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Abstract
This paper is a review prepared for the second Marseille Colloquium on the mechanics of turbulence, held in 2011, 50 years after the first. The review covers recent developments in our understanding of the large-scale dynamics of cumulus cloud flows and of the atmospheric boundary layer in the low-wind convective regime that is often encountered in the tropics. It has recently been shown that a variety of cumulus cloud forms and life cycles can be experimentally realized in the laboratory, with the transient diabatic plume taken as the flow model for a cumulus cloud. The plume is subjected to diabatic heating scaled to be dynamically similar to heat release from phase changes in clouds. The experiments are complemented by exact numerical solutions of the Navier–Stokes–Boussinesq equations for plumes with scaled off-source heating. The results show that the Taylor entrainment coefficient first increases with heating, reaches a positive maximum and then drops rapidly to zero or even negative values. This reduction in entrainment is a consequence of structural changes in the flow, smoothing out the convoluted boundaries in the non-diabatic plume, including the tongues engulfing the ambient flow. This is accompanied by a greater degree of mixedness in the core flow because of lower dilution by the ambient fluid. The cloud forms generated depend strongly on the history of the diabatic heating profile in the vertical direction. The striking effects of heating on the flow are attributable to the operation of the baroclinic torque due to the temperature field. The mean baroclinic torque is shown to peak around a quasi-cylindrical sheet situated midway between the axis of the flow and the edges. This torque is shear-enhancing and folds down the engulfment tongues. The increase in mixedness can be traced to an explosive growth in the enstrophy, triggered by a strong fluctuating baroclinic torque that acts as a source, especially at the higher wave numbers, thus enhancing the mixedness. In convective boundary layers field measurements show that, under conditions prevailing in the tropics, the eddy fluxes of momentum and energy do not follow the Monin–Obukhov similarity. Instead, the eddy momentum flux is found to be linear in the wind speed at low winds; and the eddy heat flux is, to a first approximation, governed by free convection laws, with wind acting as a small perturbation on a regime of free convection. A new boundary layer code, based on heat flux scaling rather than wall-stress scaling, shows promising improvements in predictive skills of a general circulation model.
Acknowledgements
During the last two decades while the work reported here was being carried out, I have had the pleasure of working with many students, colleagues and post-docs. Among the first of these were G.S. Bhat, Prof V.H. Arakeri, R. Elavarasan, Amit Basu, and Prof. A. Prabhu. More recently, in rough anti-chorological order, I am grateful to Prof. K.R. Sreenivas, Prof. G.S. Bhat and Dr Sourabh S. Diwan, and to D. Subrahmanyam, G.R. Vybhav Rao, Dr L. Venkatakrishnan, Prof. A. Prabhu, Dr Kusuma G. Rao, Dr S.V. Kailas, H.V. Raju, Dr S. Rudrakumar, S. Ameenulla, S. Siddhartha, V. Saxena, and Dr U.N. Sinha. Mr Sukruth Satheesh helped in preparing . The work has been supported at various times by the Department of Science and Technology, New Delhi; the Defence Research and Development Organization, New Delhi; US Office of Naval Research, Arlington, VA; Tata Computing Research Laboratories, Pune; and, most recently, by JNC and by Intel Technology India Private Limited, Bangalore. I am grateful to the Centre for Atmospheric and Oceanic Sciences, Indian Institute of Science, for their continued hospitality.
Notes
In tensor notation (∂2/∂xj ∂xk ) u′jω′k , after using div u ′ = 0.