Related papers: Eulerian Derivation of the Coriolis Force
In this paper we show how the non-relativistic transport equations for a simple fluid can be obtained using a 3+1 representation. A pseudo-galilean transformation is introduced in order to obtain the Euler conservation laws. The…
The governing equations of Brownian rigid bodies that both translate and rotate are of interest in fields such as self-assembly of proteins, anisotropic colloids, dielectric theory, and liquid crystals. In this paper, the partial…
We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
Micropolar fluid theory, an extension of classical Newtonian fluid dynamics, incorporates angular velocities and rotational inertias and has long been a foundational framework for describing granular flows. We propose a macroscopic model of…
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well…
We propose a new Eulerian turbulence theory to obtain a closed set of equations for homogeneous, isotropic turbulent velocity field correlations and propagator functions by incorporating constraints of random Galilean invariance. This…
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into…
This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complex-steerable pyramid.…
In this paper, we present several geometric ways to incorporate gyroscopic and dissipative forces to curl forces. We first present a proper metriplectic geometry. Then, using the Herglotz principle and generalized Euler-Lagrange equation,…
The purpose of this paper is two-fold. First, to provide a straightforward proof of the Cauchy's invariants (CIs) from the particle relabeling symmetry of the action functional for rotational barotropic flows, using pure geometric…
In this paper, we present a Newton-Euler formulation of the equations of motion for underwater vehicles with an interntal moving mass actuator. Furthermore, the moving mass dynamics are expressed as an extension to the manoeuvring model for…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
These lectures notes give an introduction to the fast developing area of research dealing with perturbative descriptions of the gravitational instability in an expanding universe. I just sketch the outlines of some proofs, and many…
High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a…