Related papers: Free-Surface Hydrodynamics in the conformal variab…
It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between…
In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
Simple, self-similar, elliptic solutions of non-relativistic fireball hydrodynamics are presented, generalizing earlier results for spherically symmetric fireballs with Hubble flows and homogeneous temperature profiles. The transition from…
We study the problem of the motion of the free surface of a liquid. We prove existence and stability for the linearized equations.
We report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, we perform spatiotemporal…
The $p$-Laplacian evolution equation and the $\alpha$-Gauss curvature flow with a flat side are degenerate parabolic equations with evolving free boundaries. We give proofs of smooth short-time existence, up to the free boundaries, using a…
A statistical theory of two-dimensional Laplacian growths is formulated from first-principles. First the area enclosed by the growing surface is mapped conformally to the interior of the unit circle, generating a set of dynamically evolving…
Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations…
Hydrodynamic discontinuities in an external potential and incompressible flow are investigated. Using the reaction front as an example in a 2D stream, an overdetermined system of equations is obtained that describes its motion in terms of…
We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the…
We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time…
We consider the well-posedness and numerical approximation of a Hamilton--Jacobi equation on an evolving hypersurface in $\mathbb R^3$. Definitions of viscosity sub- and supersolutions are extended in a natural way to evolving hypersurfaces…
We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for…
We introduce a description of a minimal surface in a space with boundary, as the world-hypersurface that the entangling surface traces. It does so by evolving from the boundary to the interior of the bulk under an appropriate geometric…
Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation…
For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including…
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…
In many applications free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight…
This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy…