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>

Solving Prandtl-Blasius Boundary Layer Equation Using Maple

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Solving Prandtl-Blasius boundary layer equation using Maple

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting.

Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation

Summary We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle $\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying $\beta\in[-0.198837735, 1]$ are considered, and the previously established non-unique solutions for $\beta<0$ having positive and negative shear rates along the wedge are accurately represented. The approximant is used to determine the singularities in the complex plane that prescribe the radius of convergence of the power series solution to the Falkner–Skan equation. An attractive feature of the approximant is that it may be constructed quickly by recursion compared with traditional Padé approximants that require a matrix inversion. The accuracy of the approximant is verified by numerical solutions, and benchmark numerical values are obtained that characterize the asymptotic behavior of the Falkner–Skan solution at large distances from the wedge.

Two-Phase Microscopic Heat Transfer Model for Three-Dimensional Stagnation Boundary-Layer Flow in a Porous Medium

This work examines the steady three-dimensional forced convective thermal boundary-layer flow of laminar and incompressible fluid in a porous medium. In this analysis, it is assumed that the solid phase and the fluid phase, which is immersed in a porous medium are subjected to local thermal nonequilibrium (LTNE) conditions, which essentially leads to one thermal boundary-layer equation for each phase. Suitable similarity transformations are introduced to reduce the boundary-layer equations into system of nonlinear ordinary differential equations, which are analyzed numerically using an implicit finite difference-based Keller-box method. The numerical results are further confirmed by the asymptotic solution of the same system for large three-dimensionality parameter, and the corresponding results agree well. Our results show that the thickness of boundary layer is always thinner for all permeability parameters tested when compared to the nonporous case. Also, it is noticed that the temperature of solid phase is found to be higher than the corresponding fluid phase for any set of parameters. There is a visible temperature difference in the two phases when the microscopic interphase rate is quite large. The physical hydrodynamics to these parameters is studied in some detail.

The Unsteady MHD Flow Under the Action of Chemical Reaction and Thermal Radiation at the Stagnation Point of a Rotating Sphere

In the present work, we have studied the unsteady MHD flow under the action of thermal radiation and chemical reaction at the stagnation point of a rotating sphere. By using similarity transformation, the unsteady non-linear boundary layer equation obtained as a result of heat transfer and mass transfer along with momentum were changed to a set of ordinary differential equations. Through the use of MATLAB’s built in solver bvp4c, the obtained differential equations were solved. Fluid velocity profile along with temperature profile and species concentration profiles are drawn for radiation parameter Ra  and chemical reaction parameter Kr  and the obtained results are discussed.