Energy Transfers in Hydrodynamics

This course covers the comprehensive understanding of energy transfers in hydrodynamic flows, with a focus on turbulence and the Navier-Stokes equation. It delves into the concept of mode to mode energy transfer, explaining how energy moves from one region to another, and how to compute them in simulations. For instance, the course explains the concept of turbulent flux or spectral energy flux and shell to shell transfer. It further elaborates on the concept of energy conservation in a triadic interaction, also known as triadic conservation. The course provides a derivation of the formula for mode to mode transfer, useful in describing various quantities like energy flux and pattern formation. It also covers the concept of energy transfer in physics, focusing on the mode-to-mode transfer. It explores the use of tensor analysis to validate the solution and the properties of the energy transfer equation. The course also touches on the Craya-Herring method and its application in energy transfer. It provides a detailed walkthrough of how energy transfers occur in a co-linear triad, explaining why the energy transfer in such a triad is zero. It further explores the energy transfers in different modes, using illustrative examples such as the 1 0 1, 0 1 1, and 1 1 2 triads. The course also highlights the importance of understanding energy transfers in comprehending how patterns evolve over time and how energy is exchanged between different entities.