In fluid dynamics, an eddy is the swirling
of a fluid and the reverse current created
when the fluid is in a turbulent flow regime.
The moving fluid creates a space devoid of
downstream-flowing fluid on the downstream
side of the object. Fluid behind the obstacle
flows into the void creating a swirl of fluid
on each edge of the obstacle, followed by
a short reverse flow of fluid behind the obstacle
flowing upstream, toward the back of the obstacle.
This phenomenon is naturally observed behind
large emergent rocks in swift-flowing rivers.
== Swirl and eddies in engineering ==
The propensity of a fluid to swirl is used
to promote good fuel/air mixing in internal
combustion engines.
In fluid mechanics and transport phenomena,
an eddy is not a property of the fluid, but
a violent swirling motion caused by the position
and direction of turbulent flow.
== Reynolds number and turbulence ==
In 1883, scientist Osborne Reynolds conducted
a fluid dynamics experiment involving water
and dye, where he adjusted the velocities
of the fluids and observed the transition
from laminar to turbulent flow, characterized
by the formation of eddies and vortices. Turbulent
flow is defined as the flow in which the system's
inertial forces are dominant over the viscous
forces. This phenomenon is described by Reynolds
number, a unit-less number used to determine
when turbulent flow will occur. Conceptually,
the Reynolds number is the ratio between inertial
forces and viscous forces.
The general form for the Reynolds number flowing
through a tube of radius r (or diameter d):
R
e
=
2
v
ρ
r
μ
=
ρ
v
d
μ
{\displaystyle \mathrm {Re} ={2v\rho r \over
\mu }={\rho vd \over \mu }}
where v is the velocity of the fluid, ρ is
its density, r is the radius of the tube,
and μ is the viscosity of the fluid.
The transition from laminar to turbulent flow
in a fluid is defined by the critical Reynolds
number
R
e
c
≈
2000.
{\displaystyle \mathrm {Re} _{\text{c}}\approx
2000.}
In terms of the 
critical Reynolds number, the critical velocity
is represented as
v
c
=
R
e
c
μ
ρ
d
.
{\displaystyle v_{\text{c}}={\frac {\mathrm
{Re} _{\text{c}}\mu }{\rho d}}.}
== Research and development ==
=== Hemodynamics ===
Hemodynamics is the study of blood flow in
the circulatory system. Blood flow in straight
sections of the arterial tree are typically
laminar (high, directed wall stress), but
branches and curvatures in the system cause
turbulent flow. Turbulent flow in the arterial
tree can cause a number of concerning effects,
including atherosclerotic lesions, postsurgical
neointimal hyperplasia, in-stent restenosis,
vein bypass graft failure, transplant vasculopathy,
and aortic valve calcification.
=== Industrial processes ===
Lift and drag properties of golf balls are
customized by the manipulation of dimples
along the surface of the ball, allowing for
the golf ball to travel further and faster
in the air.The data from turbulent-flow phenomena
has been used to model different transitions
in fluid flow regimes, which are used to thoroughly
mix fluids and increase reaction rates within
industrial processes.
=== Fluid currents and pollution control ===
Oceanic and atmospheric currents transfer
particles, debris, and organisms all across
the globe. While the transport of organisms,
such as phytoplankton, are essential for the
preservation of ecosystems, oil and other
pollutants are also mixed in the current flow
and can carry pollution far from its origin.
Eddy formations circulate trash and other
pollutants into concentrated areas which researchers
are tracking to improve clean-up and pollution
prevention.
Mesoscale ocean eddies play crucial roles
in transferring heat poleward, as well as
maintaining heat gradients at different depths.
=== Computational fluid dynamics ===
These are turbulence models in which the Reynolds
stresses, as obtained from a Reynolds averaging
of the Navier–Stokes equations, are modelled
by a linear constitutive relationship with
the mean flow straining field, as:
−
ρ
⟨
u
i
u
j
⟩
=
2
μ
t
S
i
,
j
−
2
3
ρ
κ
δ
i
,
j
{\displaystyle -\rho \langle u_{i}u_{j}\rangle
=2\mu _{t}S_{i,j}-{2 \over 3}\rho \kappa \delta
_{i,j}}
where
μ
t
{\displaystyle \mu _{t}}
is the coefficient termed turbulence "viscosity"
(also called the eddy viscosity)
κ
=
1
2
(
⟨
u
1
u
1
⟩
+
⟨
u
2
u
2
⟩
+
⟨
u
3
u
3
⟩
)
{\displaystyle \kappa ={\tfrac {1}{2}}(\langle
u_{1}u_{1}\rangle +\langle u_{2}u_{2}\rangle
+\langle u_{3}u_{3}\rangle )}
is the mean turbulent kinetic energy
S
i
,
j
{\displaystyle S_{i,j}}
is the mean strain rateNote that that inclusion
of
2
3
ρ
κ
δ
i
,
j
{\displaystyle {\tfrac {2}{3}}\rho \kappa
\delta _{i,j}}
in the linear constitutive relation is required
by tensorial algebra purposes when solving
for two-equation turbulence models (or any
other turbulence model that solves a transport
equation for
κ
{\displaystyle \kappa }
.
== Mesoscale ocean eddies ==
Eddies are common in the ocean, and range
in diameter from centimeters to hundreds of
kilometers. The smallest scale eddies may
last for a matter of seconds, while the larger
features may persist for months to years.
Eddies that are between about 10 and 500 km
(6.2 and 310.7 miles) in diameter and persist
for periods of days to months are known in
oceanography as mesoscale eddies.Mesoscale
eddies can be split into two categories: static
eddies, caused by flow around an obstacle
(see animation), and transient eddies, caused
by baroclinic instability.
When the ocean contains a sea surface height
gradient this creates a jet or current, such
as the Antarctic Circumpolar Current. This
current as part of a baroclinically unstable
system meanders and creates eddies (in much
the same way as a meandering river forms an
ox-bow lake). These types of mesoscale eddies
have been observed in many of major ocean
currents, including the Gulf Stream, the Agulhas
Current, the Kuroshio Current, and the Antarctic
Circumpolar Current, amongst others.
Mesoscale ocean eddies are characterized by
currents that flow in a roughly circular motion
around the center of the eddy. The sense of
rotation of these currents may either be cyclonic
or anticyclonic (such as Haida Eddies). Oceanic
eddies are also usually made of water masses
that are different from those outside the
eddy. That is, the water within an eddy usually
has different temperature and salinity characteristics
to the water outside the eddy. There is a
direct link between the water mass properties
of an eddy and its rotation. Warm eddies rotate
anti-cyclonically, while cold eddies rotate
cyclonically.
Because eddies may have a vigorous circulation
associated with them, they are of concern
to naval and commercial operations at sea.
Further, because eddies transport anomalously
warm or cold water as they move, they have
an important influence on heat transport in
certain parts of the ocean.
== See also ==
Eddy diffusion
Haida Eddies
Reynolds number - a dimensionless constant
used to predict the onset of turbulent flow
Reynolds experiment
Kármán vortex street
Whirlpool
Whirlwind
River Eddies in Whitewater
Wake turbulence
Computational Fluid Dynamics
Laminar flow
Hemodynamics
Modons, or dipole eddy pairs
