Investigating Nonlinear Dynamics in Atmospheric Aerosols during the Transition from Laminar to Turbulent Flow

Abstract

This paper investigates the nonlinear dynamics of atmospheric aerosols during the transition from laminar to turbulent flows using the framework of Scale Relativity Theory. It is proposed that the transition from multifractal to non-multifractal scales (in the dynamics of the atmospheric aerosols) can be assimilated to the transition between laminar and turbulent states. These transitions are determined by the multifractal diffusion and deposition processes. The methodology used involves the application of the principle of scale covariance, which states that the laws of atmospheric physics remain invariant with respect to spatial and temporal transformations as well as scale transformations. Based on this principle, several conservation laws are constructed. In such context, the conservation law of the density of states associated with the multifractal-non-multifractal scale transition in a one-dimensional case is then considered. The model describes the non-linear behaviour of atmospheric aerosols undergoing diffusion and deposition processes. The theoretical approach was correlated using experimental data from a ceilometer and radar reflectivity factor data.