This lesson covers the in-depth understanding of Kolmogorov's turbulence theory. It explains the properties of turbulent flow, the derivation of the energy spectrum, and the concept of energy cascading from large to small scales. The lesson also discusses the assumptions made in Kolmogorov's theory and its limitations. For instance, it is applicable to isotropic, incompressible, and 3D flows with nonzero viscosity. The lesson further illustrates these concepts with the help of numerical simulations and provides a detailed explanation of the results. It also highlights the importance of local energy transfer in turbulence and the challenges in simulating high Reynolds number flows.

- Kolmogorov's turbulence theory provides a framework for understanding the properties of turbulent flow and the energy spectrum.
- The theory assumes energy cascades from large to small scales in a turbulent flow.
- The theory is applicable to isotropic, incompressible, and 3D flows with nonzero viscosity.
- Numerical simulations can validate the predictions of Kolmogorov's theory.
- Local energy transfer is a crucial aspect of turbulence.
- Simulating high Reynolds number flows is computationally challenging due to the need for a large number of grid points.

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