JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 89, NO. C4, PAGES 6525-6531, JULY 20, 1984 Wind-Driven Ice Drift in a Shallow Sea J. E. OVERLAND,H. O. MOFJELD, AND C. H. PEASE Pacific Marine Environmental Laboratory,NOAA The free-drift equations are solved for icefloes in a shallow sea of neutralstratification, typical of many high-latitude continental shelves. Solutions for icedrift and current velocity are obtained as a function of wind stress, ice thickness, and water depth. The oceanis modeledby second-order closure, which allows continuous solutions from 5 m total depthto deepwater. Results are presented with drag coefficients for the air/ice, ice/water, and water/bottom interfaces specified from recent surveys from the Bering Sea Shelf, a region with broad areas of water depths between 20 and 50 m. The solution showslittle dependence on water depth for depthsgreaterthan 30 m. This occurs because turbulent mixing is a decreasing function of water depthand offsets otherinfluences of finite depth. However, for water depths less than 30 m, ice velocities can change rapidly with wind speed and water depth,and the presence of turbulence from tidal shearis very important for coupling wind-driven ice drift to the bottom. For the deep-water limit, the second-order closure solutionconfirms analyticsolutions that indicatean increase of 20% in the ratio of ice speed to wind speed as the wind speed increases from 10 to 25 m/s. INTRODUCTION It is important to understand the influence of bathymetry on the wind drift of ice in shallow seas of the seasonal ice zone. Simple Ekman theory predicts for constant eddy vis- cosity that the speedand direction of wind-driven ice should be a function of water depth if the Ekman layer under the ice extends to the bottom. It is not clear, however, whether a more realistic treatment of turbulent intensity would yield the same behavior in shallow water, nor is it clear for which wind speeds and depthsthe ice drift differs significantly from that in deepwater. We shall investigate this problem by extending the solutions for the coupled ice-oceanproblem for free-drifting ice [Shuleikin, 1938• Reed and Campbell, 1962; Neralla et al., 1981; Pease and Overland, 1984] to finite depth. We shall show using ice parameters typical of the Bering Sea that the influence of finite depth is generally constrained to water depths less than 30 m. We begin by assumingthat the ice drift respondsto the local wind and thus exclude regionsdirectly adjacent to coast- lines. Large portions of the Chukchi, East Siberian, Laptev, Kara, Barents, Baltic, and Bering seas fit this criterion and have extensive area with depths less than 60 m (Figure 1). For example, the width of the Bering Sea Shelf is of the order of 500 km, while the 25-m isobath occurs seaward of a typical barotropic Rossby radius (• 100 km). The central Bering Sea Shelf responds directly to rotating winds rather than as coastalcurrent induced by sea level changes [Schumacher and Kinder, 1983]. Observed ice drift farther than 100 km from the Alaskan coast in 1981 [Pease et al., 1983] and during the MIZEX West Experiment [MIZEX West Study Group, 1983] was consistent with local wind forcing.There is also very little topographic relief on the Bering Sea Shelf to influence cur- rents. We further assume that the ocean is neutrally stratified under the ice. This assumption is valid for almost the entire Bering Sea Shelf in winter, away from the outer marginal ice zone [Kinder and Schumacher, 1981], becauseof cooling and salt rejection during ice production [Pease, 1980; Muench, 1983]. Ocean turbulence is modeled using second-orderclo- sure for shear generation of turbulent intensity [Mellor and Yamada, 1982; Mojield and Lavelle, 1984]. Extension of the Ekman-Taylor, analytical solution under the ice [McPhee, 1982] with an additional bottom boundary layer did not pro- vide a satisfactory continuous solution from shallow to deep water. The following section presentsthe derivation of the second-order closure model, and the third section discusses the results and their implication for the observedparameter range of the Bering Sea. DRIFT SOLUTION WITH AN OCEAN MODELED BY SECOND-ORDER CLOSURE The steady state, vertically integrated momentum equation for ice in free drift using complex notation (i2 = _ 1)is ia-i-c=0 with and Pt= ut + ivt, where ut and vt are the eastand north components of the ice velodity, f is the Coriolis parameter, Pt is ice density, and ht is ice thickness (Figure 2). Symbols with carets indicate vector quantities, while those without carets denotescalarmagnitudes. Air/ice stress is given by a drag law: (2) where •a is therelative air-ice velocity •A- •, Pa is theair density, and Ca is the air/ice drag coefficient.The reference level in the air for the drag coefficient is set at 10 m [Macklin, 1983]. Given Pt, ht, f, Pa, Ca and VA, an additional relation is needed to close the system of equations [Shuleikin, 1938' Reed and Campbell, 1962] between the ice-water stress, qw,and V• for a finite depth ocean. This relation is obtained by solving the stress-driven flow problem in the ocean. The steady state momentum equation for the ocean is This paper is not subjectto U.S. copyright. Publishedin 1984 by the American Geophysical Union. Paper number4C0294. ionf e= where • is the water velocity, u + iv, pw (3) is the mean water 6525