The modeling of buoyancy driven turbulent flows is considered in conjunction with an advanced statistical turbulence model referred to as the BHR (Besnard-Harlow-Rauenzahn) $k\text{−}S\text{−}a$ model. The BHR $k\text{−}S\text{−}a$ model is focused on variable-density and compressible flows such as Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) driven mixing. The BHR $k\text{−}S\text{−}a$ turbulence mix model has been implemented in the RAGE hydro-code, and model constants are evaluated based on analytical self-similar solutions of the model equations. The results are then compared with a large test database available from experiments and direct numerical simulations (DNS) of RT, RM, and KH driven mixing. Furthermore, we describe research to understand how the BHR $k\text{−}S\text{−}a$ turbulence model operates over a range of moderate to high Reynolds number buoyancy driven flows, with a goal of placing the modeling of buoyancy driven turbulent flows at the same level of development as that of single phase shear flows.

The purpose of this study is to analyze the heat-affected zone in materials such as meat samples, araldite resin-simulating tissue phantoms, and fiber composites irradiated using a mode-locked short pulse laser with a pulse width of 200 ps. The radial surface temperature profiles are compared with that of a continuous wave (CW) laser of the same average power. The short pulse laser results in a more localized heating than a continuous laser with a corresponding high peak temperature. A parametric study addressing the effect of pulse train frequency, material thickness, and amount of scatterers and absorbing agent in the medium and different initial sample temperatures is performed, and the measured temperature profiles are compared with the theoretical non-Fourier hyperbolic formulations and Fourier parabolic heat conduction formulations for both CW and pulsed laser cases.

A total internal reflection fluorescence microscopy technique coupled with three-dimensional tracking of nanoparticles is used to experimentally verify the theory on near-wall hindered Brownian motion [Goldman et al., Chem. Eng. Sci. 22, 637 (1967); Brenner, Chem. Eng. Sci. 16, 242 (1967)] very close to the solid surface (within $\sim 1\mu \mathrm{m}$). The measured mean square displacements (MSDs) in the lateral $x\text{−}y$ directions show good agreement with the theory for all tested nanoparticles of radii 50, 100, 250, and 500 nm. However, the measured MSDs in the $z$ direction deviate substantially from the theory particularly for the case of smaller particles of 50 and 100 nm radius. Since the theory considers only the hydrodynamic interaction of moving particles with a stationary solid wall, additionally possible interaction forces like gravitational forces, van der Waals forces, and electro-osmotic forces have been examined to delineate the physical reasons for the discrepancy.