Journal of Fluid Mechanics


A new complementary mild-slope equation

a1 Department of Ocean and Resources Engineering, SOEST, University of Hawaii at Manoa and American Bureau of Shipping, 16855 Northchase Drive, Houston, TX77060, USA
a2 RIMSE and Department of Naval Architecture and Ocean Engineering, Seoul National University, Korea

Article author query
kim j   [Google Scholar] 
bai k   [Google Scholar] 


A new depth-integrated equation is derived to model a time-harmonic motion of small-amplitude waves in water of variable depth. The new equation, which is referred to as the complementary mild-slope equation here, is derived from Hamilton's principle in terms of stream function. In the formulation, the continuity equation is satisfied exactly in the fluid domain. Also satisfied exactly are the kinematic boundary conditions at the still water level and the uneven sea bottom. The numerical results of the present model are compared to the exact linear theory and the existing mild-slope equations that have been derived from the velocity-potential formulation. The computed results give better agreement with those of the exact linear theory than the other mild-slope equations. Comparison shows that the new equation provides accurate results for a bottom slope up to 1.

(Received March 15 2001)
(Revised September 25 2003)