Turbulence regeneration in non-uniform body force influenced flows

Turbulence plays a key role in a wide variety of engineering applications,
and there are often varied objectives. If one is concerned with the efficiency of fluid transport, aerodynamics, or energy losses, then the aim
is to reduce frictional losses. If one is concerned with the efficiency of
cooling systems, then enhancing the turbulent mixing is advantageous.
Body forces cause changes in the turbulence, resulting in altered skin friction and turbulence mixing. He et al. [J. Fluid Mech. 809, 31 (2016)]
introduced a new theory where body-force-induced laminarisation could
be explained by a reduced ‘apparent Reynolds number’ (ARN) which is
defined by a reference flow with an equal pressure gradient to the bodyforce influenced flow. We hereby refer to this theory as the ARN theory.
The theory allowed turbulent shear stress and skin friction to be easily
predicted simply from the non-uniform body force profile and reference
data despite the non-equilibrium nature of the flow. In this study, we
extend the ARN theory to explain turbulence enhancement, demonstrate
the applicability of the theory in high Reynolds number flows, and further
support the ARN theory with linear stability analysis.
The first investigation uses the direct numerical simulation (DNS) solver
CHAPSim to study pipe flows with non-uniform near-wall body forces that
act against the main flow. Such opposing flows are known to cause turbulence enhancement. It is found that the key turbulence characteristics can
be explained by the ARN, even though the theory was initially proposed
for relaminarising turbulence. We analyze the flow in the context of the
turbulence regeneration cycle and provide evidence that complements the
recent study from Jim´enez [J. Fluid Mech. 945, R3 (2022)], which suggests that streaks are more decoupled from the regeneration cycle than
previously thought.