Numerical Study of Baroclinic Wave Dynamics and Plume Behavior in Rotating Rectangular Annulus
Researchers report numerical simulations of a rotating rectangular annulus with localized heated plume forcing, finding that baroclinic wave mode selection and plume regime are governed by largely independent parameters. The study uses OpenFOAM finite-volume simulations across a range of Richardson and Rossby numbers, identifying geostrophic-hydrostatic balance as the dominant bulk state and characterizing wave transitions and plume morphology. The findings offer a cleaner framework for understanding rotating stratified flows relevant to atmospheric and oceanic dynamics by isolating bulk behavior from Ekman-layer effects.
A preprint submitted to Physics of Fluids presents numerical simulations of a rotating rectangular annulus designed to isolate the Ekman-free bulk region of the classical cylindrical baroclinic annulus, forced by a cooled inner wall and a localized heated plume at the outer bottom. Simulations span source Richardson numbers of Ri₀ = 99, 4, and 1 and Rossby numbers of Ro = 0.3, 0.1, and 0.07, with momentum budget analysis confirming geostrophic-hydrostatic balance as the leading-order state. Baroclinic wave modes shift from m=2 at Ro=0.3 to m=3 at lower Ro, consistent with contraction of the Eady deformation radius, while Complex Empirical Orthogonal Function analysis detects a Hopf-bifurcated vacillating state at Ri₀=99, Ro=0.1. Plume morphology transitions from weak, laterally-swept structures at high Ri₀ to sustained columnar plumes at Ri₀ ≤ 4, with the plume entrainment coefficient showing opposite rotational sensitivities at low versus high Ri₀, organized through a local plume Rossby number. A mixing-length argument predicts turbulent heat flux scaling as Ri₀^(-1/2), implying an order-of-magnitude enhancement from Ri₀=99 to Ri₀=1, in agreement with simulation results. The central finding is that within the explored parameter range, the plume-regime and wave-selection problems are approximately separable: Ri₀ controls plume behavior while Ro selects the dominant baroclinic wave mode.
What's missing
As a preprint not yet peer-reviewed, the results have not undergone formal external validation. The study is limited to a rectangular annulus geometry and a specific range of Ri₀ and Ro values, so the separability result may not generalize to wider parameter spaces, three-dimensional cylindrical geometries, or flows with active Ekman layers. The authors do not address how the localized plume forcing compares quantitatively to distributed heating scenarios relevant to geophysical applications.
What different sources said
- arXiv physicsCenter
Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume
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