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Related Concept Videos

Turbulent Flow01:24

Turbulent Flow

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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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Introduction to Types of Flows01:23

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Fluid flows are categorized by dimensionality and behavior, with one-dimensional flow being the simplest form, where properties like velocity and pressure change only along a single axis. Water moving through straight pipes exemplifies this flow type, as variations in other directions are minimal. One-dimensional analysis helps simplify understanding such flows, focusing solely on changes along the pipe's length.
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Laminar and Turbulent Flow01:07

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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Plane Potential Flows01:23

Plane Potential Flows

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Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform...
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Poiseuille's Law and Reynolds Number01:10

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Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of pressure difference and resistance through a horizontal tube. The greater the pressure difference, the higher the flow rate. The flow resistance is expressed as:
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General Characteristics of Pipe Flow I01:22

General Characteristics of Pipe Flow I

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Pipe flow refers to the movement of fluids within fully enclosed conduits, typically cylindrical in shape, such as water pipes or hydraulic hoses. These conduits are designed to withstand high-pressure gradients that drive fluid movement, contrasting with open-channel flows, where gravity is the primary driving force. Rectangular conduits, like air conditioning and heating ducts, generally operate at lower pressures and are less suited for high-pressure applications.
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Updated: Jun 25, 2025

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods
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Recurrent flow patterns as a basis for two-dimensional turbulence: Predicting statistics from structures.

Jacob Page1, Peter Norgaard2, Michael P Brenner2,3

  • 1School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom.

Proceedings of the National Academy of Sciences of the United States of America
|May 31, 2024
PubMed
Summary
This summary is machine-generated.

Researchers reconstructed turbulent flow statistics using unstable periodic orbits. This dynamical systems approach overcomes previous limitations, offering a new predictive framework for fluid dynamics.

Keywords:
dynamical systemsmachine learningturbulence

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Area of Science:

  • Fluid dynamics
  • Dynamical systems theory
  • Chaos theory

Background:

  • Turbulence is often modeled as a trajectory in a high-dimensional state space.
  • Unstable simple invariant solutions shape chaotic dynamics but are difficult to identify and weigh.
  • Previous attempts to predict flow statistics from these solutions were hindered by a lack of known solutions and weighting theories.

Purpose of the Study:

  • To develop a method for finding unstable solutions in turbulent flows.
  • To reconstruct probability density functions (PDFs) of turbulent flow using these solutions.
  • To establish a predictive framework for turbulence statistics based on dynamical systems.

Main Methods:

  • Utilized automatic differentiation to discover invariant solutions.
  • Employed a trajectory-dependent loss function for solution refinement.
  • Converted turbulent trajectories into Markov chains for weight learning.
  • Used deep convolutional autoencoders to identify nearest solutions.

Main Results:

  • Successfully identified hundreds of unstable periodic orbits in 2D Kolmogorov flow.
  • Demonstrated reconstruction of turbulent flow PDFs using a set of these solutions.
  • Established a connection between self-sustaining dynamical processes and statistical turbulence properties.

Conclusions:

  • The developed method substantially addresses limitations in finding and weighting invariant solutions.
  • Turbulence statistics, specifically PDFs, can be accurately reproduced using unstable periodic orbits.
  • This dynamical systems approach offers a novel perspective on understanding and predicting turbulence.