Hurricane-Generated Depth-Averaged Currents and Sea Surface Elevation

Abstract

A theory of the depth-averaged currents and sea surface elevation generated by a moving hurricane in a stratified ocean with flat bottom is presented. Using a scale analysis of the depth-integrated momentum and continuity equations, it is found that the depth-averaged currents are nearly nondivergent and determined entirely by the wind stress curl. Earth's rotation and ocean stratification have negligible effects. The sea surface elevation is decomposed into four physically different parts caused by geostrophic adjustment to the depth-averaged currents, wind stress divergence, inverted barometer offset, and baroclinic effects. When a hurricane moves with a uniform speed, it generates quasi-stationary, alongtrack, elongated depth-averaged currents. The sea surface elevation remaining after the hurricane passage is a combination of a trough geostrophically adjusted with the depth-averaged currents and a sea surface elevation associated with baroclinic effects. The barotropic response is analysed for different wind stress distribution. A universal nondimensional description of the depth-averaged flow is suggested, using scaling based on the maximum wind stress torque LTL and its radius L. This marks the primary difference with baroclinic responses where the radius of maximum winds, Rm, and maximum wind stress Tm are the determining scales. For all cases considered, the maximum depth-averaged current is proportional to LTL and the distance from the maximum to the storm track is proportional to L. The wind stress behavior at the hurricane's periphery is shown to be an important feature in .determining the sea surface response. Analytical solutions of approximated equations agree well with numerical simulations based on the full set of equations. It is demonstrated, using a two-layer model, that nonlinear coupling between the baroclinic and barotropic modes is rather weak, and therefore they may be calculated separately.