The Evolution of Turbulence Theories and the Need for Continuous Wavelets

Core Concepts

The author discusses the historical evolution of turbulence theories, emphasizing the importance of continuous wavelets in studying turbulence.

Abstract

The content delves into the history, definitions, and key figures in turbulence research. It highlights the role of Reynolds numbers, flow regimes, and turbulent diffusion. The article also explores various approaches to studying turbulence, including kinetic statistical theories, probabilistic statistical theories, and deterministic theories. Laboratory experiments and numerical simulations are discussed to provide insights into understanding turbulent flows.

Stats

"Reynolds number is quantified by the ratio between convective term norm and dissipative term norm."
"Laminar regime occurs at low Reynolds numbers (typically between 0 and 102)."
"Weak turbulence regime exists at moderate Reynolds numbers (typically between 102 and 105)."
"Strong turbulence regime occurs at high Reynolds numbers (typically above 105)."
"Turbulent flows transport quantities more efficiently than laminar flows."
"Kinetic energy reaches equipartition due to fluid viscosity."
"Turbulent dissipation refers to loss of kinetic energy in turbulent flows."
"Turbulent diffusion leads to efficient mixing in fluids."
"Vortex tubes play a dynamic role in turbulent flows."
"Energy spectrum scaling depends on non-linear dynamics of turbulent flows."

Quotes

"The most natural hypothesis is that vorticity distributions concentrate into sheets and lines under distortion." - Townsend [128]
"It seems remarkable that a flow with organized structure could exhibit randomness." - Brown & Roshko [10]
"Numerical simulation remains an art." - Orszag & Israeli [1974]

Key Insights Distilled From

The evolution of turbulence theories and the need for continuous wavelets

by Marie Farge at arxiv.org 03-12-2024

https://arxiv.org/pdf/2209.01808.pdf

Deeper Inquiries

How has computational technology influenced our understanding of turbulence?

Computational technology has revolutionized our understanding of turbulence by enabling researchers to conduct numerical experiments that provide insights into the complex dynamics of turbulent flows. With the advent of powerful computers, scientists can now simulate and analyze turbulent phenomena with high accuracy and detail. These simulations allow for the visualization of flow patterns, identification of coherent structures, and investigation of energy cascades within turbulent flows. Computational fluid dynamics (CFD) techniques have provided a platform for studying turbulence in various scenarios, from simple geometries to real-world applications like atmospheric modeling and aircraft design.

What are the implications of coherent structures on predicting turbulent behavior?

Coherent structures play a crucial role in predicting turbulent behavior as they represent organized regions within chaotic flow fields. These structures, such as vortex tubes or sheets, exhibit distinct characteristics that influence the overall dynamics of turbulence. By identifying and analyzing coherent structures, researchers can gain valuable insights into how energy is transferred through the flow field, how mixing occurs between different fluid layers, and how vorticity concentrations impact momentum transport. Understanding these implications allows for more accurate predictions of turbulence evolution over time scales ranging from seconds to days.

How can deterministic theories enhance our comprehension of complex fluid dynamics?

Deterministic theories offer a unique perspective on complex fluid dynamics by focusing on specific mechanisms driving flow behavior. By considering non-linear interactions between vortices or filaments in turbulent flows, deterministic approaches aim to identify key features that govern flow evolution at different scales. These theories help elucidate how coherent structures emerge from random fluctuations in velocity fields and contribute to energy transfer processes within turbulent systems. Additionally, deterministic models provide insights into the formation and stability of quasi-singularities like cusp-shaped vortices or spiral filaments which influence overall flow patterns significantly.