Ripples from a splashing drop

When Jordan Spieth failed to make the green on the 12th at Augusta in 2016 and saw his ball plunge into the lake, his dismay was perhaps tempered by the beautifully symmetric ripples or waves emanating from the point where the ball entered the water. An example of such a splash can be seen in Figure 1.

This is a classical free surface fluid mechanics problem involving the Navier–Stokes equations together with the conservation of mass. These may be solved by a variety of methods. We choose a finite difference method employing marker and cell (MAC method) on a staggered grid, which we have been developing over many years. A review of the MAC method may be found in [1]. Figure 2 displays the numerical solution of a splashing drop at three different times using the MAC method (albeit, in a confined region with wave reflection). Note that in Figure 1, a series of concentric crests and troughs are observed whose amplitudes are not constant, nor are the distances between the crests.