Kinetic Reduction and Hydrodynamics under Time-Dependent Helical Symmetry

Abstract

Translational and helical symmetries provide idealized descriptions of many flows encountered in nature and engineering. While translationally symmetric flows have been extensively studied within kinetic and continuum frameworks, the corresponding connection between microscopic dynamics and continuum behaviour for helical flows is less developed. Here, we investigate this connection for a dilute gas with time-dependent helical symmetry. Using the objective molecular dynamics framework, we derive a reduced Boltzmann equation that retains radial variations while preserving the classical collision operator under helical symmetry. Formal hydrodynamic expansions then yield the corresponding Euler and Navier-Stokes-Fourier equations. The resulting models describe how cylindrical geometry and axial deformation influence transport, including viscous transport and heat conduction, and how deformation generates unequal stresses along and across the axis in competition with collisional relaxation. Comparisons with direct simulation Monte Carlo solutions examine both spatially uniform and radially varying flows. In the cases studied, the first-order fluid corrections capture the leading stress anisotropy and improve the prediction of radial temperature variations, while larger Knudsen numbers expose limitations of the approximation.