Internal friction in certain tidal currents

Abstract

1. In the application of hydrodynamical theory to the motion of the water in the sea or ocean it has long been desirable to obtain some measure of the internal friction. Most writers on the subject have considered this to be equivalent to the determination of a "virtual kinematic coefficient of viscosity" ( k ), taken to represent the combined effect of molecular viscosity and eddy viscosity, and which was supposed to play a part in turbulent motion analogous to that of ordinary viscosity in non-turbulent motion, except that k might vary from place to place. The validity of this supposition has, however, recently been questioned. The importance of a knowledge of the internal friction was realised in 1902, when Nansen published the results of the Norwegian North Polar Expedition of 1893-96. Subsequently methods for the determination of k were proposed, the majority of which, however, involve the assumption that at a particular place k may be considered to be independent of the depth. The only tidal work on the subject is due to J. Proudman and J. H. Powell. At the present time, however, no laws are known for the accurate prescription of the internal frictional forces, they are certainly not the simply viscous forces of non-turbulent motion.