Гидродинамика

476 ON SHOWDRITS AND ON SILTING OF RIVERS c o n s t a n t s are determined by the condition that at t — Q the particle having the x-coordinate equal t o X q slides along the ground with the velocity of wind and is lifted with a velo­ city ЧУо> A peculiarity of the integral (12) expressing x in function of time is that at the instant t = determined by equation (13), the abscissae of all points for which are satisfied the initial con ­ ditions stated above ЬесЪте epual, whatever the initial abscissa .Гд. Hence, if f = " corresponds to the instant at which the falling particles come in contact with the ground, all snowflakes will fall at the same place whatever the value of Xq at the Instant when they were lifted, and there will be formed a mound. A s the equation (13) is satisfied by all values of pif =P " w h e r e n is an integer, there will be formed in front of the obstacle a number of mounds determined by abscissae (14). The mound nearest to the obstacle and the largest of all has the abscissa Ak In the second case the differential equations of motion of the snowflakes have the form (18). The general solutions are repre ­ sented by the sum of integrals (24) and (26). The motion of a snowflake is composed of two motions. The first motion is along a path having t he form of an ellipse concentric with and similar t o the lines of flow, having indeterminately increasing axes, and depending on the arbitrary constant A\ the second motion is along a similar ellipse having the centre displaced along the x-axis t o the left, t o the point F, the distance OF being equal t o and the semi-axes diminishing and tending t o zero. If Аф^ a snowflake moving along an ellipse having increa ­ sing axes is thrown out of the elliptic vortex. If the initial conditions make A equal t o zero, the snowflake moving along an ellipse with diminishing axes describes a spiral- shaped path and approaches the point F, as shown in Fig. 7; at F fhe snowflake will be in equilibrium. Thus the snowflakes are sucked in by the vortex, and in the rear of the obstacle is a mound of snow.