A numerical prediction method has been developed for local scour on a sand bed due to turbulent flows on the basis of the arbitrary Lagrangian-Eulerian formulation, in which three-dimensional body-fitted coordinates are properly generated for the sand bed profile unsteadily deformed by the flows. The curvilinear coordinates are generated with reasonable accuracy by means of cubic spline interpolations. The equations for momentum,turbulent quantities, and sand concentration are discretized in a Lagrangian scheme so as to preserve second-order accuracy with respect to time and space. The convection of the variables are evaluated with third-order accuracy, taking account of the velocity of the grid point caused by ALE formulation, On the other hand, the sand bed profiles are predicted with the continuity equation for sand by evaluating the total flux consisting of the bed and suspended loads caused by the tractive and convective forces of the turbulent flows. This prediction method is applied to the results of a three-dimensional local scour experiment. From the comparison with the experimental results, it is verified that the sand bed profiles are satisfactorily predicted and that the predicted results are largely improved compared with those based on the Eulerian coordinate system. (C) 1996 Academic Press, Inc.