Novel heat-flux scaling for convection at low winds

Abstract

An analysis of atmospheric observational data indicates that the conventionally defined drag and heat transfer coefficients increase rapidly as wind speed falls. It is shown here that, at low winds, (i) there is a linear increase of drag with wind speed and (ii) the observed heat flux is independent of wind speed. These findings are not consistent with the so-called free-convection limit of Monin-Obukhov theory. They are instead best seen as the result of a new regime of 'weakly forced convection', in which the heat flux is determined solely by temperature differentials as in free convection, and the momentum flux by a perturbation linear in wind on free convection. This regime is governed by a new velocity scale determined by the heat flux (rather than by the friction velocity as in classical turbulent boundary layer theory). Novel definitions of the drag and heat exchange coefficients, based on appropriate heat-flux velocity scales, are found to be independent of wind speed at low winds. The height of the capping inversion in this regime is proportional to the surface heat flux, and is determined by a simple argument balancing energy supply at surface to rate of work done to lift air parcels to inversion height.