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# Turbulence

Turbulent flow around an obstacle; the flow further away is laminar
Laminar and turbulent water flow over the hull of a submarine

In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low-momentum diffusion, high momentum convection, and pressure and velocity variation with time. Flow that is not turbulent is called laminar flow. The (dimensionless) Reynolds number characterizes whether flow conditions lead to laminar or turbulent flow.

If you consider the flow of water over a simple smooth object, such as a sphere, at very low speeds the flow is laminar; i.e., the flow is smooth and the drag is relatively low. As the speed increases, at some point the transition is made to turbulent ("chaotic") flow, where there is a large increase in drag, and often vortices behind the object. The same transition occurs if you gradually increase the size of the object or decrease the viscosity of the fluid.

### Examples of turbulence

• A faucet goes from
• Off. No flow
• Drip. Which would be modeled as a free boundary problem
• Laminar flow. A smooth and regular flow which looks somewhat solid because the flow maintains a fixed shape. In this regime, the water acts as a transparent lens.
• Turbulent flow. At a certain point the water will start to break up. The water no longer stays contained in a stable region in space. The stream ceases to be transparent, due to the extreme convolution of the surface of the fluid.
• A drop of cream in a cup of coffee.
• Smoke from a cigarette -- for the first few centimetres it remains laminar, and then becomes unstable and turbulent.

According to an apocryphal story, Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."