Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer

Abstract

(Received xx; revised xx; accepted xx)In order to improve the physical understanding of the development of turbulent structures, the compressible evolution equations for the first three invariants P ,Q and R of the velocity gradient tensor have been derived. The mean evolution of characteristic turbulent structure types were studied and compared at different wall-normal locations of a compressible turbulent boundary layer. The evolution of these structure types are fundamental to the physics that need to be captured by turbulence models. Significant variations of the mean evolution are found. The key features of the changes of the mean trajectories in the invariant phase space are highlighted and the consequences of the changes are discussed. Further, the individual elements of the overall evolution are studied separately to identify the causes that lead to the evolution varying with the distance to the wall. Significant impact of the wall-normal location on the coupling between the pressure-Hessian tensor and the velocity gradient tensor was found.

Characterization of velocity-gradient dynamics in incompressible turbulence using local streamline geometry

“…The last few decades have witnessed many important advances toward understanding the internal structure of A ij (Ashurst et al 1987;Kerr 1987) and describing local streamline topology in terms of A ij invariants (Chong, Perry & Cantwell 1990). The topological classification of local streamline structure has enabled further advances in (i) identifying key universal features of local streamline structure (Soria et al 1994;Blackburn, Mansour & Cantwell 1996;Chacín, Cantwell & Kline 1996;Chacin & Cantwell 2000;Elsinga & Marusic 2010b), and (ii) characterization of important velocity gradient processes conditioned upon topology (Martín et al 1998b;Ooi et al 1999;Elsinga & Marusic 2010a;Atkinson et al 2012;Bechlars & Sandberg 2017). Other studies on the structure of A ij have led to improved understanding of internal alignment properties, characteristic length scales and non-normality in different topologies (Chevillard et al 2008;Hamlington, Schumacher & Dahm 2008;Danish & Meneveau 2018;Keylock 2018).…”

Statistical properties of pressure-Hessian tensor in a turbulent channel flow

“…Generally, the distribution of invariants in the P-Q-R space is very complex and not easy to describe intuitively. Therefore, the distribution and evolution of the flow topology in the Q-R plane can usually be studied for compression, expansion or incompressible regions by fixing the value of P (Suman & Girimaji 2010;Wang & Lu 2012;Chu & Lu 2013;Bechlars & Sandberg 2017), respectively. In this case, the interface of flow topologies degenerates to the borderline in the plane Q-R.…”

“…To study the effect of the pressure-Hessian tensor on the evolution of VGT dynamics, one can investigate the conditional mean trajectory (CMT) of the second invariant (Q) and the third invariant (R) of the VGT in the Q-R plane and the contribution of off-diagonal terms of the pressure-Hessian tensor (Martín et al 1998b). Previous studies illustrate that, in isotropic turbulence (Ooi et al 1999;Chevillard et al 2008;Lüthi et al 2009) and wall turbulence (Chu & Lu 2013;Bechlars & Sandberg 2017), the contribution of the pressure-Hessian tensor to the mean evolution of the VGT invariants is almost contrary to the action of the nonlinear self-amplification term, which counteracts the singularity of the RE equation.…”

Density effects on post-shock turbulence structure and dynamics

“…1998; Ooi et al. 1999; Wang & Lu 2012; Bechlars & Sandberg 2017). Previous studies on single-fluid STI have examined the probability density function (PDF) of the VGT.…”

“…The statistics regarding the invariants of the VGT and their Lagrangian dynamics have been used to understand the structure of turbulence in many canonical flows, such as isotropic turbulence, turbulent boundary layers and mixing layers (e.g. Chong et al 1998;Ooi et al 1999;Wang & Lu 2012;Bechlars & Sandberg 2017). Previous studies on single-fluid STI have examined the probability density function (PDF) of the VGT.…”