Theoretical characterization of viscous conduit breathers (envelope solitary waves) - Part I

The spatio-temporal evolution of the circular interface between two miscible fluids of high viscosity contrast, a viscous conduit has proven to be an ideal platform for studying nonlinear dispersive hydrodynamic (DH) excitations. Despite the bulk, two-fluid dynamics at low Reynolds numbers, the fluid conduit interface is effectively non-dissipative, thanks to extremely slow rates of mass diffusion. The present study investigates the existence and characterization of breather solutions of the conduit equation, a long wavelength, fully nonlinear PDE model of conduit interfacial dynamics. Bright and dark breathers represent a class of fundamental multi-scale, propagating DH excitations. Bright breathers have been obtained numerically and investigated across the entire range of nonlinearity. Crucially, the study has suggested a three-parameter characterization of these solutions, with a counterintuitive, continuous deformation into the dark breathers across the zero-dispersion line. The talk will highlight the novelties of the numerical scheme used to compute conduit breathers, the identification of universal frameworks to study such solutions, and future applications in internal oceanic waves.