Extended Data Fig. 4: Transverse mode in a shock wave.
a. Shock wave. A piston moving at speed U = 1.9d/Δt (faster than the speed of sound c = 1.4d/Δt) generates a shock wave accompanied with transverse flows, which is characterized by the vertical flow velocity uy (gradient coloring). The particles self-spin counter-clockwise at speed Ω = 25.3/Δt and have an initial global density n0 = 0.125d−2. According to the viscid Burgers’ equation \({\partial }_{t}u+u{\partial }_{x}u=\nu {\partial }_{x}^{2}u\), the width of this shock is approximately λs = 4ν/U, where ν = η/n0m is the kinematic viscosity. Hydrodynamic profiles are quantified near the wave front. Also see Supplementary Mov. S8. b. Density profile n(x). The simulation results are compared with continuum hydrodynamic theory (solid line), which employs parameters measured in a separate homogeneous microscopic systems of number density n0 (dashed line). Thus, theoretical predictions would break down at extreme densities (shaded region). c. Horizontal flow velocity ux(x). d. Vertical flow velocity uy(x). The same color coding as panel A is applied here. Predictions using continuum hydrodynamic theory are plotted as solid lines.
