arXiv subjects

Ayan Kumar Banerjee

Publications and source records attributed to Ayan Kumar Banerjee.

5 recordsLinked to original sources

arXiv2026

Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume

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 $L_\rho = NH/f$; 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 $Ri_0 \leq 4$. The plume entrainment coefficient $\Gamma(z)$ shows opposite rotational sensitivities at low and high $Ri_0$, which we organize through a local plume Rossby number $Ro_p = w/(2\Omega b)$. A mixing-length argument predicts a bulk turbulent heat flux $\overline{u'T'} \propto Ri_0^{-1/2}$, 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.

physics.flu-dyn↗

arXiv2026

Linear Stability Analysis of convective flows in Rotating Baroclinic Annulus with Localized Peripheral Heating: A Floquet-BiGlobal Approach

We investigate the linear stability of a rotating fluid annulus subjected to localized heating at the outer periphery of the bottom surface and uniform cooling at the inner cylindrical wall through a rigorous stability analysis. The localized forcing generates a non-axisymmetric base state, invalidating the classical normal-mode decomposition. We employ Floquet-Bloch theory in the azimuthal coordinate combined with a BiGlobal eigenvalue formulation in the meridional plane. The non-axisymmetric base state is expanded in azimuthal Fourier harmonics; perturbations are expressed as quasi-periodic Bloch modes that couple all azimuthal wavenumbers through base-state harmonics. Full linearised perturbation equations, the BiGlobal block-operator structure, pressure elimination, solenoidal projection, and the modal energy budget are derived. Instability is driven by cross-modal baroclinic energy release and shear production - mechanisms absent in classical axisymmetric theory.

physics.flu-dyn↗

arXiv2026

Reduced Order Model for a Convective Rotating Annulus with Localized Forcing

A low-order Galerkin model is developed for a rotating fluid annulus driven by localized heating at the outer bottom periphery, with uniform cooling at the inner cylindrical wall. The model retains the full cylindrical geometry and employs Bessel-function radial eigenfunctions satisfying physically correct Dirichlet-Neumann boundary conditions. A dual-series least-squares procedure determines the conductive base state under the mixed thermal boundary condition. Galerkin projection onto the leading radial and vertical basis functions yields a 10-variable dynamical system governing the mean meridional overturning, thermal wind, baroclinic wave amplitudes, and their nonlinear interactions. Linear stability analysis yields explicit critical Rayleigh numbers for both mean and wave instabilities, showing that rotation raises Ra_c in proportion to T^2. The model reproduces the Nu ~ Ra^(1/4) scaling, rotational suppression at low Ra, and the boundary-layer-dominated flow structure observed in companion axisymmetric simulations.

physics.flu-dyn↗

arXiv2026

Influence of Aspect ratio in the Convection in Rotating Annulus In the Presence of Localized Heating

Two-dimensional (2D) axisymmetric simulations are conducted to investigate convection in a rotating cylindrical annulus with localized heating at the outer bottom edge and uniform cooling at the inner cylindrical wall. The resulting radial and vertical temperature gradients generate buoyancy-driven motion and produce a stratification pattern relevant to atmospheric circulation. The effects of aspect ratio ($\Gamma$), Rayleigh number ($Ra = 2.4 \times 10^{7}$--$1.2 \times 10^{9}$), and Taylor number ($Ta = 1.6 \times 10^{7}$--$1.2 \times 10^{9}$), including the non-rotating limit ($Ta=0$), are examined. Convection is largely confined to thin boundary layers, while the fluid interior remains diffusion dominated. Without rotation, the temperature field exhibits nearly horizontal isotherms. Rotation establishes quasi-hydrostatic and geostrophic balances that redistribute heat and promote deeper penetration of isotherms into the interior. Heat transfer, quantified by the Nusselt number ($Nu$), depends strongly on $Ra$, $Ta$, and $\Gamma$. For moderate and high $Ra$, $Nu$ follows the scaling $Nu \sim Ra^{1/4}$ and is only weakly influenced by rotation. At low $Ra$ and high $Ta$, rotational suppression of buoyancy reduces $Nu$ significantly. Increasing $\Gamma$ enhances heat transfer, although the growth rate diminishes for $\Gamma > 1$. The relative thermal and Ekman boundary-layer thicknesses govern the sensitivity of heat transfer to rotation.

physics.flu-dyn↗

arXiv2016

Convection in rotating flows with simultaneous imposition of radial and vertical temperature gradients

Laboratory experiments were conducted to study heat transport characteristics in a nonhomogeneously heated fluid annulus subjected to rotation along the vertical axis (z). The nonhomogeneous heating was obtained by imposing radial and vertical temperature gradient (ΔT). The parameter range for this study was Rayleigh number, Ra=2.43x10^8-3.66x10^8, and Taylor number, Ta=6.45x10^8-27x10^8. The working fluid was water with a Prandtl number, Pr=7. Heat transport was measured for varying rotation rates (Ω) for fixed values of ΔT. The Nusselt number, Nu, plotted as a function of Ta distinctly showed the effect of rotation on heat transport. In general, Nu was found to have a larger value for non-rotating convection. This could mean an interplay of columnar plumes and baroclinic wave in our system as also evident from temperature measurements. Laser based imaging at a single vertical plane also showed evidence of such flow structure.

physics.flu-dyn↗