A molecular theory of the onset of turbulence

Abstract

We review experimental data which shows the dependence of the critical Reynolds number on molecular composition. We then use the cell model of a gas to explain the onset of turbulence by the excitation of the internal degrees of freedom of molecules. Two sources of internal energy states are identified: quantum confinement for monoatomic molecules and rotational states for diatoms.
The Navier-Stokes equation from the continuum model of hydrodynamics is a very successful equation for describing laminar flow. It is also used extensively, but not so successfully, for describing turbulent flow. For this reason, as an alternative, it may be useful to adopt a molecular approach. Recent experiments by S. Novopashin and J. Sommeria seem to support the idea that turbulence may have a molecular origin, instead of a flow, or mathematical provenance, as conventionally accepted. If a molecular origin for the onset of turbulence is established, this will put into question the exclusive use of the continuum model expressed by the Navier-Stokes equation for understanding turbulence. A molecular approach in simulating hydrodynamics has also been developing, illustrating for example, how molecular dynamics may be brought to the level of dissipative particle dynamics. This is of some interest to our own works, which require radiation as a mechanism for dissipation to arrive at some turbulent-like behavior. For these reasons, we summarize relevant experimental results to date, and further interpret and describe our molecular theory of turbulence presented earlier in several mathematical papers, arriving at a simple interpretation of the theory. With this paper, we will also suggest further experiments to test our ideas.