Exact(7)
We describe our numerical model in detail, and we test it by examining purely thermal convection in a rapidly rotating fluid shell and by examining Kumar Roberts kinematic dynamos (modified for the spherical shell).
The probability of each bin is defined as the volume of the fluid shell that is occupied by the respective range of force ratio values relative to the total volume of the fluid shell.
Gravity is assumed to vary linearly with radius; g o is acceleration at the top of the fluid shell.
The SKA simulations are carried out on numerical grids that range from 37 fluid shell radial levels and 42 spherical harmonic degrees (near onset at E=10−3) to 73 radial levels and 213 spherical harmonic degrees (highest Ra for E=10−5).
Linear asymptotic analyses of quasigeostrophic convection predict that the azimuthal wavenumber of these columns relative to the thickness of the fluid shell varies as ℓ U /D∝E 1/3, where the Ekman number, E=ν/(2Ω D 2), represents the ratio of viscous to Coriolis forces (e.g., Roberts 1968; Julien et al. 1998; Jones et al. 2000; Dormy et al. 2004).
In our models, the imposed Elsasser number is calculated from the dimensionless magnetic energy density, (mathcal {E}_{M}), within the fluid shell of volume V: Lambda_{i} =2 Pm E mathcal{E}_{M} text{ where } mathcal{E}_{M} = frac{1}{2~Pm~E~V} int_{V} mathbf{B} cdot mathbf{B} text dV, (12).
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As two-dimensional fluid shells, lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses.
Continuum hypothesis, scalar and vector fields, fluid statics, non-Newtonian fluids, shell momentum balances, equations of motion and the Navier-Stokes equations, creeping and potential flow, parallel and nearly parallel flows, time-dependent parallel flows, boundary layer theory and separation, introduction to drag correlations.
The permeability condition on the fluid-shell interface is applied to ensure the contact between the fluid and shell wall.
This investigation is a follow-up of an earlier study of the two-fluid shell-shock interaction [S.
The dynamics of a bar-fluid-shell system simulating an hydraulic cylinder subjected to arbitrary axial excitation is studied analytically.
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