ANALYSIS OF MEANDERING WATER RIVULETS OF FINITE-AMPLITUDE

Water rivulets on inclined smooth plate form a stable meandering patte rn under certain conditions. The bend theory for describing the meande ring water rivulet includes the effect of the surface-tension force. T he governing equations are the St. Venant equations of shallow water a s shown in curvilinear coordinates. The resultant bend equation is non linear. The linear stability analysis of this equation with minute dis turbance was done by the senior author. In that analysis, all the smal l terms (nonlinear terms) were omitted. The stable meander trajectory formed by streams has finite amplitude as derived from Cartesian sinus oidal patterns. These patterns are very similar in shape to those of m eandering rivers. The pattern of meandering rivers can be expressed by sine-generated curves. The meandering river trajectory derived from t he first-order sine-generated curve contains periodic deviation charac teristics. This deviation is caused by either fattening and/or skewing from the first-order sine-generated curve. The approximate solution f or the nonlinear analysis of the bend equation (including the surface- tension force) demonstrated that the deviations could be well formulat ed by the third-order sine-generated curves. Furthermore, the derived water rivulet forms of finite amplitude were verified by laboratory ex perimental results.