Turbulence represents chaotic fluid motion characterized by irregular pressure and velocity changes. It contrasts with laminar flow, where fluid moves in parallel layers without disruption.
Nature and Characteristics
Turbulence emerges in everyday phenomena like surf, fast rivers, storm clouds, and chimney smoke. The physics behind it stems from excessive kinetic energy overcoming fluid viscosity. When turbulent flow occurs, unsteady vortices of various sizes interact and increase friction drag.
Richard Feynman called turbulence “the most important unsolved problem in classical physics.” The phenomenon affects multiple fields including fish ecology, air pollution, and climate change.
Reynolds Number Predicts Turbulent Flow
The dimensionless Reynolds number determines when turbulence occurs. It represents the ratio between kinetic energy and viscous damping in fluid flow. The formula is:
$$ Re = \frac{\rho vL}{\mu} $$
Where:
- ρ = fluid density
- v = fluid velocity
- L = characteristic length
- μ = dynamic viscosity
Flows with Reynolds numbers above 5000 typically become turbulent, while lower numbers remain laminar. In Poiseuille flow, turbulence first appears at Re ≈ 2040.
Energy Cascade Process
Turbulent flow follows an energy cascade where large eddies break into progressively smaller ones. The process continues until reaching the Kolmogorov length scale, where viscosity dissipates kinetic energy into heat.
Real-World Applications
Engineers use turbulence understanding to design:
- Golf balls with dimples that reduce drag
- Aircraft that handle clear-air turbulence
- Industrial equipment like pipes and heat exchangers
- Vehicle aerodynamics for cars, motorcycles, planes, and ships
Medical applications include using turbulent blood flow sounds for cardiac diagnosis. In nature, swimming animals generate turbulence that affects ocean mixing, while snow fences use induced turbulence to control snow drifts.
Mathematical Analysis
Osborne Reynolds pioneered the mathematical study of turbulence in 1895 by decomposing flow variables into mean values and fluctuations. This led to the statistical treatment of turbulent flow as a sub-field of fluid dynamics.
The Kolmogorov theory of 1941 provided the first statistical framework for understanding turbulence, though modern research shows some deviations from its predictions at smaller scales.
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between those layers.
Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason, turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases.
The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence create a very complex phenomenon. Physicist Richard Feynman described turbulence as the most important unsolved problem in classical physics.
The turbulence intensity affects many fields, for examples fish ecology, air pollution, precipitation, and climate change.
English
Etymology
Borrowed from Latin turbulentia, or from turbulent + -ence.