The non-linear transient response of a continuously stratified, baroclinic ocean to stationary and transitory axially-symmetric atmospheric cyclones

Abstract

Considered in the present study is the temporal and spatial theoretical description of circulation and mixing of sea water induced in an initially motionless, continuously stratified, uniformly rotating, baroclinic ocean by steady as well as transitory, axisymmetric, cyclonic atmospheric vortices. The nonlinear processes of lateral and vertical advection of momentum, heat, and salt are explicitly included in flux form in the governing hydro-thermodynamic equations. Lateral as well as vertical turbulent diffusion of momentum and thermal properties are included in gradient form, but all exchange coefficients are held constant, with assumed Prandtl numbers of unity in the respective horizontal and vertical directions. Additional pertinent constraints include Coriolis parameter, use of the hydrostatic approximation in an incompressible ocean, and imposition of the "rigid-lid" approximation along the sea surface. Changes in thermal properties across the air-sea interface are permitted, although not formally through the classical bulk aerodynamic relations. Attention is confined to an Eulerian N-level upper ocean region located above a deep and dynamically motionless reservoir. The particular cosine-profile of continuous density stratification used in the upper region to represent the ocean's permanent thermocline is not linear in vertical; distribution, which thereby permits spatial and temporal variation of the Brunt- --Väisälä frequency. The lateral velocity components are forced to zero at a large but specific horizontal distance from the region of hurricane-force winds which thus imposes an outer cylindrical wall on the stratified ocean. Time-marching numerical integration of an appropriate set of partly explicit and partly implicit finite-difference relations is used for obtaining solutions to the system of primitive equations. The various finite-difference expressions are formulated in such a manner that the prognostic variables (radial and tangential velocity as well as density anomaly) are evaluated at alternating points on a radial, vertical, and temporal staggered grid network. The diagnostic variables (vertical velocity and pressure) are accordingly evaluated at interlocking (or off-staggered) points. ...