"Dissertation: "Experimental studies of anomalous diffusion, blocking phenomena, and two-dimensional turbulence"
ER Weeks, December 1997.

We study three problems which have been studied theoretically, but problems for which little or no experimental work has been done: anomalous diffusion leading to enhanced mixing, dynamics of atmospheric blocking patterns, and two-dimensional turbulence. Our experimental apparatus is a 1 m diameter rapidly rotating annular tank filled with fluid. The Coriolis force constrains the fluid flow inside the tank to be nearly two-dimensional.

The first problem studied is mixing in a simple flow. Usually, mixing is describable by diffusion: dye in fluid spreads, with the typical size of the dye spot growing as ~sqrt(Dt) with diffusion constant D. We examine flows with jets carrying tracer particles long distances. Ensembles of tracer particles grow in size as ~ t^h with h>1/2 (D=infinite). In our experiments, this anomalous diffusion is due to Levy flights: the mean square time spent in a jet before being trapped in a vortex is infinite. This is the first direct experimental observation of Levy flights. Our experiments suggest that jet structures in general may lead to anomalous diffusion. We also study a model which determines circumstances which produce anomalous diffusion.

The origin of atmospheric blocking in the Northern Hemisphere is our second problem. Normally mid-latitude weather is determined by the zonal flow of the jet stream, but several times each winter this flow is diverted poleward by a blocking vortex, which lasts several weeks. Models have proposed that blocking patterns are due to interactions of the zonal flow with the Rockies and Alps. We place two ridges on the bottom of our tank; by forcing a zonal flow across the ridges we observe blocking and zonal patterns. These are the first experimental observations of such patterns. The experiments also find a broad parameter range for which the flow intermittently switches between zonal and blocked, as is observed for the atmosphere.

The interaction between two-dimensional (2D) and three-dimensional (3D) turbulence is our third problem. Rotating 2D turbulence is especially relevant to geophysical flows, but remains largely unexamined by experiments. The possibility of studying the transition from 2D to 3D turbulence in our apparatus is examined.