A Model of Undertow in the Surf Zone

This paper deals with basic equations for velocity profile of undertow in the surf zone. Svendsen's boundary condition at the wave trough level is modified by matching the time-changing rates of momentum and turbulent shear stress produced by breaking waves. A velocity profile of undertow is expressed as a parabolic function of the distance from the bottom. The solution involves two important parameters which represent the nonlinearity of wave motion and the magnitude of turbulence produced by surface rollers. After determining both the parameters in simple forms, theoretical profiles of the undertow velocity are calculated and compared with Svendsen's solutions and experimental results of Stive and Wind. A reasonable agreement is found for the inner region, whereas the agreement is not sufficient for the outer region immediately shoreward of the break point.