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Related Concept Videos

Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

Design Example: Creating a Hydraulic Model of a Dam Spillway

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Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
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Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

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 streamlines...
Navier–Stokes Equations01:28

Navier–Stokes Equations

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Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
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Multiscale model of gradient evolution in turbulent flows.

Luca Biferale1, Laurent Chevillard, Charles Meneveau

  • 1Dipartimento Fisica and INFN, Università di Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy.

Physical Review Letters
|August 7, 2007
PubMed
Summary

A new multiscale model for turbulent velocity gradients combines restricted Euler dynamics with a cascade model. This approach regularizes singularities and accurately captures turbulence geometry and non-Gaussian fluctuations.

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Area of Science:

  • Fluid dynamics
  • Turbulence modeling
  • Statistical mechanics

Background:

  • Turbulence presents a significant challenge in fluid dynamics due to complex, chaotic velocity fluctuations.
  • Existing models often struggle to capture the full range of turbulent phenomena, including singularities and non-Gaussian statistics.
  • Understanding the evolution of the velocity gradient tensor is crucial for developing accurate turbulence models.

Purpose of the Study:

  • To propose a novel multiscale model for the evolution of the velocity gradient tensor in turbulence.
  • To investigate the role of energy cascade and restricted Euler dynamics in regularizing turbulent singularities.
  • To validate the model's ability to reproduce key geometrical and statistical features of real turbulence.

Main Methods:

  • Coupling restricted Euler (RE) dynamics, which describes gradient self-stretching, with a cascade model for inter-scale energy transfer.
  • Analyzing the mathematical properties of the coupled model to demonstrate singularity regularization.
  • Comparing model predictions for vorticity alignment, gradient tensor invariants, and derivative flatness coefficients with experimental data.

Main Results:

  • The inclusion of the cascade process effectively regularizes the finite-time singularity inherent in restricted Euler dynamics.
  • The multiscale model successfully reproduces preferential alignments of vorticity and joint statistics of gradient tensor invariants observed in experiments.
  • Gradient fluctuations predicted by the model are non-Gaussian and exhibit longitudinal skewness, with derivative flatness coefficients aligning well with experimental findings.

Conclusions:

  • The proposed multiscale model offers a robust framework for studying turbulent velocity gradients.
  • The interplay between gradient dynamics and energy cascade is essential for a complete description of turbulence.
  • The model's success in replicating key turbulence features validates its potential for future research and applications in fluid dynamics.