From Teacups to Tornadoes: The Science of Vortices and Turbulence
Stir a cup of tea and the liquid does not simply travel around the spoon. It curves, spirals, climbs slightly at the edges and forms a small depression near the centre.
Watch water flowing around a bridge support and you may see swirling eddies forming downstream. Look behind a moving boat and its wake becomes a complicated mixture of waves, bubbles and rotating water. On a much larger scale, clouds spiral around powerful weather systems.
These examples are enormously different in size, speed and energy, but they are all connected by the same broad area of science: fluid dynamics.
The mathematics of fluid dynamics can become extremely complicated. However, the basic behaviour of fluids is highly visual and can be investigated using bottles, water, food colouring, cardboard, ribbons and a fan.
The central question is:
Why do smoke, water and air form vortices instead of simply travelling in straight lines?
The answer reveals why aircraft leave dangerous wakes, why racing cyclists follow closely behind one another, why ships and cars are carefully streamlined and why a small change in the flow of water can eventually reshape a riverbank.
What Counts as a Fluid?
When we hear the word fluid, we often think only of liquids. In physics, however, both liquids and gases are fluids.
Water is a fluid.
Air is also a fluid.
So are oil, blood, steam, petrol and the gases moving through an aircraft engine.
A fluid is a substance that continually changes shape when a force is applied. Unlike a solid, it does not retain one fixed shape. It flows around obstacles, fills containers and responds to differences in pressure.
This means that the air moving around a car and the water moving around a boat can be studied using many of the same physical principles.
Fluids Can Move in Straight Lines — But Usually Something Disturbs Them
A fluid can move smoothly in a nearly straight path. In carefully controlled conditions, neighbouring layers may slide past one another with very little mixing.
This is called laminar flow.
Real fluids, however, encounter walls, corners, rough surfaces, changes in temperature and objects placed in their path. Different parts of the fluid begin moving at different speeds or in different directions.
A layer of water touching the wall of a pipe is slowed by friction. Water closer to the centre may continue moving more quickly. Air flowing over the surface of a car is slowed near the body while the air farther away moves more freely.
The thin region in which the speed changes from almost zero at the surface to the speed of the surrounding flow is called the boundary layer. Depending on the conditions, this layer may remain relatively smooth or become unsteady and turbulent. It may also separate from the surface, producing a larger wake and increased drag.
Once different regions of a fluid begin moving at different speeds, the flow can curl, stretch and rotate. Small disturbances may fade away, but under other conditions they grow.
That growth is the beginning of a fluid instability.
What Is a Vortex?
A vortex is a region of rotating fluid.
It does not have to be a dramatic tornado-shaped funnel. A small rotating eddy behind a stone in a stream is also a vortex. So is a smoke ring, although in that case the vortex is shaped like a three-dimensional ring rather than a vertical spiral.
Vortices frequently form because one part of a fluid is moving faster than another. The faster layer pulls on the slower layer, while the slower layer resists. This difference in speed is known as shear.
The boundary between the two regions can begin to roll up, producing rotation.
Once formed, a vortex can:
travel through a fluid;
stretch into a longer, thinner structure;
combine with other vortices;
break into smaller vortices;
transfer energy from one part of the fluid to another;
gradually disappear as its organised motion is converted into heat.
This is why turbulence often looks like a complicated collection of spirals within spirals.
Laminar Flow and Turbulent Flow
Laminar flow is smooth and organised. Fluid particles follow relatively predictable paths, with neighbouring layers moving alongside one another.
Turbulent flow is irregular and constantly changing. It contains eddies and vortices of many different sizes.
It is tempting to describe laminar flow as “orderly” and turbulent flow as “random”, but turbulence is not completely without structure. A turbulent wake may contain repeating patterns, spinning regions and recognisable instabilities.
The difficulty is that these patterns interact with one another. A large vortex may stretch and break into smaller vortices. Those smaller vortices may divide again, transferring energy to progressively smaller scales.
Eventually, viscosity converts much of that organised motion into thermal energy.
The Reynolds Number: Predicting the Type of Flow
Scientists and engineers use a quantity called the Reynolds number to compare the effects of inertia and viscosity.
It can be written using standard text characters as:
Re = (rho x v x L) / mu
where:
Re is the Reynolds number;
rho is the density of the fluid;
v is the speed of the fluid;
L is a characteristic length, such as the diameter of a pipe;
mu is the dynamic viscosity.
