Mean zonal flow driven by precession in planetary cores: numerical simulations with a semi-lagrangian scheme

<p>We revisit the generation of mean zonal flows in fluid planetary interiors subjected to precession.<br>The main effect of precession on a (nearly) spherical fluid envelope is to make the fluid rotate along an axis tilted with respect to the rotation axis of the solid mantle. This is the so-called "spin-over" response of the fluid.<br> also shows that a steady shear flow develops on top of the spin-over mode due to non-linear effects in the boundary layer equation.<br>This mean zonal shear flow has been studied theoretically and numerically by .</p><p>With faster computers and more efficient codes, we compute this flow down to very low viscosity and compare with the inviscid theory of Busse (1968).<br>In addition we investigate the width and the intensity of the detached shear layer, which is controlled by viscosity and therefore not present in the theory.</p><p>We also use this problem as a benchmark to assess the benefits of using a semi-lagrangian numerical scheme, where solid-body rotation is treated exactly.</p>

An analytical anisotropic compact stellar model of embedding class I

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration has unequal principal stresses i.e. fluid is locally anisotropic. A certain physically motivated geometry of metric potential has been chosen and codependency of the metric potentials outlines the formation of the model. The exterior spacetime is assumed as described by the exterior Schwarzschild solution. The smooth matching of the interior to the exterior Schwarzschild spacetime metric across the boundary and the condition that radial pressure is zero across the boundary lead us to determine the model parameters. Physical requirements and stability analysis of the model demanded for a physically realistic star are satisfied. The developed model has been investigated graphically by exploring data from some of the known compact objects. The mass-radius (M-R) relationship that shows the maximum mass admissible for observed pulsars for a given surface density has also been investigated. Moreover, the physical profile of the moment of inertia (I) thus obtained from the solutions is confirmed by the Bejger–Haensel concept.