An approximate method for estimation of fluid motion in a lake containing islands

The physical phenomenon considered in the paper deals with flow in a lake, which contains one or several islands. The flow is generated by rivers, their inlets and outlets being distributed on the shoreline of the lake. The problem to be solved consists in determination of the velocity field - in the domain bounded by the shorelines of the lake and the islands. In fact, it is attempted to arrive solely at an estimation of the field. Consequently, a rather simple physical model of the phenomenon, as well as its simple mathematical description has been applied. In particular, plane, irrotational and steady flow of ideal liquid has been introduced, the inlets and outlets of the rivers being simulated by sources and sinks. Hence, the problem reduces to determination of a complex function, representing the complex velocity field, which satisfies the impermeability condition on all contours representing the shorelines, the field being generated by the singularities already mentioned. Unfortunately, the so formulated problem is "overconditioned" or "too stiff", what means that the impermeability condition on the outer contour cannot be satisfied. Nevertheless, we arrived at a simple method for circumventing this obstacle, the payoff consisting in some modification of this contour. We had this particular modification in mind, applying the word "approximate" in the title of the paper. The paper contains results - in the form of streamline patterns - for lakes containing from 1 to 3 islands. In the relevant figures the distances between the given and the modified exterior contours can be seen distinctly - allowing the reader to draw conclusions, whether the errors due to the modifications are admissible or not. Of course, it depends anyway on the point of view of the user of the results.