This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of the inviscid Burgers equation and then showing that the weak solution is the entropy solution. Then t...

A new finite difference scheme on a non-uniform staggered grid in cylindrical coordinates is proposed for incompressible flow. The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is satisfied. A novel pole treatment is also introduced, where a discrete radial momentum equation with ...

We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a strong compactness argument to justify the inviscid limit. Our approach does not rely on the justification of asymptotic expansions. In particular, we get a new ...

We study inviscid limits of invariant measures for the 2D Stochastic Navier-Stokes equations. As shown in [Kuk04] the noise scaling p ν is the only one which leads to non-trivial limiting measures, which are invariant for the 2D Euler equations. We show that any limiting measure μ0 is in fact supported on bounded vorticities. Relationships of μ0 to the long term dynamics of Euler in the L∞ with...

We investigate the effect of the viscosity on disk-planet interaction and type I migration of planets. We have performed a linear calculation using shearingsheet approximation and obtained the detailed, high resolution density structure around the planet embedded in a viscous disk with a wide range of viscous coefficients. We find that the density structure in the vicinity of the resonance is m...

Recent numerical studies in the area of transition to turbulence discovered that the classical plane Couette flow, plane Poiseuille flow, and pipe Poiseuille flow share some universal 3D steady coherent structure in the form of a “streak-roll-critical layer”. As the Reynolds number approaches infinity, the steady coherent structure approaches a 3D limiting shear of the form (U(y, z), 0, 0) in v...

The motion of a buoyant inviscid drop rising vertically along the rotation axis of a rapidly rotating low viscosity tluid bounded above and below by rigid horizontal boundaries is considered in the case that the drop is circumscribed by a Taylor column that spans the entire fluid depth. Both the shape and steady rise speed of the drop are deduced as a function of the interfacial tension. The an...

The physical mechanisms for vortex breakdown which, it is proposed here, rely on the production of a negative azimuthal component of vorticity, are elucidated with the aid of a simple, steady, inviscid, axisymmetric equation of motion. Most studies of vortex breakdown use as a starting point an equation for the azimuthal vorticity (Squire 1960), but a departure in the present study is that it i...