Mass of Turbulence: Does Turbulent Fluid Have More Energy?

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Turbulent fluid possesses more energy compared to laminar fluid due to the chaotic motion and mixing that occurs in turbulence. The discussion clarifies that the same fluid can exhibit different energy levels before and after transitioning from laminar to turbulent flow. This difference in energy is attributed to the increased velocity gradients and eddies present in turbulent flow. Understanding these energy variations is crucial for applications in fluid dynamics. The relationship between turbulence and energy levels is a significant aspect of fluid behavior.
Abel Cavaşi
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Turbulent fluid has more energy (mass) than laminar fluid?
 
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Are you asking whether the same fluid in some (laminar) flow has a different amount of energy (mass) before and after the onset of turbulence?
 
Yes. Thanks for clarification. I would like to know if there are differences in energy (mass) of its kind between the turbulent fluid and the same fluid but laminar.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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