## Turbulence

**Introduction: **Let us first define what a flow is: a flow is the continuous movement of a fluid, i.e. either a liquid or a gas, from one place to another. Basically there exist two types of flows, namely laminar flows and turbulent flows. Roughly speaking we can say that a laminar flow is a 'simple' flow while a turbulent flow is a 'complicated' flow. We will illustrate what we mean by 'simple' and 'complicated' using the following, simple experiment. Go to your kitchen sink and open the faucet. The stream of water that emerges from your faucet is very smooth and very regular. The flow of water is smooth because all the water molecules move, at more or less the same speed, in the same direction. This is called a laminar flow. Furthermore, if you did not open the faucet too much, the water will also flow down the drain in a laminar flow. Now place a cup under the stream of water emerging from the faucet. Although the stream is still laminar, the flow pattern of the water in the sink has become very complicated. This is due to the fact that now the water molecules tend to move in different directions at different speeds. Such a flow is called turbulent.

**In fluid dynamics**, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic [citation needed] property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Nobel Laureate Richard Feynman described turbulence as "the most important unsolved problem of classical physics. “Flow in which the kinetic energy dies out due to the action of fluid molecular viscosity is called laminar flow. While there is no theorem relating the non-dimensional Reynolds number (Re) to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In Poiseuille flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040;

**Turbulence is highly characterized by the following features:**

**Irregularity**: Turbulent flows are always highly irregular. This is why turbulence problems are always treated statistically rather than deterministically. Turbulent flow is always chaotic but not all chaotic flows are turbulent.

**Diffusivity**: The readily available supply of energy in turbulent flows tends to accelerate the homogenization (mixing) of fluid mixtures. The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is called "diffusivity".

**Rationality**: Turbulent flows have non-zero vorticity and are characterized by a strong three-dimensional vortex generation mechanism known as vortex stretching. In fluid dynamics, they are essentially vortices subjected to stretching associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum. On the other hand, vortex stretching is the core mechanism on which the turbulence energy cascade relies to establish the structure function.

**For example**: atmospheric cyclones are rotational but their substantially two-dimensional shapes do not allow vortex generation and so are not turbulent. On the other hand, oceanic flows are dispersive but essentially non rotational and therefore are not turbulent.

**Dissipation:**To sustain turbulent flow, a constant source of energy supply is required because turbulence dissipates rapidly as the kinetic energy is converted into internal energy by viscous shear stress.

**Energy cascade:**Turbulent flow can be realized as a superposition of a spectrum of velocity fluctuations and eddies upon a mean flow. The eddies are loosely defined as coherent patterns of velocity, vorticity and pressure. Turbulent flows may be viewed as made of an entire hierarchy of eddies over a wide range of length scales and the hierarchy can be described by the energy spectrum that measures the energy in velocity fluctuations for each wave number.

**Kolmogorov length scales**: Smallest scales in the spectrum that form the viscous sub-layer range. In this range, the energy input from nonlinear interactions and the energy drain from viscous dissipation are in exact balance. The small scales are in high frequency which is why turbulence is locally isotropic and homogeneous.

**Examples of turbulence:**

- Smoke rising from a cigarette is turbulent flow. For the first few centimeters, the flow is certainly laminar. Then smoke becomes turbulent as its Reynolds number increases, as its velocity and characteristic length are both increasing.
- The mixing of warm and cold air in the atmosphere by wind, which causes clear-air turbulence experienced during airplane flight, as well as poor astronomical seeing (the blurring of images seen through the atmosphere.)
- Most of the terrestrial atmospheric circulation
- The oceanic and atmospheric mixed layers and intense oceanic currents.