Model of oscillatory instability in vertically-homogeneous atmosphere

Instability Analysis of Miscible Displacements in Homogeneous Porous Media

Homogeneous Estimates for Oscillatory

Let u(x; t) be the solution to the free time-dependent Schrr odinger equation at the point (x; t) in space-time R n+1 with initial data f. We characterize the size of u in terms L p (L q)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces _ H s (R n). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interpo...

Weakly nonlinear model for oscillatory instability in Saturn's dense rings.

Viscous overstability (oscillatory instability) may play an important role in the formation of small scale structure in dense planetary rings such as Saturn's B ring. We investigate the growth and saturation of such modes in local particle simulations. Starting from a hydrodynamic model, we develop a set of ordinary differential equations to model the evolution of the amplitudes of the linearly...

Oscillatory transverse instability Oscillatory transverse instability of interfacial waves in horizontally oscillating flows

We present the results of an experimental investigation into the stability of steep interfacial waves in two immiscible liquid layers subject to horizontal oscillations. Two-dimensional waves, which arise beyond a critical forcing speed Vc (product of forcing frequency and amplitude), can in turn lose stability to oscillatory transverse amplitude modulations with a near sub-harmonic response at...

Homogeneous Estimates for Oscillatory Integrals

Abstract. Let u(x, t) be the solution to the free time-dependent Schrödinger equation at the point (x, t) in space-time Rn+1 with initial data f . We characterize the size of u in terms Lp(Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Ḣs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interp...