Statistics at small scales of a passive scalar field with a uniform mean scalar gradient in isotropic turbulence

This talk presents a theory of the statistics at small scales of a scalar field convected passively by statistically homogeneous and isotropic incompressible turbulent flow under a uniform mean scalar gradient. The theory is based on an extension of the idea of linear response theory of turbulence reviewed by Y. Kaneda [J. Stat. Mech. (2020) 034006]. In order to examine the theory, we performed direct numerical simulation (DNS) of a passive scalar field under periodic boundary conditions for the velocity field u_i (i=1,2,3) and the fluctuating part θ of the scalar field. The velocity field is forced at low wavenumbers so that the total kinetic energy per unit mass is kept time-independent. The DNS is based on an alias-free spectral method and a fourth-order Runge-Kutta method. In the main DNS, the Schmidt number is unity and the Taylor-microscale Reynolds number is approximately 260. Particular attention is paid to the effects of the mean scalar gradient on the anisotropy of the mixed velocity-scalar structure function <δu_i (r)δθ(r) δθ(r) > in the inertial-convective range, where δf(r)≡f(x+r)-f(x). Results from the theory are consistent with those of the DNS.