In this explainer, we will learn how to describe the difference between the motion of fluids in steady and turbulent fluid flow.
Liquids and gases are fluids, as they are characterized by having no fixed shape and flowing easily. We encounter fluids often in nature and everyday life, so we might already be familiar with the difference between steady and turbulent flow, for example, from experiencing turbulence in an airplane. When an aircraft travels through a patch of turbulent air, it gets bumped around and experiences rapid changes in motion. Turbulence is characterized by this kind of chaotic fluid motion that is rapidly changing in direction or speed.
Fluids are able to move at high speeds without being turbulent, such as in a steadily flowing river. Steady flow is characterized by the fluid particles all traveling with similar speed and direction, making for a calm motion that we call steady flow.
The terms “steady” and “turbulent” describe opposite types of flow, and we can characterize flow along a spectrum depending on the change in speed and direction of the fluid. We can say that a fluid is flowing steadily if its direction and speed change less, and by contrast, a flow is turbulent if the fluid changes in direction and speed more. The image below illustrates the contrast between steady and turbulent flow. The water starts as a fairly steady flow, but it mixes up after it drops down a ledge. The flow at the bottom of the ledge is far more turbulent since the water is experiencing rapid changes in speed and direction.
Fluids can be difficult to model quantitatively because they are made of vast numbers of moving particles, but there are more qualitative methods of describing patterns of fluid flow. We will model a flowing fluid as consisting of individual streams, or layers, in which the fluid may flow at different speeds. We will use these flow lines, or streamlines, to illustrate how a fluid flows, with the lines representing the direction of the fluid’s flow. From this information, we can make some other associations about the flow, as we will explore next.
Below is a diagram that represents a perfectly steady flow. The lines represent paths that a particle could take in the fluid; so since all the lines are uniform, straight, and parallel, we can tell that there is little disturbance or chaos in this flow. A steady flow is characterized by such uniform lines.
However, most real-life fluids do not have perfectly steady flows. For example, if we place an obstacle in a steadily flowing fluid, the fluid’s particles have to move around the obstacle. This disrupts the smooth, even flow and creates turbulence since the particles have to change direction and speed quickly to get past the object. Such turbulence is characterized by streamlines that are curved or bunched together.
When we see flow lines that bunch together, this represents many layers of fluid moving close to one another. If the different layers are moving with different speeds, the layers exert forces on one another. For example, if we have a fast-moving layer coming into close contact with a slow-moving layer, the layers exert a sort of friction on each other: the fast layer wants to speed up the slow layer, and the slow layer wants to slow down the fast layer. This results in chaotic mixing between the layers such that the molecules in the fluid quickly change speed and direction. This kind of fluid friction is typical of a viscous fluid.
Let us begin to explore this consequence with an example.
Example 1: Graphically Recognizing Steady and Turbulent Flow around an Airfoil
The diagram shows the flow of a fluid past an airfoil. The gray lines represent the direction of the fluid’s flow. Black regions represent solid obstacles to the flow.
In which of the three regions within the dashed lines is the fluid’s flow most turbulent?
We know that turbulence occurs when a fluid changes speed or direction more, and obstacles redirect fluid flow, which is why the most turbulence occurs close to the airfoil. The shape of an airfoil is designed to push the fluid above it along a longer, less direct path, while the fluid below it remains relatively undisturbed. Thus, most of the turbulence occurs in the fluid traveling over the top of the airfoil, and the appearance of the closed loop above the airfoil confirms this. Closed loops in flow lines represent extreme turbulence because a loop traces out a flow that moves in all directions. This change in direction results in a net decrease in speed, so not only is the direction changing rapidly, but the speed also is.
Therefore, we can tell that region I, the only region to contain a closed loop, is the most turbulent.
The example above illustrated how obstacles in a flowing fluid can create areas of turbulence. The severity of the turbulence depends on the shape of the obstacles. Let us consider another example of an obstacle in a flowing fluid.
