EXTENSION OF THE LAWS OF THERMODYNAMICS TO TURBULENT SYSTEMS

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  • 1 New York University
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Abstract

The energy equations applicable to the mean state of a turbulent fluid are reviewed, and a concept of the relative flux of turbulent kinetic energy is defined. It is shown that such irreversible processes as the decay of mean motion into turbulence, the relative flux of turbulent energy, and eddy diffusion are not governed by the classical laws of thermodynamics, but properly belong in the field of eddy thermodynamics proposed by Richardson. It is found that there exists an eddy analogue of the entropy which is a function of the eddy energy and partial densities of the various constituents of a fluid, and which observations suggest is consistently created by irreversible phenomena of turbulence. This property of eddy entropy is incorporated into a statement which is called the second law of eddy thermodynamics.

Abstract

The energy equations applicable to the mean state of a turbulent fluid are reviewed, and a concept of the relative flux of turbulent kinetic energy is defined. It is shown that such irreversible processes as the decay of mean motion into turbulence, the relative flux of turbulent energy, and eddy diffusion are not governed by the classical laws of thermodynamics, but properly belong in the field of eddy thermodynamics proposed by Richardson. It is found that there exists an eddy analogue of the entropy which is a function of the eddy energy and partial densities of the various constituents of a fluid, and which observations suggest is consistently created by irreversible phenomena of turbulence. This property of eddy entropy is incorporated into a statement which is called the second law of eddy thermodynamics.

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