Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: What have we learned about turbulence?

Abstract

Twenty years ago there was no experimental access to the velocity gradient tensor for turbulent flows. Without such access, knowledge of fundamental and defining properties of turbulence, such as vorticity dissipation, and strain rates and helicity, could not be studied in the laboratory. Although a few direct simulations at very low Reynolds numbers had been performed, most of these did not focus on properties of the small scales of turbulence defined by the velocity gradient tensor. In 1987 the results of the development and first successful use of a multisensor hot-wire probe for simultaneous measurements of all the components of the velocity gradient tensor in a turbulent boundary layer were published by Balint et al. [Advances in Turbulence: Proceedings of the First European Turbulence Conference (Springer-Verlag, New York, 1987), p. 456]. That same year measurements of all but one of the terms in the velocity gradient tensor were carried out, although not simultaneously, in the self-preserving region of a turbulent circular cylinder wake by Browne et al. [J. Fluid Mech. 179, 307 (1987)], and the first direct numerical simulation (DNS) of a turbulent channel flow was successfully carried out and reported by Kim et al. [J. Fluid Mech. 177, 133 (1987)], including statistics of the vorticity field. Also in that year a DNS of homogeneous shear flow by Rogers and Moin [J. Fluid Mech. 176, 33 (1987)] was published in which the authors examined the structure of the vorticity field. Additionally, Ashurst et al. [Phys. Fluids 30, 2343 (1987)] examined the alignment of the vorticity and strainrate fields using this homogeneous shear flow data as well as the DNS of isotropic turbulence of Kerr [J. Fluid Mech. 153, 31 (1985)] who had initiated such studies. Furthermore, Metcalfe et al. [J. Fluid Mech. 184, 207 (1987)] published results from their direct simulation of a temporally developing planar mixing layer in which they examined coherent vortical states resulting from secondary instabilities. Since then several experimentalists have used multisensor hot-wire probes of increasing complexity in turbulent boundary layers, wakes, jets, mixing layers, and grid flows. Numerous computationalists have employed DNS in a wide variety of turbulent flows at ever increasing Reynolds numbers. Particle image velocimetry and other optical methods have been rapidly developed and advanced during these two decades which have provided other means of access to these fundamental properties of turbulence. This paper reviews highlights of these remarkable developments and points out some of the most important things we have learned about turbulence as a result.