DIRECT NUMERICAL-SIMULATION OF TURBULENT-FLOW OVER A WAVY WALL

The Navier-Stokes equations have been solved, by a pseudospectral meth od, for pressure-driven flows between a no-slip wavy wall and a slip f lat wall. Periodic boundary conditions were used in the streamwise and spanwise directions. The physical domain is mapped into a computation al domain that is a rectangular parallelepiped using a nonorthogonal t ransformation. The pseudospectral solution procedure employed in previ ous studies, for example, Lam and Banerjee [Phys. Fluids A 4, 306 (199 2)], eliminated the pressure and solved for the wall-normal velocity a nd vorticity. The other velocity components were calculated using the definition of vorticity, and the continuity equation. This procedure l eads to oscillations in the pressure held when solutions were attempte d in the mapped computational domain. To overcome the problem, the pro cedure had to be modified and the pressure served for directly using a fractional time step technique. For the cases examined here, these mo difications resulted in spectral accuracy being maintained. Flow over sinusoidal wave trains has been simulated and the results compare well with available experiments. The simulations show significant effects of the wavy boundary on the mean flow and the turbulence statistics. T he mean velocity profile differs substantially from the profile for th e flat-wall case, particularly in the buffer region where the fluid is under the influence of both the wavy wall and the slip boundary. The velocity fluctuations in the streamwise direction decrease in the buff er region. This effect becomes more pronounced when the wave amplitude increases. Most of the redistribution of energy, from the streamwise direction to the spanwise and wall-normal directions, occurs in a thin layer close to the boundary, downstream of the wave troughs. The ener gy primarily redistributes into spanwise fluctuations. High shear stre ss regions form downstream of the wave troughs, and streaky structures and quasi-streamwise vortices are also seen to initiate in these regi ons. The length of the streaks, and the extent of the quasi-streamwise vortices, scale with wave length for the two cases investigated. (C) 1997 American Institute of Physics.