Nonlinear Theories — Inertial 107 



limits us. We want to describe more minute features of the Stream: a 5 or 

 10 km. scale is more appropriate to our purpose. In this case, of course, the 

 meanders and eddies cannot be regarded as turbulence, and the mean 

 motion exhibits the structure observed by a single hydrographic section: 

 we speak of this narrow filament of moving water as the instantaneous Gulf 

 Stream. It is the Stream described in Chapter V. 



In attempting to frame a theory of the instantaneous Gulf Stream we do 

 not have meanders and eddies at our disposal to provide large lateral 

 stresses. As was mentioned in an earher chapter (pp. 62 fF.), water-mass 

 analysis indicates that there is not much mixing on a scale smaller than 

 10 km. In an attempt to obtain some quantitative information on lateral 

 shearing stresses, I recently (Stommel, 19556) analyzed a set of current 

 observations made by Pillsbury in the Florida Straits, and found that the 

 coefficient of eddy viscosity was probably less than 10® cm.^/sec, a value less 

 than 2 per cent of the coefficient employed by Munk. Of course, these 

 observations were not made in the Stream beyond the Straits, and the 

 coefficient for that region is the one which we are really interested in 

 knowing, but there are no long series of observations made there. Thus it 

 seems difficult to discover enough turbulence of a scale smaller than 10 km. 

 to provide important lateral-eddy stresses in the instantaneous Gulf Stream. 

 We should emphasize here that apparently Munk was under the impression 

 that he was deahng with the instantaneous Gulf Stream ; his comparisons 

 with hydrographic data indicate that. As I have suggested here, however, 

 there is reason to suppose that his theory really applies to the climatological- 

 mean Gulf Stream. We shall therefore attempt to frame a theory of the 

 instantaneous Gulf Stream which does not take account of any important 

 friction, but treats the Stream as essentially an inertial phenomenon. 



Before leaving this vexed question of the importance of lateral stresses 

 we should note an argument proposed by Rossby (1936 a) and Montgomery 

 (1940) and recently questioned by Morgan (1956). Rossby asserted that 

 since there is little bottom friction in the ocean, the torque of the wind 

 stress applied to the surface of the sea can only be balanced by the torque 

 of lateral shearing stresses around the coasts of the sea. Morgan (1956) has 

 shown that there are other torques that need to be considered: a Coriolis 

 torque, and a torque produced by differences of pressure at different parts 

 of the coast. The relative importance of these various torques has not yet 

 been ascertained; but much of the moral support for the indiscriminate use 

 of lateral mixing and eddy coefficients has been removed. 



Let us now explore some ideas which may provide an explanation of the 

 detailed structure of the Gulf Stream independent of friction. 



