Identification of the continuum field structure at multiple scale levels.

Area of Science:

• Fluid dynamics
• Complex systems analysis
• Geometrical field theory

Background:

• Continuum field analysis, like turbulence, requires quantitative methods for kinematic and dynamic insights.
• Traditional dissipation element (DE) structures are susceptible to noise, limiting large-scale feature extraction.
• Space-filling and structure quantification are crucial for accurate field analysis.

Purpose of the Study:

• To introduce a multi-level dissipation element (DE) structure based on extremal points for improved field analysis.
• To demonstrate the method's ability to represent field geometry and extract large-scale features.
• To validate the approach using artificial fields, fractal Brownian motion, and two-dimensional turbulence.

Main Methods:

• Decomposition of fields into space-filling, non-overlapping multi-level DEs at each scale level.
• Characterization of DEs by length scale (l) and scalar difference (Δϕ).
• Introduction of structure function and energy spectrum equivalents for fractal Brownian motion analysis.

Main Results:

• Decomposed units accurately represent the geometry of an artificially constructed two-scale field.
• Derived scaling relations from the structure function equivalent correlate with the Hurst number.
• The multi-level DE structure effectively distinguishes two inertial ranges in two-dimensional turbulence.

Conclusions:

• The proposed multi-level DE structure offers a robust method for analyzing continuum field geometry.
• This approach overcomes limitations of traditional DE methods by reducing noise sensitivity.
• The technique shows significant potential for advanced analyses of complex field structures.