An empirical relationship between the Deacon profile number and the Richardson number under convective conditions

Abstract

Mean low-level temperature and wind profiles were constructed for 44 cases of free convection using the data O'Neill, Nebraska, during July and August 1956. Based upon the expression for the normalized logarithmic wind shear first suggested by Ellison and later refined by Panofsky, a theoretical formula for the Deacon number as a function of the Richardson number was derived, and values of the Deacon profile were computed. One of the parameters entering into this formula is the ration of the eddy diffusitivities for heat and momentum. This parameter was, in turn, computed from Priestley's expression for the dimensionless heat flux for free-convective cases. In using observed wind data from the mean profile in order to verify the theoretical computations of B, some marked discrepancies occurred above the 100 cm level. These were due to inconsistent wind speed readings, and it was necessary to employ control data, based on neutral profiles to correct the wind speed. When this was done, the theoretical and observed Deacon profile nurnbers were in very good agreement. The author is deeply indebted to Dr. F.L. Martin (Professor of Meteorology) for his suggestions and continued help throughout the investigations and during preparation of this paper. Special credit is due to Professor Martin for his large share in developing the derivations in this study.