Giuseppe Buffoni and Andrea Cappelletti

Ekman equations for wind-driven currents: a theoretical analysis of some related numerical integration schemes

Pages: 407-421
Received: 13 May 2010   
Accepted.: 8 November 2010
Mathematics Subject Classification (2000): 65M06, 65M12.

Keywords: Ekman equations, wind-driven currents, time integration schemes, stability.

Abstract: The Ekman equations for wind driven ocean currents are summarized, and the associated boundary conditions are discussed. The discrete space equations of the numerical approximation are formulated in both real and complex form, because both these forms are used in the analysis of their integration in time. Time integration procedures for the discrete space equations to simulate different responses of the system, either undamped or damped oscillations, are illustrated. Upper bound conditions on the size of the time step are given for the stability and convergence of the numerical schemes.