Journal of Wind Engineering and Industrial Aerodynamics, 46 & 47 (1993) 245-254 245 Elsevier Numerical Modelling of Flow Over A Rigid Wavy Surface by LES ZHENDONG LIU Department of Civil and Environmental Engineering, University of Wisconsin-Madison, Mad- ison, Wisconsin 53706 AHSAN KAREEM and DAHAI YU Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, Indiana 46556-0767 Abstract A flow field over a rigid wavy surface is numerically generated. The general concept of the large eddy simulation that captures the large scale flow structure is utilized. A coordinate transformation scheme is developed to transform any wavy surface to a flat surface. The numerical computations are carried out in the co - ~ domain. The subgrid scales are resolved by utilizing a Smagorinsky subgrid model. The fourth-order central difference and the third- order upwinding schemes are used for the diffusive and convective terms, respectively. Adams-Bashforth and Dufort-Frankel schemes are used to solve the equations of the fluid motion. The computational scheme ensured a non-penetration and a no-slip boundary condi- tion. The velocity profile, and the separation and reattachment locations are found to agree well with an experimental investigation. 1. INTRODUCTION Applications of flow over wavy surfaces span many areas of interests that include genera- tion of water waves, development and migration of sand dunes in deserts and sediment dunes in rivers. In this study, to improve our understanding of the flow over fully developed sea states, the simulation of wind flow over a rigid wavy surface is conducted. The compliant nature of offshore drilling platforms, being developed for deep water drilling, has increased their sensitivity to the dynamic effects of fluctuations in the wind loads. Limited full-scale information concerning the wind field characteristics over the ocean has prompted the exten- sion of onshore practice for the wind field analysis to offshore practice. However, there exist major differences that concern the variable nature of the sea surface which translates and deforms. Locally, the wind profile may be influenced by the changes in the sea surface and may also influence the turbulence structure. Many previous studies have addressed the topic of wind-wave interaction, but the focus has been in the interaction, wave momentum flux and pressure on the wave surface. Most of the theoretical investigation of wind-wave interaction are based on work by Miles (1957 and 1959), and Benjamin (1959). Most recent studies include modelling of wave boundary layer, based on the nonlinear Reynolds equations in a curvilinear system of coordinates (Chalikov and Makin, 1991). These studies are primarily focused on developing wave boundary layer models for input to wave prediction models. 0167-6105/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All fights reserved.