THEORY OF FULLY-DEVELOPED TURBULENCE IN BUOYANCY-DRIVEN FLUIDS AND PRESSURE-GRADIENT-DRIVEN PLASMAS

A new theoretical method is presented to analyse turbulence and associ ated transport in far-non-equilibrium fluids and plasmas. First, direc t nonlinear interactions with background turbulence are renormalized i nto nonlinear dielectric form. The relation between the turbulent inte nsity spectra of energy and temperature, E(k) and Ee(k), and the nonli near transfer rates (dielectric) of momentum and energy, nu(N) and kap pa(N), are obtained as recurrent formulae of integral equations. Secon d, nonlinear marginal stability conditions are examined by introductio n of dressed test mode analysis. Solutions have a power law which are analogous to critical exponents in renormalization group theory. The s ame paradigm is first applied to neutral fluids to recover conventiona l results. For two-dimensional (2D) buoyancy-driven turbulence, where a supercritical turbulence appears, spectral forms of E(k), E-theta(k) proportional to \g . del T\k(-3) and nu(N)(k), kappa(N)(k) proportion al to (\g . del T\)(1/2)k(-2) are obtained in the energy containing ra nge (or subrange). (VT is the temperature gradient and g is the gravit y.) The relation between global turbulent transport coefficients, such as nu(T) and kappa(T), and nonlinear transfer rates nu(N) and kappa(N ) is obtained. A global spatial structure of the turbulent fluid, whic h is consistent with the spectrum, is solved. The Nusselt number is ob tained as Nu similar or equal to 0.4(R-a/R-ac)(1/3) and the relations kappa(T) proportional to (R-a/R-ac)(4/9) and nu(T) proportional to (R- a/R-ac)(4/9) are obtained. (R-a is the Rayleigh number and R-ac is the critical Rayleigh number.) To turbulence in the magnetized plasma, wh ere a subcritical turbulence appears, this paradigm is applied. The co mbination of the pressure gradient (Vp) and magnetic held gradient (Om ega'), G(0) = del p.Omega', characterizes the non-equilibrium form of the plasma The spectral intensity of the fluctuating fields for the po tential, current and pressure E(k), E-J(k), E-theta(k) proportional to G(0)k(-3) and the nonlinear transfer rates mu(N)(k), lambda(N)(k), ch i(N)(k) proportional to (G(0))(1/2)k(-2) are first Obtained (symbols m u, lambda and chi correspond to the ion viscosity, current diffusivity and heat diffusivity, respectively) in the energy containing range. T he turbulence level, W, and the transport coefficients, chi(T), are de rived as W proportional to G(0)(2) and chi(T) proportional to G(0)(3/2 ). The dissipation balance is also examined. These analyses demonstrat e that this method is applicable to both the supercritical and subcrit ical turbulences in neutral fluid and plasma turbulences, i.e. in syst ems which are far from the thermal equilibrium.