Example 2: Graphically Recognizing Steady and Turbulent Flow through an Aperture
The diagram shows the flow of a fluid through an aperture. The gray lines represent the direction of the fluid’s flow. Black regions represent solid obstacles to the flow.
- After passing through the aperture, in which of the regions that the fluid passes through within the dashed lines is the fluid’s flow most turbulent?
- After passing through the aperture, in which of the regions that the fluid passes through within the dashed lines is the fluid’s flow steadiest?
Here, we see fluid passing through a small opening, which disturbs the flow and creates some areas of high turbulence where the fluid rapidly changes direction and speed. When we see flow lines that are curved, we know that the fluid is changing direction, which causes some of the fluid to bump into itself. Chaotic motion in fluids is often best recognized by the appearance of closed loops in flow lines, since a closed loop draws out a line that points in all directions over the course of one loop. Thus, region IV, which contains part of a closed loop, has the most turbulent flow of the regions shown.
By contrast, some areas of the fluid flow are well behaved. Recall that when a fluid is allowed to flow easily, with the same speed and direction as the fluid surrounding it, the flow is steady. Steady flow is represented by more straight and parallel flow lines, like in region II.
Although region III has steadier flow than what we see in region IV, notice how the flow lines diverge, indicating a rapid change in direction (and therefore speed). Because the lines in region II are more uniform, we can say that region II has the steadiest flow after the fluid passes through the aperture.
In the next example, we will further explore how turbulence affects the speed of a fluid.
Example 3: Recognizing Flow Speed around an Obstacle Graphically
The diagram shows the flow of a fluid past a circular obstacle. The gray lines represent the direction of the fluid’s flow. The black region represents a solid obstacle to the flow. In which of the two regions within the dashed lines is the fluid’s flow faster?
The obstacle in this fluid is small and round, which helps it to not create any areas of extreme turbulence. Most of the flow lines stay fairly straight and parallel, although there is still some disturbance in the area surrounding the obstacle. So even though both regions I and II are fairly steady, we can tell that region I is slightly less steady since its flow lines are not as parallel as those in region II.
This might not seem to indicate anything about flow speed, but recall that steadily flowing fluid particles “go with the flow,” which maximizes a fluid’s speed. By contrast, turbulence causes particles to bump into each other, which complicates the flow and slows it down.
Areas of steadier flow generally have a higher speed, and thus we can tell that region II is steadier than region I and that it also has a faster fluid flow.
Let us apply the concept of the correlation between steadiness and fast speed to another example.
Example 4: Recognizing Flow Speed and Steadiness around an Obstacle Graphically
The diagram shows the flow of a fluid past a line perpendicular to the flow. The gray lines represent the direction of the fluid’s flow. The black region represents a solid obstacle to the flow.
- In which of the two regions within the dashed lines is the fluid flow faster?
- In which of the two regions within the dashed lines is the fluid flow steadier?
The obstacle in the fluid disrupts the flow, as illustrated by the chaotic flow lines. Closed loops in flow lines are a great indicator of turbulence, since a closed loop traces out a path that heads in all directions. Because turbulence is characterized by rapid changes in flow speed and direction, we know that region I is not steady. Region II has flow lines that are roughly parallel, and therefore it has the steadier flow.
Fluids reduce speed when they change direction, and so generally, steadier fluids move faster. Thus, region II has a flow that is both steadier and faster than region I.
Let us finish by summarizing a few important concepts.
- A flowing fluid can be modeled as consisting of individual streams or layers in which the fluid may flow at different speeds.
- A viscous fluid is one for which streams or layers with different speeds that are in contact exert forces on each other that act to divert the flow direction.
- A steadier flow corresponds to flow direction and speed remaining more constant over a flow region.
- A more turbulent flow corresponds to flow direction and speed changing over a flow region more than it would for a smoother flow.
- We can interpret the flow of a fluid in diagrams of lines depicting the direction and speed of streams of the fluid.