Related papers: Instability patterns, wakes and topological limnit…
Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary…
The effect of random surface roughness on hydrodynamics of viscous incompressible liquid is discussed. Roughness-driven contributions to hydrodynamic flows, energy dissipation, and friction force are calculated in a wide range of…
In this work we consider the effect of a small-scale helical driving force on fluid with a stable temperature gradient with Reynolds number Re<<1. At first glance, this system does not appear to have any instability. However, we show that…
From a scale analysis of hydrodynamic phenomena having a significant action on the drift of an object in coastal ocean waters, we deduce equations modeling the associated hydrodynamic fields over a time period of several weeks. These models…
The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model.…
We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model, consisting of…
A central challenge in hydrodynamic turbulence is identifying precisely when, and at which length scales, strong turbulent fluctuations (STFs) emerge and develop into intermittent events, which are often obscured by conventional statistical…
We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited…
Turbulent flows above a solid surface are characterised by a hydrodynamic roughness that represents, for the far velocity field, the typical length scale at which momentum mixing occurs close to the surface. Here, we are theoretically…
Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the…
Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that…
We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minimal horocyclic orbit closures and of infinite locally-finite…
The dropwise condensation underneath a horizontal super-hydrophobic surface having unidirectional wettability gradient is modeled with implication to enhance the rate of condensation. The mathematical model includes nucleation, growth by…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds…
Flexible structures in an incoming perpendicular flow typically undergo elastic reconfiguration that reduces drag; however, at higher velocities, they are prone to dynamical instabilities that entail complex wake dynamics and fluctuating…
Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…
It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytical vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this…