If we resolve the pressure of the wind into its component parts , we obtain 



Pn = P sin a, (j^j 



Pt = P COS a, (2) 



where Pr, is the wind pressure on the plane, perpendicular to the wind — the active force-power of 

 the wind; p+ the pressure gliding along the windward surface of the hummocks (therefore, insig- 

 nificant in the first approximation of the movement and heaping of ice); p the pressure in the di- 

 rection of the wind; and a the slope angle of the hummocks . 



Resolving further the operating power-force of the wind on the vertical and horizontal com- 

 ponents, we obtain 



Ph = Pn Sin a=p sin^ a, 



p„ = p„ cos a = -|- sin 2a, W 



where Py is the moving force of the wind, or the power-force, which causes the drift of the ice; 

 and Ph is the drowning power of the wind, or the power which causes vertical fluctuation of the 

 ice cover. 



From formulas (4) and (3), it follows that the wind attains its maximmn moving force with 

 ice blocks having perpendicular walls. However, the maximum drowning force of the wind is at- 

 tained with hummocks having slopes of 45° . In this case, we have 



P = -^ (5) 



^" 2 • 



Furthermore, we know that the wind pressure on a unit area, perpendicular to the wind, is 

 approximately proportional to the square of the wind velocity, 



p = aw\ (6) 



where w is the wind velocity; a is the coefficient of proportionality. 



From the formulas cited above, it follows that with an adequate wind velocity and with a 

 small hummock-floating, the drowning power of the wind may be greater than the floating of the 

 hummocking and thus cause it to sink. 



Since the drowning power-pressure of the wind is determined also by the inclination and the 

 area dimensions of the windward slope of the hummock, individual parts of the ice fields with an 

 irregular upper surface are subjected to various stresses. This generates vertical movements of 

 separate parts of the ice field, and thus its eventual break-up. 



In the derivation of the cited formulas, I took into consideration the laminar motion of the 

 air current, but the air is turbulent and its vertical components create disproportionate stress, 

 even on completely level fields. As a result, vertical fluctuations are caused in the ice, similar 

 to a wind wave on the surface of the sea. 



Observers repeatedly noted the appearance of wind ripples on the thin ice. Bernstein points 

 out that the instrument observations carried out in 1927 on the Volga established, without a doubt, 

 the origin of the wind fluctuations of the ice level. Thus , with a wind of 13 m/sec . (which 



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