On the Vertical and Horizontal Concentration of Momentum in Air and Ocean Currents: I. Introductory Comments and Basic Principles, with Particular Reference to the Vertical Concentration of Momentum in Ocean Currents

In this and a following paper an investigation is made into the factors which are responsible for the characteristic “streakiness” of certain atmospheric and oceanic current systems. As a first step a search is made for the factors which might give rise to the striking vertical concentration of momentum observed in many well-defined atmospheric and oceanic jet streams. A straight, parallel, heteorogeneous and incompressible current with a free surface, hydrostatic pressure distribution and a continuous density field is analyzed theoretically to determine the particular distribution of velocity with depth which, for a prescribed volume transport within each isopycnic layer, leads to a minimum value for the transfer of momentum. This requirement leads to a certain “critical” relationship between the velocity and density distribution which in the case of a two-layer system reduces to the well-known critical relative speed at an internal fluid boundary. In the general case of a continuous density distribution it is found that currents which are subjected to momentum losses and hence tend to approach the “critical” velocity distribution in many cases must shrink vertically and develop a sharp velocity maximum at or below the free surface. The nature of the structural changes to be anticipated depends ultimately upon the numerical value of a certain “internal” Froude Number which is a function of the initial velocity distribution as well as of the total density range.