Initiation Of Drop Velocity Oscillations During Their Fall In A Vertically Sheared Flow With Embedded Velocity Fluctuation

Drops’ fall in the horizontal sheared flow with an embedded “frozen” sinusoidal velocity fluctuation is studied. It is shown that drops’ trajectory and velocity appear to be very complicated even in this simple case. The fluctuation “frozen” in the flow concentrates droplets in certain points of equilibrium, located spatially in certain places relative to the phase of the fluctuation. The distance between these points depends on the “wavelength” of the fluctuation. Thus, “frozen” turbulence can lead to an increase of the concentration of water drops (especially small droplets) in certain zones and to a decrease of drop concentration between these zones. At a certain drop fall distance in a sheared flow a qualitative change of the drop motion character takes place: due to the saddle-node bifurcation drop velocity (and trajectory) oscillations are generated. This critical fall distance and parameters of oscillations depend on the drop mass and flow parameters: the wind shear value, amplitude and “wavelength” of the fluctuation. Below this level the amplitude of horizontal drop velocity deviation from that of the flow increases with the falling distance up to the amplitude of the flow velocity fluctuation. Drop velocity oscillations lead to the formation of a drop velocity difference in the horizontal direction (relative drop velocity), so that additional relative droplet velocity can be of the same order as the difference in their terminal fall velocities. The increase of relative velocities can be interpreted as an increase of the swept volume and an increase of the number of drop collisions per unit of time. Hence, an increase of the collision rate can be expected. Applications of the results to the problem of broadening the water droplet spectrum in clouds are discussed.