Abstract
Abstract. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.
Highlights
For over a century, geoscientists have invoked the principles of dynamical similarity (e.g. Douglas and Gasiorek, 2000) and geometrical similarity in order to study planetary atmospheres and oceans indirectly in the laboratory
We describe the development of a numerical model for simulating fluid flows in the multi-layer rotating annulus
We choose to apply these conditions in QUAGMIRE, except that the latter condition leads to an ill-posed PPV inversion for the special case of n=0 and m=bt, as we will see
Summary
Geoscientists have invoked the principles of dynamical similarity (e.g. Douglas and Gasiorek, 2000) and geometrical similarity in order to study planetary atmospheres and oceans indirectly in the laboratory. The main benefits of laboratory experiments are that they are under the complete control of the operator; that global highresolution measurements may be taken; and that controlled experiments may be repeated as many times as required None of these statements holds when the atmosphere and oceans are studied directly. At around the same time, Vettin (1884) was probably the first to exploit dynamical similarity by carrying out rotating laboratory experiments as analogues of geophysical flows. He studied the surface flow in a rotating dishpan of fluid with a lump of ice near the centre, representing a polar ice cap, and he drew meteorological conclusions from his results (to the scorn of his contemporaries).
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