Stability and the transition to turbulence in the flow through conduits with compliant walls

The mechanisms of destabilisation the flow through soft-walled channels/tubes are qualitatively different from those in rigid-walled conduits. stability depends on two dimensionless parameters, Reynolds number $(\rho _f V_f h_f/ \mu _f)$ and $\varSigma = (\rho G h_f^{2}/\mu _f^{2})$ , where $\rho _f$ $\mu fluid density viscosity, $h_f$ $V_f$ length velocity scale $G$ is wall elasticity modulus. There an instability at zero when parameter $\varGamma (\mu / h_f G)$ exceeds a critical value. low-Reynolds-number Couette past compliant surface well understood, has been confirmed experiments, but that pressure-driven not completely understood. Two modes high have predicted: inviscid mode with internal viscous layer, for which transition scales as ${Re}_t \propto \varSigma ^{1/2}$ ; layer wall, ^{3/4}$ . observed experiments low 300 tube 100 channel one though scaling differs theoretical prediction due to substantial deformation. Though after shares many characteristics hard-wall turbulence, it significant ways, suggesting soft-wall turbulence separate class distinct turbulence.