The Non-Linear Response of a Two-Layer, Baroclinic Ocean to a Stationary, Axially-Symmetric Hurricane. Part II. Upwelling and Mixing Induced by Momentum Transfer

Abstract

This study is concerned with the theoretical description of upwelling induced in & str&tified, rot&ting, twG-l&yer oce&n by momentum transfer from &n intense st&tion&ry, axi&1ly-symmetric &tmospheric vortex. The dyn&mic intema.l response of the ocean is assumed to be ui&lly-symmetric which permits consideration of the solution in two independent vari&bles, radial dist&nce and time. NumeriC&1 integmtion vi& the method of characteristics is utilized to obtain v&lues of radial velocity, tangenti&l velocity, &nd depth of the upper I&yer for & period of two d&ys. Transfer of momentum between the air &nd the se& &nd between the upper and lower layers &re allowed. Transfer of he&t and moisture with the atmosphere is not considered. A general model is derived which le&ds to a hier&rchy of models of increasing complexity. The detailed solution of the first of these is illustrated. Results agree qualitatively with observ&tions taken in the Gulf of Mexico following hurricane BUda, 1964. Intense upwelling is confined to within twice the radius of maximum winds. The displaced warm central waters produce some downwelling adjacent to the upwelled region. The degree of upwelling is time-dependent &nd the hurricane-force winds must act on the ocean for several hours before significant upwelling occurs. The model indic&tes a strong coupling of the radially prop&g&Ung intema.l w&ve mode &nd the vortex mode of the system. This coupling confines the signiDcant intema.l disturbances to within the wind-forced region. pheric turbulent shear stresses are prescribed. TranSfer of momentum between the air and sea and between the upper and lower layers is included. However, transfer of sensible heat or latent heat between the model ocean and the atmosphere is not considered. An initial state of rest is stipulated for the laterally-infinite, homogeneous ocean layers. Within this framework, it is possible to consider a hierarchy of models of increasing complexity which can be studied separately. The present paper includes the development of the general model and describes the detailed solution of one specific model. This model permits momentum transfer between the air and the sea as well as between the t"f!o ocean layers. A sUbsequent paper will describe a similar model which considers the additional effect of turbulent mixing of heat and salt between the ocean layers. This second paper will also compare various energy integrals of the two models: This investigation was inspired by observations taken by Leipper (1967) who reported an observed decrease of over 5C of sea surface temperature in an area of 15,(XK) mi2 following the passage of hurricane Hilda, 1964, in the central Gulf of Mexico. He disPlayed vertical sections perpendicular to, the hurricane's path which when compared to undisturbed sections, showed the changes in temperature and salinity which appeared