Quest for a mass-weighted-averaging turbulence theory, with an unexpected finding about the countergradient diffusion and blockage of heat and matters

A mass-weighted-averaging theory is formulated of density-variable inhomogeneous turbulence. There the velocity and the concentration of matters are resolved into the mass-weighted means and the fluctuations around them. The essence of the formulation lies in the introduction of mass-weighted fluctuations. With those new variables, a statistical theory of inhomogeneous incompressible turbulence can be extended to the variable-density counterpart in a straightforward manner. One of the unexpected findings by this theory is the striking similarity between the countergradient diffusion in a turbulent combustion and the heat-transport suppression in high-mode confinements of tokamak's thermonuclear fusion.