1. Characteristics of Turbulence:
TURBULENCE (follow Kundu’s book)
Turbulent Flows
Turbulent Flows
Turbulent Flows
Characteristics of Turbulence:
1) Randomness – flows seem irregular, chaotic, unpredictable
2) Nonlinearity – results in vortex stretching and instabilities
3) Diffusivity – rapid rates of momentum and mass diffusion
4) Vorticity – eddies coalesce, divide, stretch and spin
large eddies contain most energy
energy is transferred from large to small eddies
5) Dissipation – vortex stretching mechanism transfers energy and vorticity to smaller scales until gradients are smeared out by viscosity.

2. “Big whorls have little whorls
That feed on their velocity;
And little whorls have lesser whorls,
And so on to viscosity.” (Lewis F Richardson, 1920)
Randomness
Nonlinearity
Diffusivity
Vorticity
Dissipation

4. Consider, e.g.,: Local Acceleration
Use these properties of turbulent flows (random or stochastic) in the Navier Stokes equations
Consider, e.g.,:
Local Acceleration

5. Pressure Gradient

6. Advective Terms

7. are the Reynolds stresses
arise from advective (non-linear or inertial) terms

8. Normal stresses
Off diagonal = Shear stresses

9. For isotropic turbulence: off-diagonal terms (shear stresses) are zerov’
Isotropic
Anisotropic
From Kundu’s book
For isotropic turbulence: off-diagonal terms (shear stresses) are zero

10. Isotropic Turbulence
G. Brethouwer (2000) Mixing of passive and reactive scalars in turbulent flows: A numerical study. Ph.D. dissertation, Delft University of Technology, The Netherlands.

11. Turbulence at Ichetucknee River… Isotropic?
Hour from 00:00 on

12. Turbulence at Ichetucknee River… Isotropic?
Multiplying stresses times density we obtain Force/area or Energy/volume