A model for eastward and westward jets in laboratory experiments and planetary atmospheres

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Abstract
Flows in a rotating annular tank [J. Sommeria, S. D. Meyers, and H. L. Swinney, Nonlinear Topics in Ocean Physics, edited by A. Osborne (North Holland, Amsterdam, 1991); Nature (London) 337, 58 (1989); T. H. Solomon, W. J. Holloway, and H. L. Swinney, Phys. Fluids A 5, 1971 (1993); J. Sommeria, S. D. Meyers, and H. L. Swinney, Nature (London) 331, 689 (1989)] with a sloping bottom (that simulates a barotropic atmosphere’s Coriolis force with a topographic β -effect [J. Pedlosky, Geophysical Fluid Dynamics, 2nd ed. (Springer, Berlin, 1986)]) produce eastward and westward jets, i.e., azimuthal flows moving in the same or opposite direction as the annulus’ rotation. Flows are forced by pumping fluid in and out of two concentric slits in the bottom boundary, and the direction of the jets depends on the direction of the pumping. The eastward and westward jets differ, with the former narrow, strong, and wavy. The jets of Jupiter and Saturn have the same east–west asymmetry [P. S. Marcus, Ann. Rev. Astron. Astro. 431, 523 (1993)]. Numerical simulations show that the azimuthally-averaged flow differs substantially from the non-averaged flow which has sharp gradients in the potential vorticity q . They also show that the maxima of the eastward jets and Rossby waves are located where the gradients of q are large, and the maxima of the westward jets and vortex chains are located where they are weak. As the forcing is increased the drift velocities of the two chains of vortices of the eastward jet lock together; whereas the two chains of the westward jet do not. Inspired by a previously published, [P. S. Marcus, Ann. Rev. Astron. Astro. 431, 523 (1993)] piece-wise constant- q model of the Jovian jets and based on numerical simulations, a new model of the experimental flow that is characterized by regions of undisturbed flow and bands of nearly uniform q separated by sharp gradients is presented. It explains the asymmetry of the laboratory jets and quantitatively describes all of the wave and vortex behavior in the experiments including the locking of the vortex chains of the eastward jet. The simulations and new model contradict the predictions of a competing, older model of the laboratory flow that is based on a Bickley jet; this raises concerns about previous calculations of Lagrangian mixing in the laboratory experiments that used the Bickley model for the fluid velocity. The new model, simulations and laboratory experiments all show that jets can be formed by the mixing and homogenization of q . The relevance of this to the jets of Jupiter is discussed.