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Show The viscosity of the water film on the snow crystals is the controlling factor for the visposity of wet snow; the viscosity of air for the viscosity of well- aerated snow. For this the criteria of Reynolds for the beginning of turbulence yield velocities of the magnitude of 1 m/ sec. In dense, dry snow larger viscosities will be in effect; it must include in all cases the disintegration of the snow blocks and then the turbulent movement if the shear resistance ( for example Ts~ 50 kg/ m2) in vertical sections is overcome. In turbulent flow with the average velocity, v, the flow resistance per square meter of ground surface can be equated empirically as 2 Y v •** ~ - r in . mich, by analogy to hydraulics, the velocity coefficient £ for a rough stream course can be set at g ~ 500 m/ sec2 as demonstrated below. For y = 250 kg/ m it follows that 2 2 2 v = S~ S = 500 . 50 = 100 m / sec Y 250 that is, the disintegration of the snow and its turbulent movement must in all cases begin after exceeding a flow velocity of about 10 m/ sec. Up to the critical velocity the snow either flows in laminar fashion or moves as a quasi-solid with frictional resistance. The eddies of turbulent movement result in varying vertical accelerations, which, similar to the vibration of concrete, decrease the effect of the internal friction and the viscosity, so that for further flow the prin - ciples of hydraulics are largely valid. The flow is shooting or streaming accordingly as the average flow velocity is larger or smaller than the velocity of propagation of the surface waves. A surge of incremental height A h propagates with the velocity, w, on the flowing snow layer of height, h, and the material behind the wavefront flows after with the mean velocity, w - v; thus the continuity equation for the section before and after the wave front is: h * w = ( h + A h) v The momentum equation for this section is: 2 2 ( y/ g) h w( w -• v) - Y I2 f( h + - h) " h 3 From these two equations it follows that ( 1) w= [ gh ( 1 + M / h ) ( 1 +( 1/ 2) ( A h / h ) ) ] 1 / 2 The wave velocity, w, increases with h and A h, higher waves move faster than lower ones, avalanches are not flattened out during their movement, but maintain relatively abrupt boundaries ( Figures 19 and 20). Figure 22 shows how sharply an avalanche tore out a gap from the middle of the village of Vals; a part of a house in the foreground was torn off by a sharp cut, 18 |
