Geometric Self-Similarity of Coherent Structures in Two-Dimensional Turbulent Flows

Professor Introduction

X. L |  Ph.D.

Home Institute：Xiamen University

[ Research Interests ] Turbulent boundary layer flows, time series analysis, quantitative analysis, financial series analysis
[ Teaching Experience ] Lecturer in Financial Mathematics at Chongqing University of Technology
[ Additional Experience ] Active participant in several national and international research projects

Project Description

This Project delves into the geometric self-similarity of coherent structures in two-dimensional turbulent flows, utilizing numerical simulation data to analyze the geometric shapes and aspect ratios of vortical structures of various sizes. The Project aims to uncover the self-similarity patterns within the turbulent energy cascade, enhancing the understanding of two-dimensional turbulent flows. Through a combination of theoretical analysis and practical simulations, students will develop a comprehensive understanding of the self-similar nature of turbulence.

Project Keywords

Project Outline

Part 1 : Fundamentals of Turbulent Flows
• Introduction to turbulence and its characteristics
• Overview of two-dimensional turbulence
• Key concepts and definitions

Part 2 : Numerical Simulation of Turbulent Flows
• Techniques for simulating two-dimensional turbulent flows
• Data acquisition and processing
• Case studies of numerical simulations

Part 3 : Geometric Self-Similarity in Turbulence
• Definition and importance of geometric self-similarity
• Analysis of vortical structures in turbulent flows
• Aspect ratios and scaling laws

Part 4 : Energy Cascade and Self-Similarity
• Understanding the turbulent energy cascade
• Self-similarity in energy transfer processes
• Quantitative methods for analyzing self-similarity

Part 5 : Applications and Advanced Topics
• Practical applications of self-similarity in engineering and science
• Advanced topics in turbulence research
• Future directions and open questions in the study of turbulence

Suitable for

• High School Students interested in applied mathematics, fluid mechanics, and computational science.