A low Reynolds number generally indicates that viscosity has a strong stabilising effect. Disturbances tend to be smoothed out and laminar flow is more likely.
A high Reynolds number indicates that inertia is more important. Disturbances are more likely to grow, and separation, vortices and turbulence become more likely.
The Reynolds number is dimensionless, meaning that it has no unit. It allows engineers to compare flows involving different sizes, speeds and fluids. However, there is no single Reynolds number at which every flow suddenly becomes turbulent. The transition depends on the shape of the object, the roughness of its surface and the disturbances already present in the fluid.
This is extremely useful when testing models. Engineers can use water tunnels or wind tunnels to investigate a smaller version of a much larger object, provided that the important flow conditions are properly matched.
Practical Investigations
Experiment 1: Create a Vortex in a Bottle
You will need
Two clear plastic drinks bottles
Water
Food colouring
A bottle-vortex connector, or strong waterproof tape
A tray or towel
Method
Fill one bottle approximately three-quarters full of water.
Add a small amount of food colouring so that the movement is easier to see.
Connect the empty bottle securely above the filled bottle. A purpose-made connector is best, although the bottle necks can be taped together very carefully.
Turn the apparatus over so that the water-filled bottle is on top.
First, allow the water to drain without deliberately spinning it. Air attempting to enter the upper bottle will interrupt the falling water, often producing a slow, uneven “glugging” flow.
Repeat the experiment, but this time move the bottles in a circular motion before holding them still.
A vortex should form.
What is happening?
The spinning water moves around the outside of the bottle neck while air travels upwards through the centre.
The funnel is not empty. Its central region contains air and lower-pressure rotating fluid.
The vortex creates a more organised route through which water can move down and air can move up. This often allows the bottle to empty more smoothly.
Turn it into an investigation
Measure the time taken for the same volume of water to drain:
without spinning;
after one circular movement;
after several circular movements;
with different bottle openings;
with different quantities of water;
with water thickened slightly using glycerine.
Keep everything except the variable being tested as constant as possible.
Experiment 2: Build a Vortex Cannon
A vortex cannon creates a pulse of air that rolls into a travelling ring.
You will need
A sturdy cardboard box or large plastic container
Strong tape
A circular hole cut into one side
Lightweight paper cups, ribbons or hanging tissue
Optional cool theatrical fog or humidifier mist
An adult should cut the opening and check that all edges are safe.
Method
Seal the box so that air can leave mainly through the circular opening.
Point the opening towards a lightweight target, such as a stack of paper cups.
Strike the flexible sides of the box sharply with both hands.
A pulse of air will travel across the room and may move or knock over the cups, even though there is no obvious continuous wind.
To make the ring visible, a small amount of cool fog or humidifier mist can be placed inside the box.
Do not use burning materials, direct the cannon at anyone’s face or deliberately inhale fog or smoke.
What is happening?
When the box is struck, air is forced rapidly through the circular opening.
The air near the centre of the opening moves forwards quickly. At the edge, it rubs against the surrounding stationary air. This shear causes the edge of the air pulse to roll backwards and curl into a ring.
The result is a toroidal vortex — a rotating doughnut-shaped structure.
The air inside the ring is continually circulating, allowing the vortex to remain organised as it moves across the room.
Questions to investigate
Does changing the following affect the range?
The diameter of the opening
The size of the box
The strength of the strike
The distance from the target
A circular opening compared with a square opening
A smartphone recording in slow motion may reveal the ring stretching, wobbling and eventually breaking apart.
Experiment 3: Watch Laminar Flow Become Turbulent
A simplified version of Osborne Reynolds’ famous flow experiment can be constructed using transparent tubing.
You will need
A clear plastic tube
A water container or reservoir
A funnel
A clip or tap to control the flow
Food colouring
A syringe or dropper
A collecting container
Method
Arrange the tube so that water can flow steadily from the reservoir into the collecting container.
Begin with a very slow flow.
Introduce a thin stream of food colouring close to the entrance of the tube.
At low speeds, the colouring may remain as a narrow line for some distance. This indicates that there is little mixing between neighbouring layers.
Gradually increase the flow rate.
The coloured line should begin to wobble, spread and eventually break into irregular patterns.
What is happening?
At low speeds, viscosity can suppress many small disturbances. The flow remains comparatively stable.
As the speed increases, the inertial effects become more important. Small disturbances grow and the dye becomes mixed through the water.
This experiment also demonstrates why “turbulent” does not simply mean “fast”. Speed matters, but so do the tube diameter, fluid density and viscosity.
