進行する重力・表面張力波の流体粒子が描く軌道(流体数理(3),一般講演)

概要

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We consider two-dimensional progressive water-waves, which propagate with a constant speed and a constant shape. Fluid motion is assumed to be irrotational. Trajectories in a coordinate system attached to the wave are easily computed by drawing contours of the stream function. On the other hand, our interest is in trajectories of fluid particles in the stationary coordinates system. It is well-known that fluid particles in a linearized water wave of small amplitude move on a circle or an ellipse, namely closed curve. It is said that the fluid particle on the average does not move while the wave itself propagates with a constant speed. This is, however, a proposition which is valid only approximately. In fact, Stokes (1847) discovered that a particle trajectory is not closed. We compute trajectories of fluid particles and draw particle paths of gravity, capillary-gravity, and pure capillary waves. The stokes drift above is proved in a new method, and some numerical examples will be presented.
2010-09-09