In September of 1976, I began work on a two-dimensional model of water and sediment routing, under the direction of Dr. Daryl B. Simons, who at that time was the associate dean for research, College of Engineering, Colorado State University, Fort Collins, Colorado. After a few months of painstaking model development, Dr. Simons had a chance to review our progress. The task at hand was to model the flow from a river, in and out of a side embayment. Our results showed that the flow appeared to convect properly, as shown in Fig. 1 (a); however, Dr. Simons was not convinced. He mentioned that in his experience, the circulating flow pattern was not supposed to be clockwise, but rather counterclockwise. We went back to the drawing board, eventually obtaining funds from the National Science Foundation to study two-dimensional flow circulation.

Our subsequent research provided an answer to the puzzle.1 Whether the flow through an embayment was clockwise, as our model originally indicated (Fig. 1 a), or counterclockwise, as Simons had experienced (Fig. 1 b), depended on the problem scale. Under large scale, friction dominated, ciculation was hampered, and the resulting flow was clockwise; conversely, under small scale, inertia played a dominant role, circulation was promoted, and the resulting flow was counterclockwise. Thus, in principle, both Dr. Simons and the model were correct.

1 Ponce, V. M., and S. B. Yabusaki. 1981. Modeling circulation in depth-averaged flow. ASCE Journal of the Hydraulics Division, Vol. 107, HY11, November, 1501-1518.

Fig. 1 (a)  Friction-dominated 2-D flow.
Fig. 1 (b)  Inertia-dominated 2-D flow.