Related papers: Exact coherent states underlying chaotic falling-f…
Several new families of nonlinear three-dimensional travelling wave solutions to the Navier-Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures…
The flow of thin liquid films on inclined or vertical surfaces is one of immense importance, with applications spanning many types of process industries, due to the increased mass and heat transfer brought about by the presence of waves on…
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has…
We consider the full 3D dynamics of a thin falling liquid film on a flat plate inclined at some non-zero angle to the horizontal. In addition to gravitational effects, the flow is driven by an electric field, which is normal to the…
We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…
This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the…
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…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…
Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low- and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are…
We investigate nonlinear periodic and solitary two-dimensional rolling waves in a falling two-layer liquid film in the regime of non-zero Reynolds numbers. At any flow rate, a falling two-layer liquid film is known to be linearly unstable…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
We analyze from a far field the evolution of an interface that separates ideal incompressible fluids of different densities and has an interfacial mass flux. We develop and apply the general matrix method to rigorously solve the boundary…
The simulation of turbulent flow requires many degrees of freedom to resolve all the relevant times and length scales. However, due to the dissipative nature of the Navier-Stokes equations, the long-term dynamics are expected to lie on a…
Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…
Exact unstable solutions of the Navier-Stokes equations are thought to underpin the dynamics of turbulence, but are usually computed in minimal computational domains. Here, we extend this dynamical systems approach to spatially extended…
Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence.…
Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role…
We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic…