Applicability of elliptic-relaxation method to free-surface turbulence

作者：Yokojima Satoshi^*; Shima Nobuyuki

来源：Fluid Dynamics Research, 2010, 42(3): 035505.

DOI：10.1088/0169-5983/42/3/035505

The elliptic-relaxation method of Durbin (1993 J. Fluid Mech. 249 465-98), which has had remarkable success in predicting benchmark flows of many different types, is applied to prediction of free-surface turbulence for the first time. An appropriate free-surface boundary condition for the elliptic-relaxation equation is derived by taking account of the balance of dominant terms in the Reynolds-stress transport equation in the vicinity of a free surface. Test calculations for a fully developed turbulent open-channel flow are conducted. The flow consists of two kinds of impermeable boundaries, a solid wall and a free surface, and hence is quite suitable as a new benchmark flow. It is demonstrated that the proposed boundary condition does enable the elliptic-relaxation method to reproduce the correct surface-induced stress anisotropy and that the model properly describes the differences in features between wall-bounded flows and free-surface flows by its main quality in reproducing the non-local blocking effect, a kind of an elementary process of boundary-turbulence interaction. It is also found that the turbulent-transport term plays a central role in characterizing free-surface turbulence, which is therefore quite suitable for critical evaluation of the model performance.

• 出版日期2010-6