This lesson covers the concept of Kolmogorov's theory, focusing on the spectrum and flux in the inertial range. It explains the role of the Reynolds number in turbulent cascade and the resulting k to minus five-third spectrum. The lesson also discusses the concept of flux, its constancy in turbulent hydrodynamic flows, and its variation in laminar flows. It introduces Pao's model for larger Reynolds numbers and its application in both inertial and dissipation ranges. The lesson concludes with an exploration of laminar flows when the Reynolds number is around 1, and the resulting implications for flux and spectrum.

- In Kolmogorov's theory, the spectrum and flux are significant in the inertial range where non-linearity is strong compared to the viscous term.
- The Reynolds number plays a crucial role in turbulent cascade, leading to a k to minus five-third spectrum.
- Flux is constant in turbulent hydrodynamic flows but varies in laminar flows.
- Pao's model is applicable for larger Reynolds numbers and works for both inertial and dissipation ranges.
- In laminar flows, when the Reynolds number is around 1, flux is not constant and the spectrum can be solved using Pao's model.

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