.