The Kinematic Behavior Of Spherical Particles In An Accelerating Environment

The Kinematic Behavior of Spherical Particles in an Accelerating Environment

The Kinematic Behavior of Spherical Particles in an Accelerating Environment

The Kinematic Behavior of Spherical Particles in an Accelerating Environment

The response of a spherical particle to an accelerating environment is investigated. When the Reynolds numbers associated with such accelerations are small, the particle is in Stokes' regime and the linear equations governing its motion can be solved analytically. Outside Stokes' regime, which is the general case for spheres comparable in size to precipitation particles, the equations are nonlinear and must be solved numerically.The numerical solution indicates that particles of all sizes falling in a sheared environment are excellent tracers of the mean air motion. Even a hailstone as large as 2 cm in diameter falling at its terminal speed can be expected to follow the mean horizontal air speed within +/- 0.5 m sec -1, provided the vertical wind shear is less than 10 -2 sec 1. However, the time response of a spherical particle to a wind gust of constant velocity is quite sensitive to particle size. This response can be approximated by an expression of the form 1 e -t/[tau] where t depends on both particle size and the magnitude of the wind gust. For wind gusts of 1.0 m sec -1, [tau] is seen to vary from less than 10 -5 sec for particles smaller than 0.02 mm in diameter to 2.5 sec for a 2.0-cm hailstone. Also, when a particle is submitted to a substantial wind gust, a significant decrease in its terminal velocity occurs.It is suggested that the response of a nonspherical particle to wind accelerations will be at least as fast as this study indicates for a spherical particle of the same mass .