We theoretically and numerically investigate the effect of temperature dependent density and viscosity on turbulence in channel flows. First, a mathematical framework is developed to support the validity of the semi-local scaling as proposed based on heuristic arguments by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)]. Second, direct numerical simulations (DNS) of turbulent channel flows with different constitutive relations for density and viscosity are performed to assess and validate the semi-local scaling for turbulent statistics. The DNS database is obtained by solving the low-Mach number approximation of the Navier-Stokes equation. Finally, we quantify the modulation of turbulence due to changes in fluid properties. In the simulations, the fluid is internally heated and the temperature at both channel walls is fixed, such that the friction Reynolds number based on wall quantities is Re_τ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity μ, but constant semi-local Reynolds number $R{e}_{\tau }^{\ast }\equiv \sqrt{(\overline{\rho }/{\rho }_w)}/(\overline{\mu }/{\mu }_w)R{e}_{\tau }$ (where bar and subscript w, denote Reynolds averaging and averaged wall quantity, respectively), across the whole channel height, the turbulent statistics exhibit quasi-similarity with constant property turbulent flows. For cases where $R{e}_{\tau }^{\ast }\ne R{e}_{\tau }$ across the channel, we found that quasi-similarity is maintained for cases with similar $R{e}_{\tau }^{\ast }$ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of $R{e}_{\tau }^{\ast }$ towards the channel center ($R{e}_{\tau }^{\ast }<R{e}_{\tau }$ ), we show that the anisotropy increases and the pre-multiplied stream-wise spectra reveal that this increase is associated with strengthening of the large scale streaks in the buffer layer. The opposite effect is observed when $R{e}_{\tau }^{\ast }$ increases towards the channel center. The present results provide an effective framework for categorizing turbulence modulation in wall-bounded flows with variable property effects, and can be applied to any Newtonian fluid that is heated or cooled.

The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel is studied by means of direct numerical simulation of the low-Mach-number approximation of the Navier–Stokes equations. Different constitutive relations for density $\unicode[STIX]{x1D70C}$ and viscosity $\unicode[STIX]{x1D707}$ as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable-property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semilocal Reynolds number, defined as $Re_{\unicode[STIX]{x1D70F}}^{\star }\equiv Re_{\unicode[STIX]{x1D70F}}\sqrt{(\overline{\unicode[STIX]{x1D70C}}/\overline{\unicode[STIX]{x1D70C}}_{w})}/(\overline{\unicode[STIX]{x1D707}}/\overline{\unicode[STIX]{x1D707}}_{w})$ (the bar and subscript $w$ denote Reynolds averaging and wall value respectively, while $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number based on wall values). This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semilocal wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role in the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasistreamwise vortices and find that, similarly to turbulence statistics, the turbulent structures are also strongly governed by $Re_{\unicode[STIX]{x1D70F}}^{\star }$ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in $Re_{\unicode[STIX]{x1D70F}}^{\star }$ ( $\text{d}Re_{\unicode[STIX]{x1D70F}}^{\star }/\text{d}y\neq 0$ ) show significant changes in inclination and tilting angles of quasistreamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the inter-component energy transfer in flows with strong near-wall $Re_{\unicode[STIX]{x1D70F}}^{\star }$ gradients.