Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume
Abstract
We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number Ri0 = 99, 4, 1 and Rossby number Ro = 0.3, 0.1, 0.07. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the x and z−momentum budgets. Baroclinic waves of mode m=2 at Ro=0.3 transition to m=3 as Ro decreases, consistent with the contraction of the Eady deformation radius Lρ= NH/f; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at Ri0 = 99, Ro = 0.1. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at Ri0 = 99 to sustained columnar plumes traversing the full baroclinic depth at Ri0 ≤ 4. The plume entrainment coefficient Γ(z) shows opposite rotational sensitivities at low and high Ri0, which we organize through a local plume Rossby number Rop = w/(2Ωb). A mixing-length argument predicts a bulk turbulent heat flux u'T'̅ ∝ Ri0−1/2, anticipating an order-of-magnitude enhancement from Ri0 = 99 to Ri0 = 1, in agreement with the simulations. A regime map in the (Ri0, Ro) plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: Ri0 sets the plume regime while Ro selects the dominant baroclinic wave mode.
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BibTeX
@misc{swarnakar2026baroclinic,
title = {{Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume}},
author = {Shivam Swarnakar and Ayan Kumar Banerjee and Sridhar Balasubramanian and Amitabh Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10386},
eprint = {2606.10386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.10386},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume
AU - Shivam Swarnakar
AU - Ayan Kumar Banerjee
AU - Sridhar Balasubramanian
AU - Amitabh Bhattacharya
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2606.10386
UR - https://arxiv.org/abs/2606.10386
AB - We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number Ri_0 = 99, 4, 1 and Rossby number Ro = 0.3, 0.1, 0.07. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the x and z−momentum budgets. Baroclinic waves of mode m=2 at Ro=0.3 transition to m=3 as Ro decreases, consistent with the contraction of the Eady deformation radius L_ρ= NH/f; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at Ri_0 = 99, Ro = 0.1. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at Ri_0 = 99 to sustained columnar plumes traversing the full baroclinic depth at Ri_0 ≤ 4. The plume entrainment coefficient Γ(z) shows opposite rotational sensitivities at low and high Ri_0, which we organize through a local plume Rossby number Ro_p = w/(2Ωb). A mixing-length argument predicts a bulk turbulent heat flux u'T'̅ ∝ Ri_0^−1/2, anticipating an order-of-magnitude enhancement from Ri_0 = 99 to Ri_0 = 1, in agreement with the simulations. A regime map in the (Ri_0, Ro) plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: Ri_0 sets the plume regime while Ro selects the dominant baroclinic wave mode.
ER -