118 WIND CURRENTS AND WIND WAVES 



The coefficient Me has the same dimensions as the dynamic viscosity 

 ju, and is called the eddy viscosity. However, a fundamental difference 

 exists between the two quantities. The dynamic viscosity is independent 

 of the state of motion and is a characteristic property of the fluid, com- 

 parable to the elasticity of a solid body, but the eddy viscosity depends 

 upon the state of motion and is not a characteristic physical property of 

 the fluid. The numerical value of the eddy viscosity varies within very 

 wide limits, according to the type of motion, and, as far as ocean currents 

 are concerned, only the order of magnitude of /Xe has been ascertained 

 (table 1, p. 23). 



In the theory of turbulence the concept of the mixing length has played 

 a prominent part. This length can be defined as the average distance 

 which the small masses travel before they attain the momentum of their 

 surroundings. According to Prandtl's theory the relation between 

 mixing length, I, and eddy viscosity can be written 



.„ dv 



Me = pl' 



dz 

 According to von Karman's general statistical theory, 



(VII, 2) 



4,- 



dH 

 dz^ 



(VII, 3) 



where /co is a nondimensional universal constant that has been found equal 

 to nearly 0.4. 



So far, only horizontal shearing stresses have been considered, but 

 recently evidence has been accumulated showing that in the ocean ver- 

 tical shearing stresses also exist. It has been found that coefficients of 

 horizontal mixing must be introduced which are so great that the corre- 

 sponding stresses cannot be neglected (table 3, p. 25). 



In dealing with wind currents, only the terms related to vertical 

 mixing have been considered, but it is probable that a complete theor}^ of 

 the dynamics of ocean currents cannot be developed without taking 

 horizontal mixing into account. 



The Stress of the Wind 



Methods used in fluid mechanics for studying frictional stresses at 

 solid boundary surfaces can be applied, as was first shown by Rossby, 

 in examining the stress that the wind exerts on the sea surface. Over an 

 absolutely smooth surface the flow will generally be laminar within a very 

 thin layer near the surface — the laminar boundary layer. Above this 

 layer, the thickness of which is a small fraction of a centimeter, turbulent 

 motion exists. On the assumption that near the boundary surface the 



