Turbulence enhancement in body force opposed flows

Turbulence may be strongly influenced by near-wall nonuniform body forces. A widely encountered example is buoyancy acting in mixed convection flows. Here we use direct numerical simulations to present two key ideas: First we show that introducing opposing body forces whilst maintaining the pressure gradient does not cause key turbulence characteristics to change. It follows that the concept of “apparent Reynolds number” introduced by He et al. [J. Fluid Mech. 809, 31 (2016)] to explain laminarization can now be extended to explain the opposite phenomena of turbulence enhancement by opposing body forces. This new understanding has allowed turbulent shear stress and skin friction to be easily predicted simply from the nonuniform body force profile and reference data despite the nonequilibrium nature of the flow. Second, we analyze the flow in the context of turbulence regeneration cycle and provide evidence that complements the recent study from Jiménez [J. Fluid Mech. 945, R3 (2022)], which suggests that streaks are more decoupled from the regeneration cycle than previously thought.

Figure 1

Profiles of flow statistics for a selection of key cases: (a) body force profiles, (b) velocity profiles, (c) turbulence shear stress, and (d) turbulence kinetic energy.

Figure 2

Eddy viscosity profiles (${\nu }_t$) in standard inner scaling (a), and EPG scaling (b).

Figure 3

Turbulent fluctuations in the streamwise, wall normal, and spanwise directions using the standard scaling (top row) and the EPG scaling (bottom row).

Figure 4

Streamwise Reynolds stress budget terms using the standard scaling (top row), and the EPG scaling (bottom row) for linear (a), (d); step (b), (e); and physical (c), (f) cases. The terms shown are production ($I$), dissipation ($II$), viscous diffusion ($III$), and pressure strain ($IV$).

Figure 5

Wall-normal Reynolds stress budget terms using the standard scaling (top row), and the EPG scaling (bottom row) for linear (a), (d); step (b), (e); and physical (c), (f) cases. The terms shown are dissipation ($II$), viscous diffusion ($III$), and pressure strain ($IV$).

Figure 6

Streamwise vorticity (a) uses the EFR reference flow, while (b) uses markers to represent each cases EPG reference flow.

Figure 7

Low speed streak visualizations for case $\text{L}4$ (a) and (b) and streamwise autocorrelations taken at $y^{+1}=12$ with aided body force influenced cases (c) and opposed cases (d); markers represent the corresponding EPG reference cases.

Figure 8

Quadrant events with strength $h=1$. Top row: contribution to the turbulent shear stress in each quadrant from such events. Bottom row: number of such events in each quadrant.

Figure 9

Anisotropic maps where nodes A, B, and C represent 1one, two, and three dimensional turbulence, respectively.

Figure 10

Comparison of the apparent-Reynolds-number predictions (red markers) with DNS of the idealized linear and step change cases (a) and (b), and the physical cases (c). The latter also includes the equivalent profiles from You et al. [30] (blue markers). Subplot (d) shows the contributions to skin friction from various terms of the FIK decomposition defined in Eq. (8).