Journal ArticleDOI
Onset of Manifest Convection in a Layer of Fluid with a Time‐Dependent Surface Temperature
TLDR
In this paper, it was found that the onset of manifest convection was independent of the thermal boundary layer depth and that the horizontal spacing of the convection cells should vary with the rate of bottom surface temperature increase within reasonable limits.Abstract:
Experiments have been performed in deep layers of fluid in which the bottom surface temperature was increased at a constant rate. It was found that when the thermal boundary layer was only a small fraction of the total depth of the fluid layer, the onset of manifest convection was independent of the layer depth. The predictions of linear time‐dependent theory that the time of onset of manifest convection should vary with the ‐ 25 power of the rate of bottom surface temperature increase and that the horizontal spacing of the convection cells should vary with the ‐ 15 power of the rate of bottom surface temperature increase were verified within reasonable limits.read more
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Pattern formation in a suspension of swimming microorganisms: equations and stability theory
TL;DR: In this article, a model for collective movement and pattern formation in layered suspensions of negatively geotactic micro-organisms is presented, where motility of an organism is described by an average upward swimming speed U and a diffusivity tensor D. The model is compared with observations of patterns formed by the ciliated protozoan Tetrahymena pyriformis.
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The amplitude equation near the convective threshold: application to time-dependent heating experiments
TL;DR: In this article, a phenomenological forcing field is added to the amplitude equation to describe the slow variations in space and time of hydrodynamic quantities near the threshold of a Rayleigh-Benard cell, and its form and magnitude are fitted to the onset time of the convective heat current.
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A Mathematical Model of Pattern Formation by Swimming Microorganisms
TL;DR: A mathematical model describing the hydrodynamics of suspension of negatively geotactic microorganisms is described which predicts the existence of critical depths and concentrations and solutions describing the "polka-dot" patterns seen at low organism concentration in suspensions slightly deeper than the critical value are presented.
Journal ArticleDOI
The method of weighted residuals and variational principles, Bruce A. Finlayson, Academic Press, New York (1972). 412 pages
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Convection into domains with open boundaries
TL;DR: In this paper, the effects of rotation, ambient stratification and the geometry of the region on these flow quantities are considered, since all affect the density and velocity distributions that result.