Semigeostrophic gravity waves associated with a coastal boundary current, which has finite and uniform potential vorticity and is bounded away from the coastline by a density front on the ocean surface, are investigated. It is shown that the semigeostrophic coastal current has two waves which are named here the Semigeostrophic Coastal Wave (SCW) and the Semigeostrophic Frontal Wave (SFW). The SCW becomes an elementary Kelvin wave at some limit while the SFW is caused by the existence of the surface density front. The SCW appears mainly as variations in the upper layer depth at the coast and as alongshore velocity at the density front. On the other hand, the SFW appears mainly as variations in the width of the current. When the weak nonlinearity and ageostrophic effect are included, these semigeostrophic gravity waves satisfy the Kortweg- de Vries equation, which suggests that the local changes in the width and/or velocity of the semigeostrophic coastal current propagate as wave-like disturbances.
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