[MUSIC PLAYING]
Cruise down the street, and
you leave chaos in your wake.
As you drive or ride
your bike, you've
probably noticed the
wind whipping around you.
Here's what the
airflow looks like.
These disturbances in
the air and other fluids
are known as turbulence.
Quantifying these
fragmented flows
is one of the greatest
problems in math.
If researchers can
find a way to capture
this chaos in an
equation, we'll be
better able to understand
this universal event,
from locomotion
to ocean currents
to how gases move
throughout galaxies.
Turbulence is everywhere
if we look close enough.
Blow out a candle and watch the
swirling of the smoke trails.
Disrupt a stream with a stick
and see the little whirlpools
form in the wake.
On larger scales, the
ocean currents sweep
across the globe.
Storms churn the atmosphere
on Earth and other planets.
How can researchers study
the chaotic phenomenon
known as turbulence, and what's
preventing them from capturing
the full picture?
Fluids are gases and
liquids that flow and adapt
to the shape of
a container think
water, honey, blood, and air.
They have quantifiable
properties
like viscosity,
velocity, pressure,
and density that mathematicians
can track over time.
They're also governed by
the laws of conservation
of mass, energy, and momentum.
Mathematicians describe fluid
flows using the Navier-Stokes
equations.
You can think of these
equations as Newton's second law
for the motion of fluids.
Force equals mass
times acceleration.
On the left side
of the equation is
the density and
acceleration, or the change
in velocity of a particle
of fluid over time.
On the right side is
change in pressure,
internal forces of stress,
and finally, external forces
acting on the fluid.
Smooth continuous fluid
flows, like in a gentle stream
or pipe, are called
laminar flows.
The equations work well for
describing how particles behave
in laminar flows, but
most fluids in nature
are not so orderly.
They can be really
chaotic, or turbulent.
In the case of your
afternoon drive,
the air starts as a
laminar flow as it
meets the front of your car.
What happens next depends
on your car's shape,
speed, texture, temperature,
as well as the properties
of the air and atmosphere.
Most cars have an
aerodynamic shape,
which minimizes the
turbulence initially.
As the air moves over
the car, the molecules
closest to your door stay put
and interact with its surface.
Further away, air molecules
travel at different speeds.
These layers of different air
create friction and turbulence,
what you'd feel as drag.
The result is
vortices and eddies
that, in turn, generate
more and more swirls.
Ever heard of the
butterfly effect?
It says a flap of a
butterfly's wing in Japan
could set off a
chain of events that
could trigger a tornado
in Texas a week later.
These eddies that beget
more eddies and vortices
and so on become too
complicated for mathematicians
to predict or quantify.
Where will eddies form?
How many will there be?
Where will energy be
concentrated or dispersed?
Plug in certain values, and
the equations may spit out
infinite values for velocity.
This breaks down or
blows up the model.
Because of these challenges
and the possibilities
that understanding
turbulence could lead to,
there's a million dollar
reward for proving either
that the Navier-Stokes
equations always work
or that they sometimes
fail, meaning velocity
becomes infinite.
Until then, who knows
what chain of events
you'll start by taking
your Sunday drive.
[MUSIC PLAYING]
