Bottom boundary currents in rotating beta plane source-sink experiments

Bottom boundary currents in rotating beta plane source-sink experiments

By

R. Krishnamurti and T. N. Krishnamurti

Florida State University

            A large number of source-sink experiments were conducted on a rotating laboratory basin with bottom topography simulating the earth's beta effect.  With source in the northeast boundary and sink anywhere along the southern boundary, and for various configurations of fluid stratification from homogeneous fluid to two-layer double diffusive, we found always a prominent bottom boundary current from eastern source to western boundary current which was an order of magnitude deeper than the Ekman layer thickness expected from linear theory.  This paper is on the nonlinear modification of that theory.

            The motivation for these experiments was to learn physical processes that govern mixing when fresh river water from an estuary flows into a basin of saline sea water.  In the Bay of Bengal a relatively fresh layer some tens of meters deep and salinity 33-34 psu lies over the more saline 35 psu seawater, for nearly the entire surface from 20° N to the equator.  Such stratification in the upper layer ocean is crucial in inhibiting vertical mixing, so that solar heating remains in the surface layers undiluted by mixing with deeper cold water.  Thus this stratification is of primary importance for cyclone and depression formation in the atmosphere above the Bay of Bengal.

            In the nonlinear governing equation for a homogeneous fluid the advection term  •  is approximated by _o •  (Oseen approximation) where U_o will be determined by relating it to source strength Q (volume per time) via W_o in a similar process in the sidewall boundary layer.  The dimensionless parameters are Rossby number  and Ekman number E where

U_o/f L,     

f is the rotation frequency, L a characteristic length scale,  the kinematic viscosity.  A boundary layer analysis is performed for small E and any , with stretching the boundary layer coordinate ϛ = E^az.  Distinguished exponents a can be found for certain relations between   and E, such as  ~ E^1/2.  This distinguished exponent gives, for our experiment parameters, a ten times deeper layer than the classical Ekman layer depth.  A similar Oseen approximation in the sidewall gives the vertical flux (related to the imposed Q) which is then equated to the horizontal flux thus relating U_o to Q.

            This research was funded by a grant from the Monsoon Mission.