Experiment 4: Investigate Vortices Behind Objects
When a fluid passes around an object, the flow may separate from its surface. Rotating regions can then form in the wake.
You will need
A long transparent tray
Water
Food colouring
A dropper
A cylindrical dowel
A flat strip of plastic or card
A spoon or streamlined object
A smartphone capable of slow-motion recording
Method
Fill the tray with a shallow layer of water.
Place a small drop of colouring near the object being tested.
Move the object steadily through the water, keeping its speed as constant as possible.
Record the wake from above.
Repeat with objects of different shapes.
What should you look for?
Behind a blunt object, the flow may separate and form alternating rotating regions.
Under suitable conditions, vortices are shed first from one side and then the other. This repeating pattern is called a Kármán vortex street.
Theodore von Kármán analysed the alternating rows of vortices that form behind broad-fronted objects in a fluid stream.
NASA flow studies around cylinders also show periodic vortex pairs being shed downstream under particular flow conditions.
Compare:
a cylindrical object;
a flat object facing the flow;
the same flat object turned edge-on;
a rounded or streamlined object.
The size of the wake provides a useful indication of the amount of energy being left behind in the fluid.
Experiment 5: Make Airflow Visible with Ribbons
Smoke is not essential for investigating airflow. Lightweight threads can provide a safer and simpler visual indicator.
You will need
A desk fan
Short pieces of wool, ribbon or lightweight thread
Cardboard shapes
A plastic bottle
Tape
Method
Tape rows of short threads to the surface of the object being tested.
Place the object in front of the fan.
Observe the movement of the threads.
When airflow remains attached and reasonably smooth, the threads should point steadily downstream.
Where the flow separates, the threads may flap, reverse direction or move irregularly.
Try comparing
a curved surface and a flat surface;
a smooth surface and a rough surface;
different angles to the airflow;
a blunt leading edge and a rounded leading edge.
This is similar to the use of tell-tales on sails. A sailor does not see the airflow directly, but the behaviour of the threads reveals whether the flow is attached or separating from the sail.
Experiment 6: Observe Convection Patterns in Water
Not all fluid movement is produced by stirring, pumps or fans. Temperature differences can also create motion.
You will need
A clear heat-resistant dish
Water
Food colouring
A dropper
A mug containing hot water, or a low-temperature warming pad
An ice cube in a sealed small bag
A tray to catch spills
Method
Fill the transparent dish with room-temperature water.
Warm one end gently by placing a mug of hot water beneath it or by using a suitable low-temperature warming pad.
Place the sealed ice cube at the opposite end.
Add a small drop of colouring near the bottom of the warmed region.
Watch the coloured water rise, spread across the surface and eventually descend as it cools.
A second colour can be added carefully near the cold end.
Do not use an open flame, and avoid boiling water.
What is happening?
Heating causes a region of water to expand slightly and become less dense. It rises.
Cooler, denser water sinks and moves in to replace it.
This produces a circulating convection current. The same basic process occurs in the atmosphere when the Sun warms the ground and the air above it begins to rise.
The resulting pattern may initially appear smooth. If the temperature difference becomes greater, the movement can develop plumes, waves and irregular instabilities.
Why Vortices Form Behind Objects
Imagine water approaching a cylinder.
The fluid must divide and travel around both sides. Near the surface, viscosity slows it down. Farther away, the water continues moving more quickly.
After passing the widest part of the cylinder, the fluid attempts to follow the surface around the back. It may not have enough momentum to do so.
The boundary layer then separates.
A low-pressure wake forms behind the object, and the separated layers begin to roll into vortices.
Frequently, one side becomes slightly stronger than the other. The first vortex is shed downstream, changing the pressure around the object. A vortex then forms on the opposite side.
The cycle repeats, producing an alternating wake.
These repeating pressure changes can push the object from side to side. At certain frequencies they may cause cables, chimneys, bridge components or other structures to vibrate.
A Personal View from Sailing
One reason I find fluid dynamics so fascinating is that it turns ordinary observation into practical science.
When sailing, the air around the sails cannot be seen directly. Instead, we watch the tell-tales. When they stream smoothly, the airflow is behaving as intended. When they flutter, lift or reverse, the flow may be separating.
The water around the hull, centreboard and rudder is equally important. Every unnecessary splash, large wake or swirling trail represents energy that has been transferred from the boat into the surrounding water.
Even the river itself is full of fluid-dynamic clues. Water accelerates through narrower sections, curls around moored boats, forms eddies behind pontoons and becomes disturbed where different currents meet.
