ON THE TRANSITION TO TURBULENT CONVECTION 



Ruby Krishnamurtl 



Florida State University 

 Tallahassee^ Florida 



I. INTRODUCTION 



The heat flow out of the sea floor has been observed in close 

 to 2000 measurements; the mean value for all the oceans is found to 

 be 1.4 X 10'® cal/cm^sec. [ Lee and Uyeda 1965] This is three 

 orders of magnitude smaller than the solar heating at the sea surface 

 and is surely negligible in any budget of the upper oceans. Yet, 

 because this heat flux is imposed from below, it may be of some 

 consequence in the dynamics of the abyssal circulation. If this heat 

 were to be transferred purely by conduction through the sea water, 

 a temperature gradient o" of 10" C /era would be required. The 

 largest depth across which such a gradient can exist without con- 

 vective overturning is determined by the critical value of the Rayleigh 

 number R, which is defined as follows: 



R = g^ crd^ 



where g is the acceleration of gravity, a the thermal expansion 

 coefficient, K the thermal diffusivity, p the kinematic viscosity, 

 and d is the depth of the layer in consideration. This largest depth 

 that can transfer the imposed heat flux by conduction is only around 

 3 cm. If there are regions or time periods of the abyssal oceans in 

 which horizontal advection of heat is not the dominant process, then 

 this vertical convection, with its attendant vertical mixing of nutrients, 

 can be an important process. 



ated 



Some understanding of convective processes can be gained 

 from laboratory studies of a horizontal layer of fluid which is heatcu 

 from below and cooled from above. The following is a review of such 

 laboratory studies and also a report of some recent experiments in 

 rotating and non- rotating systems. 



This is contribution No. 33 of the Geophysical Fluid Dynamics 

 Institute. 



289 



