Related Experiment Video
Updated: May 16, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics.
1Institut des Hautes Etudes Scientifiques, 91440 Bures sur Yvette, France. ruelle@ihes.fr
Summary
Hydrodynamic turbulence is modeled as heat flow in mechanical systems. Statistical mechanics predicts fluctuations, explaining intermittency and validating a new formula for turbulence exponents with experimental data.
Area of Science:
- Physics
- Fluid Dynamics
- Statistical Mechanics
Background:
- Hydrodynamic turbulence is a complex phenomenon characterized by chaotic fluid motion.
- Understanding the scaling exponents of turbulence remains a significant challenge in physics.
Purpose of the Study:
- To reformulate hydrodynamic turbulence as a heat flow problem.
- To develop a new theoretical framework for analyzing turbulent flows using statistical mechanics.
Main Methods:
- Modeling fluid units as a chain of mechanical systems.
- Applying methods of nonequilibrium statistical mechanics to analyze fluid units.
- Deriving a formula for the exponents of structure functions.
Main Results:
- A novel formula for turbulence exponents: ζ(p)=p/3-1/Inκ In Γ(p/3 + 1).
- The parameter κ relates eddy decay to thermal energy distribution.
- The derived formula shows good agreement with experimental data.
Conclusions:
- The heat flow analogy provides a valid physical picture of turbulence.
- This approach offers a new perspective for studying turbulence and related problems.
- Statistical mechanics fluctuations successfully explain observed intermittency in turbulent flows.
Related Concept Videos
01:24Turbulent Flow
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 spots,...
01:07Laminar 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...
01:28Euler's Equations of Motion
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:10Poiseuille's Law and Reynolds Number
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:
01:28Navier–Stokes Equations
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...