Laboratory Studies of Coherent Structures in Quasi - Flows

Computer Science

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Vortices, Jets

Scientific paper

Laboratory experiments were conducted in a large, rapidly rotating annulus of fluid. Low Rossby and Ekman numbers, 0.1 and 10^{-5} respectively, were achieved while maintaining large Reynolds number (greater than 10^4). The apparatus had a flat lid and conical bottom (slope s = -0.1) to mimic the planetary beta-effect. Motion was forced with six source-sink pairs, distributed symmetrically in a ring in the bottom of the tank. Two primary flow states were studied: marginally stable westward and eastward jets. Westward jets tended to be wide, and developed a central region of strong shear with quasi-uniform potential vorticity. Elliptical vortices of the same sign as the shear always formed. Due to design limitations, only cyclonic vortices were produced. Multiple vortex states were found for relatively narrow jets when the inertial time scale was comparable to the Ekman time scale. At increasingly shorter inertial time scale, produced with stronger forcing, the number of vortices decreased from a maximum of 5 to 1. The multiple vortex states were essentially laminar, inspite of their high Reynolds number; the single vortex state was turbulent, producing many small vortices that merged with the main vortex. The broad region of quasi -uniform potential vorticity was considered necessary for the formation of a single robust vortex. These vortices had many properties in common with vortices found on the large gaseous planets. Eastward jets tended to be narrow and exhibited Rossby wave instability. The number of waves was fairly well predicted by linear theory, except for the low forcing situation, when the pumping geometry strongly influenced the instability. Potential vorticity was quasi-uniform on either side of the jet, with a strong gradient in the jet center. This gradient was a strong barrier to particle transport. A Hamiltonian model of the flow demonstrated the presence of a robust invariant surface at the jet center, with large chaotic seas on either side. The similarity between experiment and the numerical model suggest insight might be gained into the dynamics of real planetary flows, such as the Jet Stream or the Antarctic Circumpolar Current, using the techniques of Hamiltonian mechanics.

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