Dimensionless Groups by Entropic Similarity: II-Wave Phenomena and Information-Theoretic Flow Regimes.

Area of Science:

• Fluid dynamics
• Wave propagation
• Information theory
• Thermodynamics

Background:

• Traditional dimensionless groups (geometric, kinematic, dynamic similarity) are insufficient for complex flow systems.
• Part I introduced entropic similarity based on entropy production, flow rates, or information fluxes.
• Wave propagation introduces complexities in flow regime classification.

Purpose of the Study:

• To apply the information-theoretic definition of similarity to various flow systems with wave propagation.
• To define new dimensionless groups for classifying flow regimes based on information theory.
• To extend the application of entropic similarity for analyzing complex flow phenomena.

Main Methods:

• Utilized the information-theoretic definition of similarity, forming dimensionless groups of the form Πinfo=U/c.
• Applied the definition to diverse wave phenomena: acoustic, blast, pressure, gravity, capillary, inertial, and electromagnetic waves.
• Defined and applied relevant dimensionless numbers (Mach, Euler, Froude, Rossby) and introduced new groups for specific wave types.

Main Results:

• Identified distinct information-theoretic flow regimes (e.g., subcritical/mesocritical/supercritical) for systems with wave dispersion.
• Classified acoustic waves into subsonic/mesosonic/supersonic regimes and gravity/capillary/inertial waves into subcritical/mesocritical/supercritical regimes.
• Electromagnetic waves exhibit four regimes (subluminal/mesoluminal/transluminal/superluminal) due to vacuum celerity.
• Entropic analyses provided deeper insights into frictional behavior, flow transitions, and entropy transport in various systems.

Conclusions:

• The information-theoretic definition of similarity offers a robust framework for classifying flow regimes with wave propagation.
• New dimensionless groups and expanded classifications (e.g., mesocritical, mesoluminal) enhance the understanding of complex wave dynamics.
• Entropic similarity analysis significantly advances the study of wave-driven flows and associated phenomena.