Cellular Self-Structuring and Turbulent Behaviors in Atmospheric Laminar Channels

Abstract

Assimilating the atmosphere with multifractal entities, nonlinear behaviors in the framework of scale relativity theory regarding its hydrodynamic functionality are established at various scale resolutions. From this perspective, revealing a “hidden” symmetry of the specific multifractal force with the SL(2,R) group leads to synchronization of atmospheric entities on the basis of operational procedures (differential and integral Riemann-type geometries, harmonic mappings from Euclidian to hyperbolic space, variational principles, and others) that imply cellular self-structuring, laminar channels and singularities as turbulence generators. These behaviors can then be assimilated and compared with recent discoveries regarding laminar channels found in atmospheric turbulence through lidar data processing.

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.…”

“…In the context of atmospheric dynamics, we have employed the agreed methodology proposed by Rosu et al [12,14] and Cazacu et al [13]. This methodology utilises Lyapunov exponents in order to identify laminar channels within turbulent flows [12][13][14].…”

“…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].…”

“…(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].…”

“…Accurate modelling of ice clouds is essential for assessing their role in global warming, climate change, weather forecasting, and air traffic and aviation. This paper presents an alternative approach to ice cloud dynamics by implementing the previously discussed mechanisms of atmospheric laminar channels [14]. Rosu et al [12] recently presented a mathematical model that describes the motion of atmospheric entities, considering both differential and non-differential scale resolutions.…”