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We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is…
In this article we investigate a family of nonlinear evolutions of polygons in the plane called the $\beta$-polygon flow and obtain some results analogous to results for the smooth curve shortening flow: (1) any planar polygon shrinks to a…
This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity) and threaded by a…
We analyze the steady fluid flow in a porous medium containing a network of thin fissures i.e. width $\mathcal{O}(\epsilon)$, where all the cracks are generated by the rigid translation of a continuous piecewise $C^{1}$ functions in a fixed…
We give a new application of the theory of holomorphic motions to the study the distortion of level lines of harmonic functions and stream lines of ideal planar fluid flow. In various settings, we show they are in fact quasilines - the…
We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously…
We consider laminar flow in channels constrained geometrically to remain between two parallel planes; this geometry is typical of microchannels obtained with a single step by current microfabrication techniques. For pressure-driven Stokes…
We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal con- strained on a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
The self-organization of turbulence into regular zonal flows can be fruitfully investigated with quasilinear methods and statistical descriptions. A wave kinetic equation that assumes asymptotically large-scale zonal flows is pathological.…
This work deals with stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and…
In this paper we introduce and study a new kind of hyperbolic geometric flows --dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave equations with dissipative terms. Some interesting exact…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…