- Highly unsteady: velocity at a point appears random - instantaneous field fluctuates rapidly in 3 dimensions - statistical properties constant in time - time and ensemble averages are equal - high $\mathrm{Re}$, highly nonlinear Total = average + fluctuations $u = \bar{u} + u'$ $\mathrm{Re} = \frac{\rho UL}{\mu}=\frac{UL}{\nu}$ $\mu =$ viscosity $\nu = \frac{\mu}{\rho} =$ kinematic viscosity $\mathrm{Nu_{L}}=\frac{hL}{k_{f}}=\frac{\text{convective HT}}{\text{conductive HT}}$ $\mathrm{Pr} = \frac{\nu}{\alpha}$ $a =$ thermal diffusivity $\alpha = \frac{k}{\rho c_{p}}$ $\mathrm{\mathrm{Pr}} = \frac{c_{p}\mu}{k}$ $\mathrm{Ra} = \mathrm{Gr}\cdot \mathrm{\mathrm{Pr}}$ (free convection) ### Stirring Advection process by which conserved quantities of different values are brought into contact Average effects of stirring modeled as turbulent diffusion ### Mixing Irreversible molecular diffusion Happens when stirring is large