178 MALKUS [chap. 4 



6. Large-Scale Momentum Relations 



Momentum exchange is the most direct and immediate hnk between atmos- 

 pheric and oceanic circulations and the major source of ocean movements. 

 Whenever a wind blows over any part of the sea, some of its momentum is 

 imparted by turbulent drag, or shearing stress, to the upper water layers. 

 Ripples and surface waves are generated locally even by light winds ; storm 

 winds build up towering seas which travel as swell to far distances, or pile up 

 as breakers and destructive surges on nearby coasts. The integrated action of 

 wind systems results in large-scale translation of water masses, and under the 

 influence of the earth's rotation is the primary driving force of the major 

 current systems ; these are the huge anticyclonic gyres and their intense 

 western boundary jets, such as Gulf Stream and Kuroshio whose important 

 effects on heat budget climatology we have already noted. For the atmosphere, 

 on the other hand, surface drag is the major braking force; it is the only 

 sink of the winds' momentum and the major destroyer of their kinetic 

 energy. 



Thus the understanding and evaluation of turbulent stress at the air-sea 

 boundary is of concern to nearly all aspects of the earth sciences. To the 

 oceanographer it is the key energy source for several of his most important 

 phenomena, and, to the meteorologist, it is a major constraint within which all 

 atmospheric circulations must operate. Unfortunately, the process of turbulent 

 stress production at a rough boundary of which the very shape itself depends 

 on the turbulence is, to say conservatively, complex to attack and has scarcely 

 been approached from a fundamental hydrodynamic analysis. Studies of 

 wave generation and prediction of their spectrum, where the details at the 

 interface are of primary concern, have had to draw upon ingenious hypotheses 

 and careful empiricism (see Munk, 1955; Miles, 1957 and 1959; Phil]i])s, 

 1957). 



For larger-scale processes such as the maintenance of major currents and 

 the braking of atmospheric circulations from the size of the cyclonic storm and 

 upward, what is desired is an integrated shearing-stress distribution over many 

 square miles and days, and a method of calculating it from standard and 

 readily accessible data. Theoretical models of the wind-driven ocean-current 

 patterns (Munk, 1950) show that it is the curl of the wind stress, or a combina- 

 tion of spatial derivatives of rectangular components of to, that enters the 

 equations as the driving term. To predict the mean annual picture of wind- 

 driven ocean circulations, then, the climatological stress distribution is required 

 with sufficient accuracy to obtain these derivatives. 



Oceanographers studying fluctuations and resi^onse times of water masses 

 would wish to know time variations in stress in the diff"erent portions of the 

 oceans and their functional dependence, as would the meteorologist studying 

 the dynamics of wind systems, in whose equations the turbulent stresses enter 

 as the major dissipation terms. It is with these aspects of momentum exchange 

 that we shall now concern ourselves. 



