Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets

Abstract

We study the self-similarity and dissipation scalings of a turbulent planar jet and the theoretically implied mean flow scalings. Unlike turbulent wakes where such studies have already been carried out (Dairay et al. 2015 J. Fluid Mech . 781 , 166–198. ( doi:10.1017/jfm.2015.493 ); Obligado et al. 2016 Phys. Rev. Fluids 1 , 044409. ( doi:10.1103/PhysRevFluids.1. 044409)), this is a boundary-free turbulent shear flow where the local Reynolds number increases with distance from inlet. The Townsend–George theory revised by (Dairay et al. 2015 J. Fluid Mech . 781 , 166–198. ( doi:10.1017/jfm.2015.493 )) is applied to turbulent planar jets. Only a few profiles need to be self-similar in this theory. The self-similarity of mean flow, turbulence dissipation, turbulent kinetic energy and Reynolds stress profiles is supported by our experimental results from 18 to at least 54 nozzle sizes, the furthermost location investigated in this work. Furthermore, the non-equilibrium dissipation scaling found in turbulent wakes, decaying grid-generated turbulence, various instances of periodic turbulence and turbulent boundary layers (Dairay et al. 2015 J. Fluid Mech . 781 , 166–198. ( doi:10.1017/jfm.2015.493 ); Vassilicos 2015 Annu. Rev. Fluid Mech . 95 , 114. ( doi:10.1146/annurev-fluid-010814-014637 ); Goto & Vassilicos 2015 Phys. Lett. A 3790 , 1144–1148. ( doi:10.1016/j.physleta.2015.02.025 ); Nedic et al. 2017 Phys. Rev. Fluids 2 , 032601. ( doi:10.1103/PhysRevFluids.2.032601 )) is also observed in the present turbulent planar jet and in the turbulent planar jet of (Antonia et al. 1980 Phys. Fluids 23 , 863055. ( doi:10.1063/1.863055 )). Given these observations, the theory implies new mean flow and jet width scalings which are found to be consistent with our data and the data of (Antonia et al. 1980 Phys. Fluids 23 , 863055. ( doi:10.1063/1.863055 )). In particular, it implies a hitherto unknown entrainment behaviour: the ratio of characteristic cross-stream to centreline streamwise mean flow velocities decays as the −1/3 power of streamwise distance in the region, where the non-equilibrium dissipation scaling holds.