TURBULENCE follow Kundus book Turbulent Flows Characteristics of

TURBULENCE (follow Kundu’s book) 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 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.

“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) 1) Randomness 2) Nonlinearity 3) Diffusivity 4) Vorticity 5) Dissipation

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

Pressure Gradient

Advective Terms

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

Normal stresses Off diagonal = Shear stresses

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

Isotropic Turbulence http: //www. efluids. com/efluids/gallery_pag es/iso_turbulence_page. htm G. Brethouwer (2000) Mixing of passive and reactive scalars in turbulent flows: A numerical study. Ph. D. dissertation, Delft University of Technology, The Netherlands.

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

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