Characterize the emergence and forcing dependence of large-scale hydrodynamic modes

Characterize exactly how large-scale velocity modes emerge in steady-state nanoscale flows driven by a single-mode sinusoidal force and determine how those modes depend on the externally applied driving force.

Background

Earlier studies reported large-length-scale excitations of fluid-velocity modes in steady-state nanoscale flows driven by a single sinusoidal force mode. Those additional modes were conjectured to arise from coupling to density and wall–fluid shear modes, but their precise generation mechanism and dependence on the external forcing had not been established. The present paper develops a density–acceleration mode-coupling framework addressing this issue, so the problem is stated as an unresolved question in the introduction rather than as a result left open by the paper.

References

It was conjectured that the additional modes are induced by density and wall-fluid shear modes, however, it remains to show exactly how these large scale modes emerge and how the modes depend on the external driving force.

— Hydrodynamic Mode Coupling: Effects of density variations in nanoscale channel flows  (2608.17705 - Heitmeier et al., 18 Aug 2026) in Introduction, paragraph beginning “Knudsen et al.”