PHYSICAL MATHEMATICS SEMINAR

TITLE:		ROTATING HYDRAULICS AND UPSTREAM BASIN CIRCULATION


SPEAKER:	KARL HELFRICH
		WOODS HOLE OCEANOGRAPHIC INSTITUTE

ABSTRACT: 

Flow in the abyssal oceans is often constrained to pass through narrow gaps, or over sills, 
which connect larger sub-basins (e.g., Faroe Bank Channel, Denmark Strait). These gaps 
are important for a number of reasons, not least of which is that they provide ideal locations
for monitoring the deep circulation. The topic of rotating hydraulics (e.g., Gill, 1977, JFM 80)
was developed to provide a theoretical basis for understanding such flows. However, the theory 
is inertial and inviscid, and the upstream basins are assumed infinite. Furthermore, the theory 
requires specification of potential vorticity of the overflowing fluid, a property that is set by the 
foring and dissipation of the upstream basin circulation, which is itself set, in part, by the hydraulic 
control in the strait. 

In this talk will discuss the coupled circulation in a finite source fed f-plane basin drained through a 
single strait. The problem is explored using a single-layer (reduced gravity) shallow water numerical 
model that resolves the hydraulic flow within the strait. The steady upstream basin circulation is found 
to be sensitive to the nature of the mass source. In contrast, the hydraulically controlled flow in the
strait is nearly independent of the basin circulation and agrees very well with the Gill theory solution
obtained using the numerically determined average potential vorticity in the strait entrance region. The 
coupled basin-strait system is shown to select an average overflow potential vorticity corresponding to
the Gill solution with maximum fluid depth on the strait boundaries. This state also corresponds to one 
of maximal upstream basin potential energy. This potential vorticity control is yet another manifestation 
of the upstream influence characteristic of hydraulic control. The significance of the non-unique relation 
between basin conditions and overflow transport with regard to deep overflow transport monitoring will 
be discussed.


TUESDAY, MARCH 4, 2003  
2:30 pm
Building 2, Room 338

Refreshments will be served at 3:30 PM in Room 2-349
                       

Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA  02139