Vorticity and Viscosity
Vorticity and Viscosity
z
We have seen that there is direct connection
between vorticity and the force that develops on
an object moving through a fluid
z
In this chapter, we will prove that there is no
physical mechanism for developing vorticity in an
inviscid fluid for most practical applications
–
Helmholtz’s Theorem
–
d’Alembert’s Paradox
z
We will see how viscosity provides a mechanism
for developing vorticity
–
NavierStokes Equation
–
Boundary Layers, Separation
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We will discuss lift and drag on common objects
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The Vortex Force
The Vortex Force


1
1
z
To understand the connection between vorticity
and the force on an object moving through a fluid,
recall that we can write Euler’s Equation as
z
The term proportional to
u
×
ω
acts like a Coriolis
acceleration…moving it to the righthand side…
z
As indicated, we call this the
vortex force
←
ω
=
vorticity
↑
=
ρ
(
u
•
∇
)
u
↑