Ripple Bed Effect

Influence of bottom curvature and steep slope on wave reflection and transmission

Calculated wave height profile along a wave flume with 10 sinusoidal bedforms

      Monochromic waves were generated at one end of a one-dimensional wave flume.  In the middle of the flume, there were 10 sinusoidal bedforms (amplitude, b = 0.05 m and length, L_s = 1.0 m).  The average water depth within the sinusoidal bed area was the same as the water depth before and after the sinusoidal bedforms.  When waves encountered this kind of bed, some of the wave energy reflected back and some passed through. Although this is a one-dimensional case, we can use the two-dimensional  model to simulate the wave transformation along this flume.  The positive x direction was selected as the wave propagation direction to reduce the band width of the matrix B.  In the y direction, an arbitrary number of grid points (21) was selected to represent the channel width.  At x = 0, the given wave boundary condition was specified.  At the flume end, a total passing-through boundary condi-tion was specified.  On the two y-directional borders, a total reflection boundary condition was used. There are many modes of evanescent waves that are stationary at where they were generated (Massel, 1995). The model also performed very well in identifying the maximum wave reflection.  Responses using the mild slope equation and the 1-D extended mild slope equation are also given in this diagram for comparison.  As expected, the 1-D model of the extended mild slope equation performs very close to the 2-D model.  This diagram clearly shows that the mild slope equation is not adequate for simulation of this phenomenon. For details, see Maa et al. (1998).

Comparison of calculated and measured wave reflection coefficient for 10 sinusoidal bedforms