Deep Planetary Circulation and Topography: Simple Models of Midocean Flows

Abstract

The presence of broad, flowing water masses in the deep ocean requires dynamical explanation. Vertical density diffusion and?-effect are invoked in classical theories; here we show how topographic potential vorticity can control broad baroclinic flows with diffusion playing a secondary role. The theory and numerical experiments involve a zonal flow over topography, such as one finds in the Southern Ocean, although similar effects occur in source-sink flows at middle latitudes. A 1½ layer model (that is, one active deep layer beneath a thick upper layer) of the deep circulation shows intense interactions with both small-scale O(500 km wide) and Large-scale O(2500 km wide) seafloor slopes. Broad, gentle slopes can block an initially uniform flow, expelling the circulation to an outer rim (defined by hyperbolic characteristics) where it forms into jets. With smaller-scale topography, planetary-scale flow encountering a midocean ridge develops transient distortions of the flow and density fields, which convert large-scale potential energy to kinetic energy. These distortions move up- or downstream from the topography, leaving a bound vortex permanently over the topography. The ?free? and ?bound? circulations are connected by a long ridge or trough in dynamic height, which is the site of intense jets. These features become permanent with dissipation. Small-amplitude theory resembles classic open-channel hydraulics, yet at topographic heights of only, say, 300 m and mean flow speeds of O(0.01 m s?1) one is already in a large-amplitude, nonlinear regime. Above the topography the characteristics of the wave equation form closed curves, preventing upstream boundary conditions from determining the solution there. Instead, the density interface winds into a tight spiral, with perturbation energy growing as t2. This resembles a form of shear dispersion, yet the shearing field is the group velocity rather than the fluid velocity; a theoretical calculation of the process is given, and the connection is made between energy increase in the flow and the pressure drag on the topography. The 1½ layer model exaggerates some time-dependent aspects of baroclinic adjustment. Two kinds of blocking occur, in which permanent flow and distortion of the density field are transmitted far downstream or upstream. First, the nondiffusive problem is governed by hyperbolic characteristics in (x, y, t) which can be ?reflected? from a seafloor ridge or trough, either due to shear in the upstream flow or due to the secular change in Rossby wavespeed with latitude. Second, at bounding or stagnation characteristics, dissipative terms can send a block far from the topography. Blocking occurs at infinitesmal ridge height when there is a critical characteristic intersecting the topography. Ridges even of O(300 m) in height can completely block the oncoming flow, for example sending an eastward zonal flow back to the west at a higher latitude. Elongated gyres of circulation way result, reaching far from the topography.