Related papers: A Lie Scale Invariance in Fluids with Applications
Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product…
Despite the nonlinear nature of wall turbulence, there is evidence that the energy-injection mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…
The inverse cascade in two-dimensional hydrodynamic turbulence exhibits a mysterious phenomenon. Numerical simulations have shown that the nodal isolines of certain scalars actively transported in the flow (eg, the vorticity in…
We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1].
We develop a new formalism for the study of turbulence using the scale relativity framework (applied in $v$-space according to de Montera's proposal). We first review some of the various ingredients which are at the heart of the scale…
Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a…
Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network…
We study a low-rank iterative solver for the unsteady Navier-Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once…
We study properties of the solutions to Navier-Stokes system on compact Riemannian manifolds. The motivation for such a formulation comes from atmospheric models as well as some thin film flows on curved surfaces. There are different…
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical,…
Through the asymptotic expansion, the large-time behavior of the incompressible Navier-Stokes flow in $n$-dimensional whole space is drawn. In particular, the logarithmic evolution included in the flow velocity is the focus of attention.…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
In this paper, we show that equiangular spirals (also known as logarithmic spirals) appear naturally in fluids going through sinks. We provide a simple mathematical model that explains the spiral forms in some natural formations. For this…
Laminar-turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer and Couette flow. In the latter turbulent spots can grow and form continuous stripes, yet in the…
An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow,…
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the…
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…