A note on discrete descriptions of water flows in material variables

The paper describes the problem of discrete formulation of plane fluid flows in material description. The investigation is confined to chosen cases of stationary potential and vortex motion of an incompressible inviscid fluid within circular domains with perfect boundaries. The paths of fluid particles are obtained by numerical integration of momentum equations within a discrete time space. Brownian type random disturbances are attached to the displacement field obtained by the integration. It has been shown, that the discrete formulation may lead to solutions in which a small distance between two material points may grow to a relatively large value after a finite elapse of time. The last feature of the procedure may be a serious drawback of the discrete formulation in the material variables.