The meaning of diffusion in turbulence
Can someone explain the difference between diffusion and dissipation in turbulence? I'm talking about the actual physics of turbulence not any numerical error. I know dissipation is associated with how viscosity damps out the fluctuations, but what is diffusion and convection ? Thanks.

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diffusion (molecular) is a property of the real fluid when the gradient of velocity appears (2*mu*S). It is a flux in the momentum quantity. Dissipation (molecular) is related to the energy equation (mu*S:S), as well ... Whild doing turbulence modeling such terms are also related to the SGS terms in the averaged momentum and energy balance 
Thanks. So is there a difference the physics of the two phenomena? It's just viscosity that is reducing the velocity and turning kinetic energy into heat right?

The inertial range in the energy spectrum is terminated first at the Taylor microscale where dissipation induced by molecular viscosity transfer kinetic energy in internal energy. Then the viscous range finishes at the Kolmogorov scale.
This is the general sketch of the physical transformation of energy at the viscous lenghts 
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