Three-dimensional instability and patterns of an axisymmetric flow of electrically conducting liquid in a cylindrical enclosure driven by an axial traveling magnetic field (TMF) is studied. The attention is focused on the TMF of a large axial wavenumber or large frequency, which leads to a formation of the skin layer near the sidewall. It is shown that the flow intensity grows with the increase...

[I] The slopes of the wavenumber spectra of sea surface height (SSH) and kinetic energy (KE) have been used to infer "interior" or surface quasi-geostrophic (QG or SQG) dynamics of the ocean. However, inspection of spectral slopes for altimeter SSH in the mesoscale band of 70 to 250 km shows much flatter slopes than the QG or SQG predictions over most of the ocean. Comparison of altimeter waven...

The purpose of this thesis is to study the problem when a microorganism swims very close to a shaped boundary. In this problem, we model the swimmer to be a two-dimensional, infinite periodic waving sheet. For simplicity, we only consider the case where the fluid between the swimmer and the washboard is Newtonian and incompressible. We assume that the swimmer propagates waves along its body and...

We study correlations among diierent components of the spectrum of the light intensity eld close to a pattern forming instability associated with the polarization of the light eld. In particular we nd strong correlations between opposite wavevectors of critical wavenumber and anticorrelations of the zero wavenumber and the critical one. These anticorrelations are a manifestation of nonlinear cr...

For a model Helmholtz problem at high wavenumber we present a wavenumber-explicit error analysis in weak norms such as L, H. In 1D, we analyze the convergence behavior of the lowest order optimally blended spectral-finite element scheme of [Ainsworth & Wajid, SIAM J. Numer. Anal. (2010)].