A sailor may not solve the full mathematical equations while on the water, but sailing constantly teaches the practical consequences of pressure, drag, lift, separation and turbulence.
In that sense, every sailor becomes a working fluid dynamicist.
From Small Eddies to Hurricanes
The vortex in a cup of tea and the circulation of a hurricane are not identical. Their scales, energy sources and controlling forces are very different.
However, both involve fluids moving around a centre.
Hurricanes are rotating weather systems driven by interactions between warm ocean water, moisture, convection, pressure differences and the rotation of the Earth. Their circular structure is associated with air moving around a low-pressure centre.
This demonstrates one of the most powerful ideas in physics: the same broad principles can appear at many different scales.
A small tank experiment cannot reproduce every feature of a storm, but it can make particular processes — such as rotation, convection or mixing — visible and understandable.
Why Vortices and Turbulence Matter
Weather and climate
Atmospheric circulation transfers energy and moisture from one region to another. Convection produces rising air, clouds and storms, while rotating systems can grow into large weather patterns.
Forecasting these systems requires extremely powerful computer models because small changes in atmospheric conditions can grow and interact.
Aircraft
Aircraft wings produce lift by changing the motion and pressure of the surrounding air. At the wingtips, pressure differences contribute to powerful counter-rotating vortices.
These vortices contribute to induced drag and can remain in the air behind a large aircraft, creating a potential hazard for aircraft following too closely.
Sailing
Sails and keels work as fluid-dynamic surfaces. Their performance depends on maintaining useful flow while controlling separation, wake formation and drag.
The disturbed air behind another boat can reduce the quality of the wind reaching a following competitor, while disturbed water can affect control and speed.
Blood flow
Blood normally flows through much of the circulatory system in a predominantly laminar or pulsatile pattern. At branch points, narrowed arteries, damaged valves and aneurysms, the flow may become disturbed or transitionally turbulent.
These patterns matter because blood flow produces forces on the cells lining the blood vessels, and medical imaging can be used to investigate unusual circulation.
Rivers and erosion
Vortices can lift and transport sediment. Around bridge supports and other obstacles, local acceleration and rotating flow can remove material from the riverbed.
This process, known as scour, is an important consideration in bridge design and river management.
Industrial mixing
Factories need to mix liquids, gases, powders and chemicals efficiently.
Turbulence can improve mixing by bringing different regions of a fluid into contact. However, creating turbulence requires energy. Engineers therefore have to balance rapid mixing against electricity use, heat production and possible damage to delicate materials.
Cars, cycling and swimming
A large turbulent wake usually represents lost energy.
Car designers aim to control separation and reduce the size of the wake. Cyclists reduce air resistance by riding behind one another, while swimmers adopt streamlined positions to minimise the energy transferred into turbulent water.
Energy efficiency
Fans, pumps, pipes, turbines, heat exchangers, aircraft and boats all move fluids.
Poorly controlled turbulence increases noise, vibration and energy loss. In other situations, deliberate vortices can improve mixing, heat transfer or combustion.
The goal is not always to eliminate vortices. It is to understand when they are useful and when they are wasteful.
Turbulence Is Not Just Disorder
Turbulence is sometimes described as chaos, but it is more useful to think of it as structured complexity.
There are patterns, but they continually change.
There are rules, but the outcome is highly sensitive to the starting conditions.
There are large vortices containing smaller vortices, which may themselves contain even smaller ones.
This combination of recognisable structure and unpredictable detail is what makes fluid dynamics so challenging — and so visually compelling.
Conclusion: The Hidden Spirals Around Us
Fluids rarely move through the real world without encountering obstacles, temperature differences, friction or changes in pressure.
These influences produce differences in speed. Different speeds create shear. Shear can produce rotation, and small disturbances can grow into waves, eddies, vortices and turbulent wakes.
The same broad physics helps us understand:
the spiral in a bottle;
the ring from a vortex cannon;
the wake behind a bridge support;
the fluttering tell-tales on a sail;
the airflow behind an aircraft;
the movement of blood;
the erosion of a riverbed;
the circulation of the atmosphere.
Fluid dynamics reminds us that some of the most advanced scientific ideas are already visible in ordinary life.
The next time you stir a cup of tea, watch a stream passing around a stone or see clouds curling across the sky, look carefully.
You are not simply watching water or air move.
You are watching energy being transferred, instabilities growing and some of nature’s most important patterns taking shape.
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