[Paper link](https://arxiv.org/pdf/1903.01426.pdf)
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On page 4, I am trying to understand what equations 1, 3, and 4 mean. From my understanding, equation 3 comes from the first law of thermodynamics, but could someone what they all describe?
In: Physics
The equations are all material derivatives, which are a special kind of derivative used for time rate of change problems in continuum mechanics.
In this specific instance, equation 1 is the rate of change of momentum (in effect, a more complicated and generalized form of Newton’s Laws), equation 2 is the rate of change of specific internal energy (effectively, heat), equation 3 is the rate of change of specific turbulent energy (basically, the energy of eddies and flows within a given substance, from Fluid Mechanics), and equation 4 just equations 2 and 3 put together (which would be an expression of the 1st Law of Thermodynamics).
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