Durbiれ楕円緩和モデルに基づく応力方程式モデルの自由表面乱流への適用性について

摘要

乱流の一点完結モデルにおいては，圧力変動を含むrn相関項のモデリング，特にその境界近傍での取り扱いrnが予測精度の向上を図る上でボトルネックとみなされrnている．Durbinの楕円緩和モデルは様々な検討を経rnて，現在では上述の問題に対する最も有用な解決rn法のひとつと位置付けられており，様々な派生法も提rn案されている．%The elliptic relaxation model of Durbin [J. Fluid Mech., 249 (1993) 465], which has had remarkable success in predicting wide variety of flows, is applied to prediction of free-surface turbulence for the first time. A set of appropriate free-surface boundary conditions for the elliptic relaxation equations is derived by taking account of the balance of dominant terms in the Reynolds-stress transport equations in the vicinity of a free surface. Test calculations for a fully-developed turbulent open-channel flow is conducted. The flow consists of two kinds of impermeable boundaries, a solid wall and a free surface, and hence is quite suitable to the present benchmark flow. It is demonstrated that the proposed boundary conditions do enable elliptic relaxation models to reproduce the correct surface-induced stress anisotropy and that the model properly describes the differences in feature between wall-bounded flows and free-surface flows by its main quality in reproducing the non local blocking effect, 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.