An experimental study of thermal convection in a rotating liquid

Abstract

An investigation is described of the hydrodynamical flow that ensues when a liquid which rotates uniformly at O about a vertical axis is subject to a horizontal temperature gradient. Although O was sufficiently large for primary effects due to Coriolis forces to arise, centripetal forces never exceeded a small fraction of those due to gravity. Laboratory investigations of this type are of some geophysical interest. They may have a direct bearing on the study of the general atmospheric circulation, and with suitable extensions they may eventually lead to a better understanding of the hydrodynamical flow which is supposed to occur in the earth’s liquid core, where the geomagnetic field originates. Water, the only liquid which was used, filled the annular space between two concentric cylinders of radii a and b (b > a)to a depth of d cm. depth of d cm. The cylinders were maintained at different temperatures MATHS FORMULA. The general properties of the flow depend on the value of a certain parameter Θ ≡ 2 g d [ ρ ( T a ) − ρ ( T b ) ] / Ω 2 ( b − a ) 2 [ ρ ( T b ) + ρ ( T a ) ] where g is the acceleration of gravity and p(T) is the density of water at temperature T. re T. When 0 exceeds a certain value,O the flow is essentially a meridional circulation, in which the motion perpendicular to the axis of rotation is deflected by Coriolis forces. When 0 is somewhat less than O. the flow is characterized by a regular quasi-horizontal wave-like pattern in which the motion is almost but not entirely confined to a thin meandering ‘jet’ stream. The transition between these two regimes of flow takes place quite sharply when 0 = 0 Crit. = 1*58 +- 0*05. The train of waves in the wave-flow regime drifts relative to the rotating system at a uniform angular rate, in the same general direction as that of the flow in the top surface ‘jet ’ stream. The wave number m increases as 0 decreases, until a certain point is reached, corresponding to an amplitude to wavelength ratio of about two-thirds, when no further increase in m can be produced by reducing 0. At this point a steady repeating fluctuation of the flow pattern occurs. This phenomenon has been termed ‘vacillation’. At even smaller values of 0 the flow is ‘turbulent’ in the sense that rapid and complicated fluctuations occur. These flow phenomena appear to have their counterparts in the general atmospheric circulation. Specific investigations are described, including heat transport measurements and a study of the thermal structure of a typical flow field. Theoretical considerations lead to an interpretation of the meaning of 0, which is tentatively identified with appropriate Rossby and Richardson numbers, and some of the results of theories due to Davies (1956) and Kuo (1953) are compared with the experimental measurements. A certain measure of agreement is found.