Under low-wind, unstable conditions over water, the Liu, Katsaros and Businger (LKB) estimate of the buoyancy flux into the atmosphere has the form nu-1/3 DELTA-B4/3 g(xi), where 22.7-xi is the ratio of the Monin-Obukhov length to the calm-water roughness length; DELTA-B is the buoyancy difference between air just above the ocean surface and the ambient air above, and nu is viscosity. An analytic expression for g(xi) is obtained, for low winds; g(xi) has a minimum at about xi = 40 (corresponding over tropical oceans to wind speeds of about 0.3-0.6 m s-1). For lower values of x the assumptions underlying the LKB algorithm are no longer valid. For a reasonable choice of dimensionless constants, g(xi) varies only by 8% over 40 < xi < 200, being just above the minimum. Thus the LKB flux estimates are nearly independent of wind speed at their lower limit of applicability; it seems reasonable to identify this LKB minimum flux with laboratory observations of fluxes at zero wind. These show that the buoyancy flux is given by C* Pr-2/3 nu-1/3 DELTA-B4/3, where maesured values of C* are about 0.14 +/- 0.01 (Golitsin and Grachev, 1986). With Pr = 0.71 for air, this implies that g(0) = 0.19 - well within the allowable range of values for the minimum of g(xi). However, the minimum in g(xi) varies as (gamma-A(T))1/3, where gamma is the dimensionless constant in the Dyer-Hicks-Businger stability profile and A(T) the constant in the scalar roughness length for low winds; this can be used to fix A(T). In field applications, buoyant motions in the planetary boundary layer ensure that r.m.s. wind speeds w(G) just above the surface are generally greater than the wind speed at the minimum of g(xi), even for dry convection - though this would not be true if the planetary boundary layer were typically 100 m thick, instead of 1000 m. This "gustiness" is allowed for by replacing mean wind speed U by (U2 + w(G)2)1/2 in the bulk formulae.
