## Abstract

A laboratory experiment is conducted where hot water is cooled by exposure to air in a cylindrical rotating tank with a flat shallow outer “continental shelf” region next to a sloping “continental slope” bottom and a flat “deep ocean” center. It is taken to be a model of wintertime cooling over a continental shelf. The flow on the shelf consists of cellular convection cells descending from the top cooled surface into a region with very complicated baroclinic eddies. Extremely pronounced fronts are found at the shelf break and over the slope. Associated with these are sizable geostrophic currents along the shelf and over shelf break contours. Eddies are particularly energetic there. Cooling rate of the hot water is determined and compared with the temperature difference between the continental shelf and deep ocean. The results are compared with scaling arguments to produce an empirical best-fit formula that agrees with the experiment over a wide range of experimental parameters. A relatively straight trend of the data causes a good collapse to a regression line for all experiments. These experiments have the same range of governing dimensionless numbers as actual ocean continental shelves in some Arctic regions. Therefore. this formula can be used to estimate how much temperature decrease between shelf and offshore will be produced by a given cooling rate by wintertime cooling over continental shelves. The formula is also generalized to include brine rejection by ice formation. It is found that for a given ocean cooling rate, shelf water will be made denser by brine rejection than by thermal contraction. Estimates of water density increase implied by these formulas are useful to determine optimum conditions for deep-water formation in polar regions. For instance, shelves longer than the length scale 0.09 *fW*^{5/3}/*B*^{1/3} (where *f* is the Coriolis parameter, *W* is shelf width, and *B* is buoyancy flux) will produce denser water than shorter shelves. In all cases, effects of earth rotation are very important, and the water will be much denser than if the fluid was not rotating.