The coastal-trapped wave paddle and open boundary conditions

The problem of the specification and interpretation of backward open boundary conditions (b.c.'s) is examined in the context of regional numerical models of wind-forced shelf circulation. (Backward here is opposite to the direction of coastal-trapped wave (CTW) propagation.) In particular, we examine the problem where the effect of the wind stress vanishes at a geographical origin. This origin (y = 0) is the point at which CTWs are generated and its inclusion or otherwise, can have an important effect on the shelf circulation. Due to computational costs however, the origin may be chosen to lie well outside the site (y = Y) of the backward open b.c. of the regional model. In order to simulate the wind-forcing over the omitted region [0, Y], previous studies have used coastal sea level data to drive a first mode CTW paddle at the backward boundary. Using linear theory, we show that if only one mode is present, then the sum of the (local) wind and paddle forced solutions obtained for y > Y is exact. That is, the total solution is identical to that obtained if the origin were included. Where higher modes are present, a first mode CTW paddle may lead to errors in the shelf break circulation and upwelling. However, using results for the CODE region, we show that these errors decrease with frequency and that relative to the first mode, may be 20% or less. A first mode paddle might be used in storm surge and models of coastal circulation. These results are used to discuss the nature and design of regional models of wind-forced shelf circulation.