1 Foundation of Fluid Mechanics
77
Fig. 1.92 Scale relation between energy-carrying eddies and dissipative eddies (Vt
= 1.46 m/s)
Fig. 1.93 Relation between scale of energy-carrying eddies and dissipation rate ε(Vt
= 1.46 m/s)
The scale of the fluctuating velocity gradient can be expressed as
∂u
i
∂ x j
≈
V t
l t
Ret
1/2
=
v
η
It is shown that the fluctuating velocity gradient can be characterized by
Kolmogorov’s microscale, which is consistent with the concept that turbulent
kinetic energy is dissipated by small-scale eddies. This shows that the fluctuating velocity gradient in the dissipation rate is determined by small-scale
eddies. According to the above analysis, the expression of fluctuating velocity
77
Fig. 1.92 Scale relation between energy-carrying eddies and dissipative eddies (Vt
= 1.46 m/s)
Fig. 1.93 Relation between scale of energy-carrying eddies and dissipation rate ε(Vt
= 1.46 m/s)
The scale of the fluctuating velocity gradient can be expressed as
∂u
i
∂ x j
≈
V t
l t
Ret
1/2
=
v
η
It is shown that the fluctuating velocity gradient can be characterized by
Kolmogorov’s microscale, which is consistent with the concept that turbulent
kinetic energy is dissipated by small-scale eddies. This shows that the fluctuating velocity gradient in the dissipation rate is determined by small-scale
eddies. According to the above analysis, the expression of fluctuating velocity