Related papers: Geometric Lagrangian averaged Euler-Boussinesq and…
In this paper, we introduce and study the primitive equations with $\textit{non}$-isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and…
Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations,…
This work presents an approach to the Navier-Stokes equations that is phrased in unbiased Eulerian coordinates, yet describes objects that have Lagrangian significance: particle paths, their dispersion and diffusion. The commutator between…
Over the last seventy years, many Finsler-type geometric and modified gravity theories have been elaborated. They have been formulated in terms of different classes of Finsler generating functions, metric and nonmetric structures, nonlinear…
Within the framework of Lagrangian variables, we develop a method for deriving explicit solutions to the 2D Boussinesq equations using harmonic mapping theory. By reformulating the characterization of flow solutions described by harmonic…
The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of…
We demonstrate that a sufficiently smooth solution of the relativistic Euler equations that represents a dynamical compact liquid body, when expressed in Lagrangian coordinates, determines a solution to a system of non-linear wave equations…
In this paper, we improve the global existence result in [9] slightly. More precisely, the global existence of strong solutions to the primitive equations with only horizontal viscosity and diffusivity is obtained under the assumption of…
We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…
In this paper, discrete analogues of Euler-Poincar\'{e} and Lie-Poisson reduction theory are developed for systems on finite dimensional Lie groups $G$ with Lagrangians $L:TG \to {\mathbb R}$ that are $G$-invariant. These discrete equations…
The purpose of this paper is twofold. First, we use a classical method to establish Gaussian bounds of the fundamental matrix of a generalized parabolic Lam\'{e} system with only bounded and measurable coefficients. Second, we derive a…
A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well-known, involving complex…
The following principle of minimum energy may be a powerful substitute to the dynamical perturbation method, when the latter is hard to apply. Fluid elements of self-gravitating barotropic flows, whose vortex lines extend to the boundary of…
The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…
We consider two-fluid flow problems in an Arbitrary Lagrangian Eulerian (ALE) framework. The purpose of this work is twofold. First, we address the problem of the moving contact line, namely the line common to the two fluids and the wall.…
The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are…
On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and atmospheric dynamics) in both two and three dimensions. We…
Statistical mechanics provides an elegant explanation to the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamented…
The Boussinesq equations are fundamental in meteorology. Among other aspects, they aim to model the process of front formation. We use the approach presented in [Hol15] to introduce stochasticity into the incompressible Boussinesq…