A gravitational circulation excited by cooling of the water surface was investigated based on laboratory experiments. Our main object is to construct a framework to predict bulk characteristics of the phenomena from a rational assemblage of the external parameters. Water surface of the shallower section of the experimental channel (bay section) was cooled by circulating a cooled, dehumidified air above, while the deeper section (outer ocean section) was thermally kept constant. This setup represented the situation of the ''inverse estuary.'' Excited flow was directed to the dead end of the shallower section in the upper layer with a remarkable turbulent convection and returned back to the deeper section in the lower layer with relatively laminar characteristics. Sixteen sets of experiments were performed by changing the buoyancy flux bf and the water depth H. The measured flow rate q distribution and the buoyancy b were basically expressed by the power of the longitudinal coordinate x and bf. However, the dependence showed a systematic departure from the power law parts of the similarity solution given by Phillips <1966>. Defining ''buoyancy flux velocity'' U* (≡bf 1/3L1/3), we derived a nondimensional equation system that is characterized by ''flux Reynolds number'' Ref (≡bf1/3 H2 L-2/3vV -1). Ref is composed solely of the external parameters and is interpreted as being the ratio of the motive force to the viscous force unlike the usual Reynolds numbers. The nondimensional flow rate q' (≡q1 U*-1 H-1) was found to increase monotonically with respect to Ref. A dimensional reasoning with the scale analysis showed the relation q'=C1 Ref1/2 and q'=C2-C3 Ref -1/2 in the ranges of substantially small and large Ref, respectively. The experimental data coincided with these two curves, and the coefficients C1, D2, and C3 were determined to be 0.044, 0.43, and 1.67, respectively.