Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion

Abstract

The accurate determination of atmospheric temperature with telemetric platforms is an active issue, one that can also be tackled with the aid of multifractal theory to extract fundamental behaviors of the lower atmosphere, which can then be used to facilitate such determinations. Thus, in the framework of the scale relativity theory, PBL dynamics are analyzed through the aid of a multifractal hydrodynamic scenario. Considering the PBL as a complex system that is assimilated to mathematical objects of a multifractal type, its various dynamics work as a multifractal tunnel effect. Such a treatment allows one to define both a multifractal atmospheric transparency coefficient and a multifractal atmospheric reflectance coefficient. These products are then employed to create theoretical temperature profiles, which lead to correspondences with real results obtained by radiometer data (RPG-HATPRO radiometer), with favorable results. Such methods could be further used and refined in future applications to efficiently produce atmospheric temperature theoretical profiles.

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

“…It is acknowledged, in accordance with references [12][13][14], that the atmosphere can be represented as a fractal/multi-fractal mathematical object, both structurally and functionally. The dynamics of this object, as described by the Multifractal Theory of Motion [10], is represented by continuous and non-differentiable curves (multifractal curves), which implies the functionality of the scale covariant derivative.…”

“…The singularity spectrum of order α, denoted by f (α), is determined by α = α(D F ), where D F is the fractal dimension of the motion curves of the structural units of any atmosphere. It is important to note that the atmosphere is always assimilated to a complex system [8,[11][12][13][14].…”

“…ii. Multifractal atmospheric dynamics by non-Markov stochasticity imposed by the following constraints [12,13]:…”

“…For 𝑡 ≪ 𝑡 = , Equation (32) becomes the following: Both Figures 1 and 2 show that both density and deposition rate stabilize in space and time. Such a situation is realised at the boundary between turbulent and laminar dynamics, i.e., according to [12,13] along the laminarity channel.…”

“…(i) A β model for the generation and analysis of atmospheric turbulence [12]; (ii) A computational method for the determination of the planetary boundary layer and its properties [13]; (iii) The removal of atmospheric turbulence through laminar channels [14].…”