@article{maiden_lowman_anderson_schubert_hoefer_2016, title={Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits}, volume={116}, ISSN={["1079-7114"]}, DOI={10.1103/physrevlett.116.174501}, abstractNote={Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.}, number={17}, journal={PHYSICAL REVIEW LETTERS}, author={Maiden, Michelle D. and Lowman, Nicholas K. and Anderson, Dalton V. and Schubert, Marika E. and Hoefer, Mark A.}, year={2016}, month={Apr} }
 @article{lowman_hoefer_el_2014, title={Interactions of large amplitude solitary waves in viscous fluid conduits}, volume={750}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2014.273}, abstractNote={Abstract}, journal={JOURNAL OF FLUID MECHANICS}, author={Lowman, Nicholas K. and Hoefer, M. A. and El, G. A.}, year={2014}, month={Jul}, pages={372–384} }
 @article{lowman_hoefer_2013, title={Dispersive hydrodynamics in viscous fluid conduits}, volume={88}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.88.023016}, abstractNote={The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous authors have proposed an approximate model equation based on physical arguments, but a precise theoretical treatment for this two-fluid system with a free boundary is lacking. Here, a derivation of the interfacial equation via a multiple scales, perturbation technique is presented. Perturbations about a state of vertically uniform, laminar conduit flow are considered in the context of the Navier-Stokes equations with appropriate boundary conditions. The ratio of interior to exterior viscosities is the small parameter used in the asymptotic analysis, which leads systematically to a maximal balance between buoyancy driven, nonlinear self-steepening and viscous, interfacial stress induced, nonlinear dispersion. This results in a scalar, nonlinear partial differential equation describing large amplitude dynamics of the cross-sectional area of the intrusive fluid conduit, in agreement with previous derivations. The leading order behavior of the two-fluid system is completely characterized in terms of the interfacial dynamics. The regime of model validity is characterized and shown to agree with previous experimental studies. Viscous fluid conduits provide a robust setting for the study of nonlinear, dispersive wave phenomena.}, number={2}, journal={PHYSICAL REVIEW E}, author={Lowman, N. K. and Hoefer, M. A.}, year={2013}, month={Aug} }
 @article{lowman_hoefer_2013, title={Dispersive shock waves in viscously deformable media}, volume={718}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2012.628}, abstractNote={Abstract}, journal={JOURNAL OF FLUID MECHANICS}, author={Lowman, Nicholas K. and Hoefer, M. A.}, year={2013}, month={Mar}, pages={524–557} }
 @article{lowman_hoefer_2013, title={Fermionic shock waves: Distinguishing dissipative versus dispersive regularizations}, volume={88}, ISSN={["1094-1622"]}, DOI={10.1103/physreva.88.013605}, abstractNote={The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas dynamics, develop a steep, localized shock front that translates at a well-defined speed, dispersively regularized shocks are distinguished by an expanding region of short wavelength oscillations with two speeds, those of the leading and trailing edges. For typical UFG experimental conditions, the theoretical oscillation length scale is smaller than the resolution of present imaging systems so it is unclear how to determine the shock type from its structure alone. Two experimental methods to determine the appropriate regularization mechanism are proposed: measurement of the shock speed and observation of a one-dimensional collision experiment with sufficiently tight radial confinement.}, number={1}, journal={PHYSICAL REVIEW A}, author={Lowman, N. K. and Hoefer, M. A.}, year={2013}, month={Jul} }