This problem was suggested by Bradley Klee. For the related case of one cylinder rolling inside another, see [1]. When one cylinder is directly above the other, we define the line of contact of the lower cylinder, 1, with the horizontal plane to be the z-axis, at x = y = 0. Then, the condition of rolling without slipping for the lower cylinder is that when it has rolled (positive) distance x1, ...

Long waves caused by storm surges or river floods can significantly impact marine and fluvial structures such as bridge piers. Apart from the forces that they generate on structure, also contribute to formation of turbulent eddies downstream obstacle. This is relevant, in this way affect both an erodible bottom ecosystem. The present study describes a medium-scale experiment, which propagation ...