Some Asymptotic and Experimental Results for a Rotating Differentially Heated Annulus

Applied Math

In the past few decades, the increasing power and availabilty of computers has caused a shift in experimental fluid dynamics away from the laboratory and onto the desktop. While the importance of computation cannot be disputed, many relatively simple fluids problems defy brute-force computation because of spatio-temporal resolution challenges. Real world experiments still offer insights and closer connection to geophysical situations. Asymptotic modeling also offers a pathway to investigating flows of geophysical interest. We outline an asymptotic reduction of the Navier-Stokes equations for a tall aspect ratio annular geometry under rapid rotation. These equations differ from the classical "Narrow-Gap" approximation by restricting the gap width to O(1), thus retaining the effects of curvature. Some basic properties of the reduced pde's are discussed. We present laboratory results of an experiment designed with these geometric restrictions in mind.