PHYSICAL MATHEMATICS SEMINAR



TITLE:		HORIZONTAL CONVECTION AND 
		THE CHOKING OF CASCADES

SPEAKER:	NEIL BALMFORTH
		DEPARTMENT OF APPLIED MATHEMATICS AND
		STATISTICS UNIVERSITY OF CALIFORNIA, SANTA CRUZ

ABSTRACT:

A widely held view in oceanography is that it is `inefficient' to rive motion by heating and cooling
a fluid at the same level. This idea stems from `Sandstrom's Theorem,' an argument made a century
ago which states that motion cannot be sustained if the source of heating lies above the source of 
cooling, and Sandstrom performed experiments that appeared to confirm this idea. Shortly thereafter,
Jeffreys showed that Sandstrom's result could not be correct, since motion always ensues due to the 
horizontal pressure gradients induced by the temperature contrast. Instead, Jeffreys suggested that 
motion, though present, simply became feeble in the limit that heat diffused slowly. I present several
recent results on the issue for a fluid with a non-uniform temperature imposed on the upper surface.
This is a crude idealization of the ocean, and is sometimes referred to as horizontal convection. The 
salient result is that there cannot be a turbulent cascade of energy in the sense of Kolmogorov (the 
second experimental law of turbulence' as christened by several authors is not satisfied). The physical 
interpretation is that the temperature difference that drives convection must diffuse into the fluid from
the boundary. In the absence of diffusion, the thermal forcing, and therefore the cascade, becomes 
choked. The choking of cascades arises in a number of physical settings, including the stirring and
mixing of a passive tracer introduced or removed through the boundaries.

TUESDAY, NOVEMBER 5, 2002
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