We describe a series of laboratory experiments to study convective structures in rotating fluids (distilled water) in ranges of Rayleigh flux number Raf from 106 to 2 × 1011 and of Taylor number Ta from 106 to 1012. An intermediate quasi-stationary ring pattern of convection was found to arise from the interaction of the onset of convection with the fluid spin-up, for which we determined the times of origin and destruction, the distances between the rings, and the diameter of the central ring in terms of Raf and Ta. The ring structure evolves into a vortex grid which can be regular or irregular. In terms of Raf and Ta the regular grid exists in the linear regime, when the number of vortices N is in accord with the linear theory, when $N \propto h^{-2} Ta^{\frac{1}{3}} \propto \Omega^{\frac{2}{3}}$, or in the nonlinear regime when N ∝ h−2Ta½Raf−⅙ ∝ where Ω is the angular velocity and h is the fluid depth. In the irregular regime we always have N ∝ Ω. The transition from the regular regime to the irregular one is rather gradual and is determined by the value of the ordinary Rayleigh number, which we found to be greater than the first critical number Ra ∝ Ta2/3 by a factor about 25–40. In the transition region vortex interactions are observed, which start with rotation of two adjacent vortices around a common axis, then the vortices come closer and rotation accelerates, following which the vortices form a double helix and then coalesce into one stronger vortex.Some other qualitative experiments show that if the rotating vessel with the convective fluid is inclined to the horizontal, the vortex grid is formed along the rotation axis in accordance with the Proudman–Taylor theorem.
The paper is a continuation of work published in Boubnov & Golitsyn (1986). We present new measurements of the temperature and velocity field patterns and their statistical characteristics. This allows us to classify regimes of convection in a plane rotating horizontal fluid layer in terms of Rayleigh and Taylor numbers. Within the irregular regimes geostrophic convection is found for which the Rossby number is much less than unity.In the regular regimes the mean temperature profiles are linear with height in the bulk of the fluid, the gradient being dependent mainly on rotation rate Ω and fluid depth h. These together with some dimensional arguments lead to the heat transfer relationship Nu ∝ Ra3 Ta−2 between Nusselt, Rayleigh and Taylor numbers. Experimental results by Rossby (1969) and theoretical work by Chan (1974) and Riahi (1977) suggested this dependence. The dependence on ωτ of the temperature power spectrum normalized by the variance was found to be universal at higher frequencies for all irregular convective motions, where τ is the timescale of the thermal boundary layer for cases with a small influence of rotation and with τ about three times larger (in numerical coefficient) for geostrophic convection. For irregular geostrophic regimes it is found that the temperature variance depends on rotation rate and heat flux, and is inversely proportional to the buoyancy parameter.Horizontal and vertical components of the velocity fields were measured for regular as well as irregular regimes, confirming, especially for geostrophic convection, the theoretical results by Golitsyn (1980). In conclusion some geophysical applications are briefly mentioned.
In a recent paper Boubnov, Dalziel & Linden (1994) described the response of a stratified fluid to forcing produced by an array of sources and sinks. The sources and sinks were located in a horizontal plane and the flow from the sources was directed horizontally so that fluid was withdrawn from, and re-injected at, its own density level. As a result vertical vorticity was imparted to the fluid with a minimum of vertical mixing. It was found that when the stratification was strong enough to suppress vertical motions an inverse energy cascade was observed leading to the establishment of a large-scale circulation in the fluid. Those experiments were restricted to eight source-sink pairs. The present paper extends this work in two ways. First, up to forty source-sink pairs are used to force the flow, thereby producing a much wider separation of scales between the forcing and the flow domain. An inverse cascade is again found, but in this case the energy transfer to large scales is more rapid. The basic pattern of the large-scale flow is independent of the number of sources but the detailed structure depends on the energy input scale. Second, the effects of rotation about a vertical axis are investigated. It is found that when the Rossby deformation radius exceeds the size of the flow domain, the inverse energy cascade still occurs. However, for smaller values of the deformation scale, which in these experiments are comparable to or smaller than the forcing scale, the inverse cascade is altered by baroclinic instability. When flow structures develop on a scale larger than the deformation scale, usually by the merging of vortices of like sign, these structures are observed to split into smaller vortices of a scale comparable to the deformation scale. The flow appears to evolve with a balance between an anticascade produced by the two-dimensionality of the flow and a cascade due to baroclinic instability. For Rossby radii much smaller than the domain size the flow evolves into finite clumps of vorticity and an asymmetry between anticyclones and cyclones develops. A predominance of coherent anticyclones is observed, and the cyclonic vorticity is contained in more diffuse structures.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.