A Variable-Depth Green's Function for Shelf Edge Tides

Abstract

The Green's function for a semi-infinite ocean with depth a function of distance from the boundary is developed numerically for the M2 frequency and with Coriolis frequency and depth profile appropriate to the continental slope off the Gulf of Maine. This involves numerical integration of the linearized shallow water equations for all longshore wavenumbers, followed by numerical Fourier transformation. This variable-depth Green's function is approximately equal to Buchwald's (1971) constant-depth Green's function for distances along the boundary greater than the width of the slope, and at very short range tends to limiting values which can be approximated analytically. The Green's function, when combined with currents from Greenberg's (1979) numerical model of the Bay of Fundy and Gulf of Maine, is used to explain substantial observed variations in M2 amplitude and phase along the edge of the shelf off the Gulf of Maine; the variable-depth Green's function produces significantly better results than the constant-depth Green's function. The results support the basic premise that the M2 elevation at the shelf edge in the absence of the Gulf of Maine would be fairly constant, and suggest ways of deriving open boundary input for tidal models of coastal seas with a minimum of offshore gaging.