Why 5/3 is a fundamental constant for turbulence

The video explores the complex nature of turbulence, a chaotic fluid flow phenomenon, and its unpredictability. It features an experiment with vortex rings, demonstrating their stability and the chaotic air patterns they create. The video delves into the challenges of defining and solving turbulence through the Navier-Stokes equations and highlights Kolmogorov's hypothesis on energy distribution in turbulent flows. It also discusses the 3D nature of turbulence and the concept of vortex stretching, providing insights into the intricate patterns of fluid dynamics.

What is the main challenge in predicting turbulent motion?

• The tools to measure turbulence are unavailable.

• The swirls are nearly impossible to predict.

• The equations are too simple.

• The motion is too predictable.

What is a vortex ring?

• A chaotic flow of air in a room.

• A mathematical equation for fluid dynamics.

• A stable doughnut-shaped region of fluid.

• A type of laminar flow.

How is turbulence different from laminar flow?

• Laminar flow has high vorticity.

• Laminar flow is chaotic and mixes things together.

• Turbulence involves chaotic swirling eddies.

• Turbulence is smooth and predictable.

What is a characteristic of turbulent flow?

• It is easy to define mathematically.

• It never mixes different parts of the fluid.

• It has a high swirly swirly factor.

• It is always smooth and predictable.

What are the Navier-Stokes equations known for?

• Having no unsolved problems.

• Being easy to solve.

• Describing incompressible fluid flow.

• Being unrelated to turbulence.

What is the prize associated with understanding the Navier-Stokes equations?

• $100,000

• $500,000

• $1,000,000

• $10,000,000

What does Kolmogorov's hypothesis suggest about energy in turbulent flow?

• Energy is only at the macro scale.

• Energy does not cascade down the spectrum.

• Energy is proportional to the diameter to the power of 5/3.

• Energy is evenly distributed across all scales.

What is the inertial subrange for air according to Kolmogorov?

• 1 centimeter to 10 meters

• 1 meter to 10 kilometers

• 0.1 centimeters to 1 kilometer

• 0.1 meters to 1 kilometer

What is vortex stretching?

• A process that prevents energy transfer in turbulence.

• A process that occurs in two dimensions.

• A process where a vortex bends around to meet itself.

• A process where a rotating fluid stretches perpendicular to its plane.

What happens to energy in a turbulent flow?

• It only exists at the molecular scale.

• It dissipates without any pattern.

• It cascades from larger to smaller eddies.

• It remains constant at all scales.