An investigation of hurricane-induced forerunner surge in the Gulf of Mexico

Abstract

A system of coupled, normal mode equations describing a two-layer ocean basin of variable depth was derived from the quasi-hydrostatic equations of motion using a general form of the method of Veronis and Stommel (1956). A finite difference, time marching, numerical model for the normal mode equations, employing an Alternating Direction Implicit (ADI) scheme, on a space-staggered grid has been developed. The model is quasi-linear and allows for variable bathymetry and variable Coriolis parameter. The model domain includes the Gulf of Mexico and the Cayman Sea with a resolution of 15'. A no flow condition is taken at all solid boundaries and the inverted barometer term is used to stipulate barotropic height anomalies on the open boundaries. Hurricanes Carla (1961) and Allen (1980) are used as historical storms to verify the model by comparing numerical and observed hydrographs. A parametric study utilizing three forward speeds, two radii to maximum winds and five paths characterizing Gulf hurricanes is presented. The results of the study show that volume transports through Florida and Yucatan Straits consisted of in-phase (both in or both out) and out-of-phase components. The in-phase volume transport excites a volume mode, nG, in the Gulf of Mexico having periods of about 28 h and 3.4 days. The nG mode of oscillation can produce a forerunner surge for many storm tracks. Although all the model storms generated nG, not all had an associated positive forerunner. The hurricane path and evolution play important roles in generating a forerunner. The out-of-phase volume transport through the ports was found to produce a Gulf-wide quasi-geostrophic tilt mode of about 6.5 day period. Surges on the shelf including the forerunner are primarily a barotropic response. The quasi-linear model transmitted only a fraction of the baroclinic energy onto the shelf. Results of a limited area model (no wind in deep water) showed that either wind or pressure forcing generates nG. The limited area model simulations also demonstrate clearly that the use of a simple inverted barometer boundary condition at the shelf break will always underestimate the peak surge at the coast.