Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion
Abstract
:1. General Considerations: From Differentiability to Non-Differentiability in Atmospheric Process Dynamics
2. Theoretical Design: Non-Differentiability Calibrated on PBL Dynamics in the Form of the Multifractal Hydrodynamic Model
- I.
- The existence of a multifractal specific force implies that all PBL structure units must be considered through a multifractal medium;
- II.
- This medium can be considered a multifractal fluid whose dynamics are characterized by the hydrodynamic model presented previously;
- III.
- Since the velocity field, , is absent from the multifractal states density conservation laws, it induces the possibility of non-manifest PBL dynamics, meaning that it facilitates the transmission of multifractal specific momentum and multifractal energy;
- IV.
- All potential issues regarding reversibility and existence of the eigenstates are solved by the conservation of multifractal energy and multifractal momentum;
- V.
- When using the tensor:
3. PBL Dynamics Mimed as a Multifractal Atmospheric Tunnel Effect
- I.
- The PBL, as a complex system both in a structural and functional perspective, can be assimilated with a mathematical object of multifractal type;
- II.
- PBL dynamics can be described through the scale relativity theory in the form of multifractal hydrodynamic equations;
- III.
- The PBL works as a multifractal atmospheric tunnel effect described through the external scalar potential (see Figure 1):
- (1).
- the multifractal atmospheric incidence zone;
- (2).
- the multifractal atmospheric barrier;
- (3).
- the multifractal atmospheric emergence zone.
- I.
- corresponds to the multifractal incident atmospheric states density (from ) in the multifractal zone (1) and to the multifractal emergent atmospheric states density (to ) in the multifractal zone (3);
- II.
- corresponds to the multifractal reflected atmospheric states density, which exists only in the multifractal zone (1), passing from to since in the multifractal zone (3), the external scalar potential is uniformly null.
- The multifractal atmospheric current density of the multifractal atmospheric incident states density in zone (1):
- The multifractal atmospheric current density of the multifractal atmospheric emergent states density in zone (3):
- The multifractal atmospheric current density of the multifractal reflected atmospheric states density:
4. Experimental Design
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Cazacu, M.M.; Roșu, I.-A.; Bibire, L.; Vasincu, D.; Rotundu, A.M.; Agop, M. Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion. Fractal Fract. 2022, 6, 747. https://doi.org/10.3390/fractalfract6120747
Cazacu MM, Roșu I-A, Bibire L, Vasincu D, Rotundu AM, Agop M. Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion. Fractal and Fractional. 2022; 6(12):747. https://doi.org/10.3390/fractalfract6120747
Chicago/Turabian StyleCazacu, Marius Mihai, Iulian-Alin Roșu, Luminița Bibire, Decebal Vasincu, Ana Maria Rotundu, and Maricel Agop. 2022. "Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion" Fractal and Fractional 6, no. 12: 747. https://doi.org/10.3390/fractalfract6120747
APA StyleCazacu, M. M., Roșu, I. -A., Bibire, L., Vasincu, D., Rotundu, A. M., & Agop, M. (2022). Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion. Fractal and Fractional, 6(12), 747. https://doi.org/10.3390/fractalfract6120747