THE EFFECT OF LANDFAST SEA ICE ON COASTAL CURRENTS DRIVEN BY THE WIND
Kay I. Ohshima*
Institute of Low Temperature Science, Hokkaido University, Japan
1. INTRODUCTION
In polar regions some coastal oceans are often covered with land-fast sea ice. Since the stationary ice prevents the water beneath it from feeling the wind blowing over it, response of the ocean to the wind strongly depends on the existence of the fast ice. Even for the uniform wind, at the edge of the fast ice infinite stress curl acts on the ocean, which gives rise to excitation of the currents (Clarke,1978). The purpose of this study is to examine the response of the coastal ocean to fluctuating and steady wind in the presence of land-fast sea ice.
2. SOLUTION FOR PERIODIC FORCING (SHELF WAVE RESPONSE)
The model equations are the same as that considered by Gill and Schumann(1974) except the presence of land-fast ice. For simplicity we consider the case that the fast ice edge is infinitely located at x=m, parallel to the coast (Figure l). In what follows, we consider the case of southern Hemisphere since this study was motivated by the Antarctic expedition program which the author participated in.
Under linear, nondivergent motions, inviscid and long-wave approximation, verticaily integrated shallow water wave equations have the form ,
where (u,υ) is the depth-averaged velocity;η is the sea level deviation; Y is the y component of wind stress, divided by the density of the water. Consider the case that wind is uniform in the cross shelf direction. Since the wind stress can not be applied to the ocean underneath the ice, Y is represented by,
where H(x) is step function.
By introducing a stream function ψ such that hu=- ψ/ x, =(2.1) and (2.2) can be written as
This forced voriticity equation is briefly expained in physical terms, as follows. In real ocean, the vorticity input is primarily caused by the response of the surface Ekman layer to the wind stress. The motion below the Ekman layer is steered by the vorticity input in two ways ,one results from the vertical motion due to divergence/convergence in the Ekman layer, the other from the topographic -β effect due to the compensated flow of the normal Ekman flux which is blocked by the coast (Gill and Schumann, 1974). The second term of right-hand side of (2.4), corresponding to the former mechanism, represents that the vorticity input occurs only at the ice edge by an infinite stress curl. The first term of right-hand side of (2.4), corresponding to the latter mechanism, occurs only in the offshore region from the ice edge under the non-divergent condition. It is noted that the vertically integrated form of (2.4) represents the sum of the motions in the surface Ekman layer and the layer below, which can be easily expressed in the separated form, as in Gill and Schumann(1974).
*Corresponding author address. K.I. Ohshima, Inst. of Low Temp. Sci., Hokkaido Univ., Sapporo 060, Japan; e-mail:ohshima@soya.lowtem.hokudai.ac.jp
