Viscous Fluid Conduit Solitons

Single Soliton

Single soliton, closed streamlines

Bimodal interaction of two solitons

Solitons transfer fluid

Unimodal interaction of two solitons

Mixed interaction of two solitons

These videos depict solitary waves or solitons at the interface of a buoyant viscous fluid conduit created by a "pulse" of additional fluid.  The geometry of soliton interaction depends on the sizes of the two solitons.  Video (except the colored ones) has been rotated 90 degrees, sped up, and aspect ratios have been changed.  The videos titled "Single soliton closed streamlines" and "Solitons transfer fluid" are rotated 90 degrees and are in real time with a 1:1 aspect ratio.  Associated paper.

Viscous Fluid Conduit Dispersive Shock Waves

Moderately sized dispersive shock wave

Large dispersive shock wave with backflow

Dispersive shock wave backflow (zoom)

Dispersive shock waves in a viscous fluid conduit are created by ramping up the injection rate to a sustained, larger value.  Wavebreaking (gradient catastrophe) eventually occurs, leading to the spontaneous emergence of coherent, rank-ordered, expanding, nonlinear oscillations.  For large jumps in the injection rate, the trailing edge envelope can propagate opposite to the direction of fluid flow upward.  Video has been rotated 90 degrees, sped up, and aspect ratios have been changed.  Associated theory and experiment

Dispersive Hydrodynamics of Viscous Fluid Conduits

Soliton overtaking dispersive shock wave

Dispersive hydrodynamics encompasses the large scale dynamics of dissipationless, dispersive fluids.  The video depicts the overtaking interaction of a soliton and a dispersive shock wave.  The image above is a space-time snapshot of the entire video (a contour plot of the experimental conduit amplitude in space-time), showing that the soliton is actually decelerated or refracted by the dispersive shock wave.  Associated experiment.

Dispersive shock wave overtaking soliton

Here, the soliton is launched first followed by a dispersive shock wave.  The soliton is eventually absorbed into the interior of the expanding dispersive shock wave.  Associated experiment.

Interaction of two dispersive shock waves

Interaction of two dispersive shock waves resulting in a merged dispersive shock wave that is decelerated (accelerated) relative to the trailing (leading) shock.  Associated experiment.

Dispersive hydrodynamics in thin film ferromagnets

Quantized topology loss at supersonic transition

Effect of non-local dipolar field and room temperature

Laminar flow, magnetic obstacle

Mach cone, ship-waves, and vortex-antivortex pairs, magnetic obstacle

Laminar flow, moving frame

Mach cone and ship-waves, moving frame

Modulational instability