1 Foundation of Fluid Mechanics
31
Fig. 1.34 Vortex core
Now, we will further discuss the physical significance of the above equations. For example, the terms contained in the equation
∂Ω x
∂t
= Ω x
∂u
∂ x
+ · · ·
represents the change rate of the vorticity as a result of the axial tension deformation of the vortex tube (the axis of the vortex tube is stretched,
∂u
∂ x > 0,
which increases the vorticity and decreases the cross section). Items contained
in the equation
∂Ω x
∂t
= Ω y
∂u
∂ y
+ · · ·
represent the change rate of the vorticity due to the shear action of the vortex
tube. Items contained in the equation
∂Ω x
∂t
= ν
∂ 2 Ω x
∂ y 2 + · · ·
are a viscous diffusion term of vorticity.