On the Abel Equation of the Second Kind with Sinusoidal Forcing

Abstract

We consider the Abel equation of the second kind with sinusoidal forcing, which is a model equation for western boundary outflow in the Stommel model of the large scale ocean circulation. Series solutions of this equation indicate the presence of resonances at certain discrete values of a parameter which measures the nonlinearity of the flow, but numerical solutions using a standard scheme show no evidence of these resonances. We discuss and resolve this apparent contradiction.

Keywords

• Abel equation
• series solution
• resonances
• boundary layer