Convection patterns in Fourier space

Abstract

Two-dimensional Fourier transforms of convection patterns are computed from data obtained by Doppler scanning of the velocity field. This new technique is used to study the time dependence of the wave-number distribution, and the variation of the mean wave number $k^{*}$ with Rayleigh number $R$. We find that $k^{*}$ increases by about 15% during the pattern evolution following a step change in $R$ from below $R_c$ to $2R_c$. This increase is associated with a reduction in the number of defects in the pattern. The dependence of $k^{*}$ on $R$ is characterized by a decline above $R_c$ and a steeper decline near $5R_c$ where the skewed varicose instability causes the flow to become time dependent. The peak in the wave-number distribution does not shift significantly in the range $6-40R_c$, and still contains about half of the spectral power at $40R_c$. The flow apparently remains largely two dimensional.