CHAPTER VII 



Wind Currents and Wind Waves 



Frictional Forces 



In the discussion of the currents related to the distribution of mass, 

 frictional forces were disregarded, but they must be taken into account 

 when considering the effect of the wind. 



Two of the fundamental concepts concerning friction in a fluid are (1) 

 that shearing stresses are produced when layers are slipping relative to 

 each other, and (2) that the shearing stresses acting on a unit area are 

 proportional to the rate of shear normal to the surface on which the stress 

 is exerted. Thus the horizontal stress parallel to the x axis is t^ = fidv^/dz, 

 where the factor of proportionality, n, is the dynamic viscosity of the 

 fluid. The quantity v = n/p is the kinematic viscosity. 



Frictional forces per unit volume are equal to the difference between 

 shearing stresses exerted on opposite sides of a cube of unit dimensions. 

 Introducing differentials, one obtains the x component of the frictional 

 force per unit volume: 



if M is a constant. 



In classical hydrodynamics the dynamic viscosity, /u, is considered to 

 be a characteristic property of the fluid — namely, the property that 

 resists angular deformation. Being a characteristic property, the magni- 

 tude of /x is independent of the state of motion, but as a rule it varies with 

 the temperature of the fluid. Within wide limits it is independent of the 

 pressure. 



In a fluid in turbulent motion, much larger shearing stresses develop 

 (Reynold's stresses) which are related to transport of momentum that is 

 caused by irregular exchange of mass between neighboring layers moving 

 with different mean velocities. If the horizontal components of the mean 

 velocities are called Vx and Vy, the components of the Reynold's stresses are 



dVx J dvy 



T. =.M.-^ and r„ = M.-^- 



117 



