We consider a model equation derived in [18] for the linear stability of a torsional ow of an Oldroyd-B uid in a parallel-plate device. Axisymmetry, small gap and zero Reynolds numbers are assumed. The equation is not separable in the radial and vertical variables. The advantage is that its eigenmodes depend only on the aspect ratio. Once evaluated, the eigenmodes are used to calculate the onse...

Characterizing the dynamic properties of the solar turbulence with 3-D simulations: Consequences in terms of p-mode excitation. Abstract. A 3D simulation of the upper part of the solar convective zone is used to derive constraints about the averaged and dynamic properties of solar turbulent convection. Theses constraints are then used to compute the acoustic energy supply rate P injected into t...

We study turbulent channel flow of an electrically conducting liquid with a homogeneous magnetic field imposed in the spanwise direction. The Lorentz force is modelled using the quasistatic approximation. Direct and large-eddy simulations are performed for hydrodynamic Reynolds numbers Re=10000 and Re=20000 and the Hartmann number varying in a wide range. The main effect of the magnetic field i...

The objective in this presentation is to briefly survey some recent developments in finite element procedures that we have pursued to solve dynamic problems more accurately and more efficiently, and to solve new classes of problems. We present some developments regarding the finite element analysis of shells, the solution of wave propagation problems with mode conversions, the time integration ...

We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. The...

The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the meth...

We demonstrate connections that exists between a conjecture of Schiffer’s (which is equivalent to a positive answer to the Pompeiu problem), stationary solutions to the Euler equations, and the convergence of solutions to the Navier-Stokes equations to that of the Euler equations in the limit as viscosity vanishes. We say that a domain Ω ⊆ R, d ≥ 2, has the Pompeiu property if, given that the i...

In this study, baroclinic-barotropic instability of the Martian atmosphere is studied for a zonal basic state based on Mariner 9 observations, using a spherical linear primitive equation model derived from a method of 3-D normal mode expansion. As a result of solving a matrix eigenvalue problem, a distinctly unstable mode at synoptic to planetary scales was found with a peak growth rate of 2.3 ...

Raman spectroscopy such as spontaneous Raman spectroscopy, coherent anti-stokes Raman spectroscopy, and stimulated Raman gain spectroscopy are widely used in physics, chemistry and biology fields for investigations of vibrational modes. To our best knowledge, very few applications of Raman spectroscopy for the in-vitro and invivo patient medical diagnostics have been reported because of low sig...

Stability of a Bingham fluid in Taylor-Couette flow is studied. Of interest is to determine the critical values of the inner and outer cylinder angular velocities which cause the linear instability in the system. We introduce a perturbation into the basic flow, and examine the linearized Navier-Stokes equations for the perturbation. Assuming a normal mode solution for the perturbation, we obtai...