Rolling stones and turbulent eddies: why the bigger live longer and travel farther.

Abstract

Here we report the discovery that even the simplest, oldest and most prevalent forms of evolutionary movement--rolling bodies and whirls of turbulence--exhibit the same body-size effect on life time and life travel as the evolutionary movement united by the body-size effect so far: animals, rivers, vehicles, jets and plumes. In short, the bigger should last longer and travel farther. For rolling bodies, the life span (t) and the life travel (L) should increase with the body mass (M) raised to the powers 1/6 and 1/3, respectively. The number of rolls during this movement is constant, independent of body size. For an eddy of turbulence, t should increase with the eddy mass (M) raised to the power 2/3, while L should increase with M(2/3) times the bulk speed of the turbulent stream that carries the eddy. The number of rolls during the eddy life span is a constant independent of eddy size.