Viscous shear-layer displacement effect on boundary pressure

Establish whether the displacement effect of the viscous shear layer at low coflow velocities modifies the jet-boundary pressure field used in the method-of-characteristics analysis, thereby accounting for the discrepancy between inviscid predictions and Navier–Stokes Mach-disk diameters.

Background

At low coflow velocities, the paper observes a substantial difference between the Mach-disk diameters predicted by Navier–Stokes simulations and the similar Mach-disk behavior suggested by the inviscid method-of-characteristics analysis. The authors propose, but do not verify, that the thicker viscous shear layer may alter the effective boundary experienced by the supersonic core by smearing or displacing the pressure field. Establishing this connection would clarify the role of viscosity in the low-coflow regime.

References

One possible, though still tentative, explanation is that at these low coflow ratios the shear layer is thick enough to itself modify the effective inviscid boundary felt by the supersonic core, for instance, by smearing the pressure field that the reflected compression waves respond to. Such an effect is not captured by the inviscid analysis of Section~\ref{sec:method-of-characteristics}, which uses the pressure profile along the streamline launched from the nozzle lip as boundary pressure. As $U_c$ increases beyond $U_c=0.2$ and $\delta_{\omega}$ decreases substantially, the viscous effects diminish, and the solutions from inviscid analysis start to agree with Navier-Stokes solutions. We note that this explanation has not been independently verified. Establishing it more firmly would require directly relating the displacement effect of the shear layer to the jet-boundary pressure field used in the MOC analysis, which we leave to future work.

Mach-disk formation and shock-structure transitions in underexpanded coflowing jets  (2608.18923 - Dhungana et al., 19 Aug 2026) in Section 3.7, Effect of coflow on viscous mixing at the jet boundary