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We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow,…
We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
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 prove non-existence of nontrivial uniformly subsonic inviscid irrotational flows around several classes of solid bodies with two protruding corners, in particular vertical and angled flat plates; horizontal plates are the only case where…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
We define a parabolic flow of pluriclosed metrics. This flow is of the same family introduced by the authors in \cite{ST}. We study the relationship of the existence of the flow and associated static metrics topological information on the…
Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
We investigate the topological structure of flows on the Girl's surfaces which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of the selfintersection. First, we describe the…
We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent…
Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
Consider the set $\chi^0_{\mathrm{nw}}$ of non-wandering continuous flows on a closed surface. Then such a flow can be approximated by regular non-wandering flows without heteroclinic connections nor locally dense orbits in…
Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2D) and three-dimensional (3D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an…
The addition of a small amount of long-chain polymers confers viscoelastic properties to Newtonian flows. The resulting non-Newtonian solution now exhibits different dynamics, such as enhanced mixing at low Reynolds, where elastic…
The relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure…
Three-dimensional anisotropic turbulence in classical fluids tends towards isotropy and homogeneity with decreasing scales, allowing --eventually-- the abstract model of "isotropic homogeneous turbulence" to be relevant. We show here that…
For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…