Related papers: Nonlinear modeling of wave-topography interactions…
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the…
We perform a detailed theoretical study of the edge fracture instability, which commonly destabilises the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
Turbulence is a complex system exhibiting both universal statistical features and prominent coherent structures. We model turbulence using coherent vortices distributed within a multi-scale statistical framework, termed `woven turbulence'.…
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the…
We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and…
This paper continues the systematic investigation of diffusive shear instabilities initiated in Part I of this series. In this work, we primarily focus on quantifying the impact of non-local mixing, which is not taken into account in Zahn's…
Discontinuous Shear Thickening (DST) fluids exhibit unique instability properties in a wide range of flow conditions. We present numerical simulations of a scalar model for DST fluids in a planar simple shear using the Smoothed Particle…
We consider the scattering of in-plane waves that interact with an edge of a structured {penetrable (inertial)} line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods.…
Laminar-to-turbulence transition in zero-pressure-gradient boundary layer at Mach 4.5 is studied using direct numerical simulations. For a given level of total disturbance energy, the inflow spectra was designed to correspond to the…
A new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four prominently used bending models. Through an essential set of elementary nonlinear bending test cases, the stresses…
Considering channel flow at Reynolds numbers below the linear stability threshold of the laminar profile as a generic example system showing a subcritical transition to turbulence connected with the existence of simple invariant solutions,…
Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a…
I shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertia-less flows with curved streamlines. Then I describe a theory of elastic turbulence and prediction of elastic waves at…
Shear-induced droplet formation is important in many industrial applications, primarily focusing on droplet sizes and pinch-off frequency. We propose a one-dimensional mathematical model that describes the effect of shear forces on the…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…