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• W2078555719 abstract "We consider unbounded precessing rotating flows in which vertical or horizontal shear is induced by the interaction between the solid-body rotation (with angular velocity ${ensuremath{Omega}}_{0}$) and the additional ``precessing'' Coriolis force (with angular velocity $ensuremath{-}ensuremath{epsilon}{ensuremath{Omega}}_{0}$), normal to it. A ``weak'' shear flow, with rate $2ensuremath{epsilon}$ of the same order of the Poincar'e ``small'' ratio $ensuremath{epsilon}$, is needed for balancing the gyroscopic torque, so that the whole flow satisfies Euler's equations in the precessing frame (the so-called admissibility conditions). The base flow case with vertical shear (its cross-gradient direction is aligned with the main angular velocity) corresponds to Mahalov's [Phys. Fluids A 5, 891 (1993)] precessing infinite cylinder base flow (ignoring boundary conditions), while the base flow case with horizontal shear (its cross-gradient direction is normal to both main and precessing angular velocities) corresponds to the unbounded precessing rotating shear flow considered by Kerswell [Geophys. Astrophys. Fluid Dyn. 72, 107 (1993)]. We show that both these base flows satisfy the admissibility conditions and can support disturbances in terms of advected Fourier modes. Because the admissibility conditions cannot select one case with respect to the other, a more physical derivation is sought: Both flows are deduced from Poincar'e's [Bull. Astron. 27, 321 (1910)] basic state of a precessing spheroidal container, in the limit of small $ensuremath{epsilon}$. A Rapid distortion theory (RDT) type of stability analysis is then performed for the previously mentioned disturbances, for both base flows. The stability analysis of the Kerswell base flow, using Floquet's theory, is recovered, and its counterpart for the Mahalov base flow is presented. Typical growth rates are found to be the same for both flows at very small $ensuremath{epsilon}$, but significant differences are obtained regarding growth rates and widths of instability bands, if larger $ensuremath{epsilon}$ values, up to 0.2, are considered. Finally, both flow cases are briefly discussed in view of a subsequent nonlinear study using pseudospectral direct numerical simulations, which is a natural continuation of RDT." @default.
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• W2078555719 date "2009-03-12" @default.
• W2078555719 modified "2023-10-18" @default.
• W2078555719 title "Precessing rotating flows with additional shear: Stability analysis" @default.
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• W2078555719 doi "https://doi.org/10.1103/physreve.79.036303" @default.
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