Karuna S. Koppula

The URAPS closure for the normalized Reynolds stress

The Reynolds-averaged Navier–Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier–Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.

Reynolds Stress Anisotropy in Rotating Homogeneous Decay

In rotating homogeneous decay, the prolate quadratic form associated with the normalized Reynolds (NR-) stress is elongated by a coupling between velocity fluctuations and the Coriolis acceleration. This paper shows that this well-known turbulence phenomenon is consistent with an algebraic anisotropic prestress (APS-) closure for the NR-stress that unifies the study of turbulent flows in rotating and non-rotating frames-of-reference. The APS-closure is a non-negative mapping of the NR-stress into itself and is, thereby, universally realizable for all turbulent flows.Copyright

Turbulent Transport of a Passive Scalar Additive in Spanwise Rotating Channel Flow With Zero Intrinsic Vorticity

In spanwise rotating channel flows, the turbulent kinetic energy near the high pressure and the low pressure walls is primarily associated with longitudinal velocity fluctuations. Consequently, the primary normal Reynolds momentum flux difference is positive and the secondary normal Reynolds flux difference is negative. In the outer region on the high pressure side of the symmetry plane, the energy is redistributed with the result that the signs of both the primary and of secondary normal differences flip. This redistribution of energy by Coriolis forces occurs in a region of zero intrinsic vorticity. In this paper, the dispersion of a passive additive within the zero intrinsic vorticity region is examined by using a recently developed universal, realizable, anisotropic prestress closure for the normalized Reynolds stress. For low rotation numbers (i.e., | Ωx | ≪ e / k), the theory shows that the transverse component of the passive additive flux is mitigated by a coupling between the shear component of the Reynolds stress and the longitudinal gradient of the mean passive additive field. At high rotation numbers (i.e., | Ωx | ≫ e / k), the dispersion coefficient in the transverse (cross flow) direction is four times larger than the dispersion coefficient in the spanwise direction. Surprisingly, the dispersion coefficient in the longitudinal direction is relatively small. The geophysical and the engineering significance of these theoretical conclusions will be highlighted in the presentation.Copyright