We describe our experience in formulating open boundary conditions to apply at the mouth of a reduced-gravity model of a bay. Our objective is to find a way to calculate the response of the bay to wind forcing over the bay itself, without being concerned about the influence of regions beyond. We show that open boundaries from which Kelvin waves can propagate along the coast into the model domain (''upstream'' boundaries) must be treated with care. We begin by considering an ''upstream'' boundary which runs perpendicular to the coast. We find that if a radiation condition is applied on such a boundary, then spurious Kelvin waves of near-inertial period can propagate in from the boundary and contaminate the solution in the interior of the model domain. Also, if there is Ekman transport at the ''upstream'' boundary away from (toward) the coast, then upwelling (downwelling) will occur indefinitely and completely swamp the model solution in the bay. This is similar to the solution we expect when the coastline is straight and extends to infinity in the ''upstream'' direction. However, it is not the same, since the rate of upwelling (downwelling) is roughly half the theoretical value for that case.

For the problem of a bay we suggest that the way to deal with this is to extend the coastline out to sea on the ''upstream'' side of the mouth and apply a condition on the artificial stretch of the boundary which suppresses Kelvin wave propagation but is also not prohibitively reflective to outgoing Poincar¿ waves. For our problem a condition of zero normal gradient in interface displacement seems to be sufficient. This condition also captures reasonably well the near-inertial Kelvin waves that are generated by the northwest corner of the bay (which are a genuine part of the solution) as long as the other boundaries are sufficiently far from the bay. We have also experimented with using sponge layers rather than radiation conditions on the other boundaries. We find that sponging only the interface displacement and leaving the velocities undamped gives results that compare well with those obtained using radiation conditions. On the other hand, sponging the velocities as well as the interface displacement leads to significantly different results. This is the case even if only the ''pressure-driven'' part of the velocities is sponged and the Ekman part is left undamped. This suggests that applying highly viscous layers around open ocean parts of model boundaries can be counter-productive. It is sometimes better to damp only the density field and leave the velocities undamped. Finally, we discuss how our results apply to three-dimensional general circulation type models. ¿ American Geophysical Union 1991