The Level of No Motion in an Ideal Fluid

Abstract

Abstract The level of no motion plays a central role in the classical dynamic method and the more advanced diagnostic schemes of the β-spiral (e.g., Stommel and Schott) and inverse method (Wunsch) to calculate the absolute velocity in the ocean. Following simple arguments, each velocity component should vanish on separate surfaces in the fluid and the absolute velocity vector vanishes on the intersection of these surfaces, i.e., on curves in the fluid. It has been suggested, however, that besides these simple configurations there may be surfaces in the fluid on which the velocity vector vanishes. Killworth has been a diagnostic scheme on this concept which is different from the β-spiral approach and the inverse method. In this note we examine the possible configuration of the level of no-motion in a fluid using ideal fluid theory. It is shown that stagnation surfaces in the fluid, i.e. surfaces on which the velocity vector vanishes, normally do not exist.