Our velocity measurements on quasi-two-dimensional turbulent flow in a rapidly rotating annulus yield self-similar (scale-independent) probability distribution functions for longitudinal velocity differences, deltav(l) = v(x+l)-v(x). These distribution functions are strongly non-Gaussian, suggesting that the coherent vortices play a significant role. The structure functions <[deltav(l)](p)> approximately l(zeta)p exhibit anomalous scaling: zeta(p) = p / 2 rather than the expected zeta(p) = p / 3. Correspondingly, the energy spectrum is described by E(k) approximately k(-2) rather than the expected E(k) approximately k(-5/3).

We have made velocity time series measurements (using hot film probes) and velocity field measurements (using particle image velocimetry) on turbulent flow in a rotating annulus. For low annulus rotation rates the Rossby number was of order unity and the flow was three-dimensional (3D), but at high rotation rates the Rossby number was only about 0.1, comparable to the value for oceans and the atmosphere on large length scales. The low Rossby number (quasi-geostrophic) flow was nearly two-dimensional (2D), as expected from the Taylor–Proudman theorem. For the 3D flow we found that the probability distribution function (PDF) for velocity differences along the direction of the flow, δv(d)=v(x0+d)−v(x0), was Gaussian for large separations d and non-Gaussian (with exponential tails) for small d, as has been found for nonrotating turbulent flows. However, for low Rossby number flow, the PDF was self-similar (independent of d) and non-Gaussian. The exponents characterizing the structure functions, Sp=〈(δv)p〉∼dζp were obtained by the extended self-similarity method. For 3D flow the exponents departed from p/3 with increasing p, as has been found for turbulence in nonrotating flows, while for the quasi-2D turbulent flow, the exponents increased linearly with p, as expected for a self-similar flow. We applied the β-test of the hierarchical structure model [She and Lévêque, Phys. Rev. Lett. 72, 336 (1994)] and found that β remained constant at β≃0.75 as the rotation was increased from the 3D to the 2D regime; this indicates that both the quasi-2D and 3D flows are highly intermittent. The PIV images provided another indication of the intermittency—both the quasi-2D and 3D flows had coherent vortices which could be distinguished from the background flow. We also applied the γ-test of the hierarchical structure model and found that γ increased from 0.18 for the 3D flow to 0.34 for the quasi-2D flow; the latter value is in accord with expectation for self-similar turbulence. We conclude that our rotating 3D flow is similar to nonrotating turbulent flows, while the rotating quasi-2D turbulence is different from both the 3D rotating turbulence and from nonrotating 2D turbulence studied in other experiments.

We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number σ ≈ 1. We observed a number of new nonlinear, mostly spatio-temporally chaotic, states. At small angles of inclination we found longitudinal rolls, subharmonic oscillations, Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in the vicinity of the transition from buoyancy-to shear-driven instability, we observed drifting transverse rolls, localized bursts, and drifting bimodals. For angles past vertical, when heated from above, we found drifting transverse rolls and switching diamond panes.

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For Rayleigh-Bénard convection of a fluid with Prandtl number s 1.4, we report experimental and theoretical results on a pattern selection mechanism for cell-filling, giant, rotating spirals. We show that the pattern selection in a certain limit can be explained quantitatively by a phase-diffusion mechanism. This mechanism for pattern selection is very different from that for spirals in excitable media.[S0031-9007(98)