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.

“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

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

Pressure Gradient

Advective Terms

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

Normal stresses Off diagonal = Shear stresses

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

Isotropic Turbulence http://www.efluids.com/efluids/gallery/gallery_pages/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