REU: Analyze Turbulence Data - 2021
REU: Analyze Turbulence Data - 2021
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Research Experiences for Undergraduates (REU) Project
Research Experiences for Undergraduates (REU) Project
Topic: Wavelet-Based Scaling Assessment and Applications
Date: Feb 2021 - April 2021
Faculty: Dr. Brani Vidakovic (Statistics Department Head at Texas A&M University)
Objective
Objective
The objective of this analysis is to determine whether the turbulence data are mono-fractal.
Background
Background
Definition
Definition
A turbulent flow is characterized by the value of its Reynolds number, a dimensionless parameter that quantifies the ratio of inertial to viscous forces. If the Reynolds number is small, the flow is laminar. With an increase of the Reynolds number, the flow becomes unstable, and when the Reynolds number exceeds a given threshold it becomes fully turbulent.
Major Problem
Major Problem
"Turbulence: motion of fluids in which the local velocities and pressures fluctuate irregularly: Most flows observed in nature such as rivers and wind are turbulent. [...] The essential characteristic of turbulent flow is that the fluctuations are unpredictable." - The McGraw-Hill Encyclopedia of Science and Technology
Measurements
Measurements
Data Visualization
Data Visualization
Mono-Fractal Diagram
Mono-Fractal Diagram
Multi-Fractal Diagram
Multi-Fractal Diagram
Conclusion
Conclusion
The turbulence is not mono-fractal. Instead, it is multi-fractal.
Amazingly, all type of turbulence flow has similar Hurst components.
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