We experimentally corroborate the core analytical deductions of Thomson’s 124-year-old theorem, vis-à-vis the stability of a ring of $N$ vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular $N$-gons are stable for $N\le 6$ and unstable for $N\ge 8$. The $N\le 6$ equilibria are exceptionally resilient. When destroyed, they reemerge in their original form. We reason that the heptagonal system either survives in an exceedingly narrow band of disk speeds or is in theory critically stable. Contrary to the results with a rotating bottom reported by Jansson et al. [ Phys. Rev. Lett. 96, 174502 (2006)], we show the interfacial axial symmetry does not break spontaneously but through spectral development, the functional relationship amongst the polygon rotation and disk speed is surprisingly simple, and the pattern to disk frequency ratio depends on both Froude and wave numbers.

This paper deals with pore-scale two-phase flow simulations in carbonate rock using the pore network method (PNM). This method was used to determine the rock and flow properties of three different rock samples, such as porosity, capillary pressure, absolute permeabilities, and oil–water relative permeabilities. The pore network method was further used to determine the properties of rock matrices, such as pore size distribution, topological structure, aspect ratio, pore throat shape factor, connected porosity, total porosity, and absolute permeability. The predicted simulation for the network-connected porosity, total porosity, and absolute permeability agree well with those measured experimentally when the image resolution is appropriate to resolve the relevant pore and throat sizes. This paper also explores the effect of the wettability and fraction of oil-wet pores on relative permeabilities, both in uniform and mixed wet systems.

This paper investigates the dynamics of the flapping regime of a filament placed in a two-dimensional soap-film flow for different filament lengths and flow speeds. It was found that the onset of flapping is quasiperiodic, with the main flapping amplitude and frequency modulated by low-amplitude, low-frequency oscillation. At higher flow velocities, the oscillation becomes chaotic. The transition to chaos occurs via the quasiperiodic route to chaos. A new bistability phenomenon was discovered in which the system alternates between the stretched-straight and oscillatory states, which is here referred to as ``switching oscillation.'' Unlike some previously reported forms of bistability, in this case the system alternates between the two states continuously, without any external perturbation.