Concentration field of particles ejected into a nonhomogeneous atmosphere by a moving source

We obtain and analyze analytical expressions describing the space-time evolution of the density of solid particles ejected into the atmosphere.Nomenclature f velocity distribution function of particles (depends on position and time) - t time - x position vector referenced to an earth-fixed coordinate system - x₁ and x₂ horizontal plane with x perpendicular to the trajectory plane - x₃ vertical coordinate - x_s position vector of the aircraft (source of particles) - v particle velocity - a particle acceleration due to braking in the atmosphere - g acceleration due to gravity - reciprocal of the velocity relaxation time - H scale height of the atmosphere - F(v) initial velocity distribution function - B(t) defined by (8) - Q(t) mass flow rate of particles - (t, x) density of particles created by a continuous source - o(t, x0, x⁰) density of particles created by an instantaneous point source at the point x^u - angle of the trajectory to the horizontal - V_s velocity of the aircraft - V_a velocity of the exhaust gases at the nozzle exit plane - F initial distribution function for the transverse components of the velocity - R transverse dimension of the exhaust trail - t^* time up to which one can neglect the effect of gravity - v ₃ ^* characteristic value of the vertical velocity - v characteristic value of the initial transverse velocity - determined by (17) - L determined by (43) Translated from Inzhenerno-Fizicheskii Zhurnal,58, No. 4, pp. 561–566, April, 1990.