3.3.5.2. Turbulent Flow

Table of Contents

From Smooth Flow to Turbulence

Turbulent flow is a type of fluid motion in which the fluid does not move in smooth, orderly layers. Instead, the velocity changes irregularly in space and time, and the fluid contains swirling structures called eddies. In turbulent flow, neighboring parts of the fluid can move in different directions or at different speeds, and mixing becomes very strong.

This is very different from laminar flow, where the fluid moves in neat layers with little mixing between them. Turbulent flow is common in fast moving rivers, smoke rising in air, water flowing from a fully opened faucet, and air moving around cars and airplanes.

Main Features of Turbulent Flow

The most important feature of turbulent flow is irregular motion. At any point in the fluid, the speed and direction may fluctuate rapidly. Even if the average flow is steady, the instantaneous motion is not smooth.

Turbulent flow also produces strong mixing. Dye dropped into turbulent water spreads quickly because the eddies carry fluid from one region to another. This mixing makes turbulence very important in engineering, weather, ocean currents, and heat transfer.

Another feature is that turbulent flow usually causes greater energy loss than laminar flow. More mechanical energy is dissipated into internal energy, so pumps must work harder to push fluids through pipes when the flow is turbulent.

Turbulent flow is characterized by irregular velocity fluctuations, eddies, and strong mixing.
Turbulent flow usually leads to larger frictional losses than laminar flow.

Velocity Fluctuations

In turbulent flow, the velocity at a point is often described as an average part plus a fluctuating part. If the flow is mainly along one direction, we may write

$$
v(t) = \bar{v} + v'(t)
$$

where $\bar{v}$ is the time averaged velocity and $v'(t)$ is the fluctuating part.

The average velocity gives the overall motion of the fluid, while the fluctuations describe the chaotic rapid changes. These fluctuations are one of the defining signs of turbulence.

Eddies and Mixing

The irregular motion in turbulence forms whirl-like regions of many sizes. These are called eddies. Large eddies can break into smaller ones, which then break into even smaller ones. This process continues until the motion reaches scales where viscous effects become strong enough to damp the motion out.

Because of these eddies, turbulence mixes momentum, heat, and dissolved substances much more effectively than laminar flow. That is why turbulent stirring is often used when rapid mixing is desired.

Rendering scientific sketch…

Laminar flow and turbulent flow

When Turbulence Appears

Turbulence usually appears when inertial effects become much stronger than viscous effects. In simple terms, if a fluid moves slowly and viscosity can keep the flow organized, the flow tends to remain laminar. If the speed becomes large enough, disturbances grow and the flow can become turbulent.

For flow in a pipe, this transition is commonly described using the Reynolds number, which is treated in its own chapter. In general, low Reynolds number flow tends to be laminar, while high Reynolds number flow tends to be turbulent.

A small disturbance in a high speed flow can grow instead of dying out. Once this happens, the flow can become chaotic and turbulent.

Turbulence tends to occur when inertial effects dominate over viscous effects.
In pipe flow, increasing speed makes turbulence more likely.

Turbulent Flow in Pipes

In pipe flow, turbulence changes the velocity distribution across the pipe. In laminar flow, the velocity profile is smooth and strongly curved, with the maximum speed at the center. In turbulent flow, mixing spreads momentum more effectively, so the profile becomes flatter in the middle, although it still drops near the walls.

Very close to the wall, viscosity still matters strongly. Even in turbulent flow, the fluid speed must be zero at the wall because of the no slip condition. Away from the wall, turbulent mixing becomes more important.

Rendering scientific sketch…

Typical velocity profiles in a pipe

Energy Loss and Drag

Turbulent flow generally creates more resistance to motion than laminar flow. In a pipe, this means a larger pressure drop is needed to maintain the same flow rate. Around an object, it often means larger drag forces, although the full story depends on shape and flow pattern.

The extra resistance comes from the chaotic transfer of momentum inside the fluid. Eddies move fluid across the flow, increasing internal friction effects on a large scale.

This is why turbulence is so important in practical systems such as pipelines, ventilation ducts, aircraft design, and ship motion.

Examples of Turbulent Flow

Many everyday flows are turbulent. Water in a mountain stream is turbulent because the speed is high and the motion is disturbed by rocks. Smoke from a candle may begin as smooth flow close to the flame and then become turbulent as it rises. Air flowing around a fast car is usually turbulent in many regions.

The table below shows some typical comparisons.

Situation	More likely laminar	More likely turbulent
Water from a faucet	Slow trickle	Fast fully opened flow
River flow	Quiet, slow stream	Rapid or rough current
Air around a vehicle	Very low speed	High speed
Dye in water	Spreads slowly	Spreads quickly

Why Turbulence Matters

Turbulence is important because it changes how fluids transport momentum, energy, and matter. It can increase friction losses, but it can also improve mixing. In some situations, turbulence is undesirable because it wastes energy. In other situations, it is useful because it helps stir fluids or enhances heat transfer.

A full mathematical description of turbulence is difficult, because the motion is highly complex. For beginners, the key idea is that turbulent flow is chaotic, strongly mixed, and usually associated with high speed flow or strong disturbances.

Key idea: turbulent flow is irregular, contains eddies, mixes fluid strongly, and usually produces greater resistance than laminar flow.

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