Equatorially trapped nonlinear water waves in a β-plane approximation with centripetal forces

In this paper we present an exact and explicit nonlinear solution of a -plane approximation to the governing equations which retains all Coriolis terms. The solution represents an equatorially trapped wave propagating in the presence of a constant underlying background current. In particular, we show that retention of the (relatively) small-scale centripetal forces in the governing equations enables us to admit currents of any physically plausible magnitude in the background flow.