Related papers: Principal Decomposition of Velocity Gradient Tenso…
The dynamics of dislocations in a two-dimensional vortex lattice is studied in the presence of a pinning potential and a transport current. In a vortex lattice drifting with velocity $v$ a glide velocity $V_d$ of the dislocation with…
This paper concerns the global nonlinear stability of vortex sheets for the Navier-Stokes equations. When the Mach number is small, we allow both the amplitude and vorticity of the vortex sheets to be large. We introduce an auxiliary flow…
Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the…
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed…
The mechanisms promoting scalar dissipation through scalar gradient production are scrutinized in terms of vorticity alignment with respect to strain principal axes. For that purpose, a stochastic Lagrangian model for the velocity gradient…
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer…
The nematic-superconductor state is an example of a quantum liquid crystal that breaks gauge as well as rotation invariance. It was conjectured to exist in the pseudogap regime of the cuprates high $T_c$ superconductors. The…
The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a…
This paper is concerned with steady vortex rings in an ideal fluid of uniform density, which are special global axi-symmetric solutions of the three-dimensional incompressible Euler equation. We systematically establish the existence,…
A relative Liutex vortex identification method is proposed in this study, together with its explicit mathematical formulation. The method is designed to identify vortical structures based solely on local flow-field information and is…
Tensor analysis provides a frame-invariant foundation for continuum mechanics, yet numerical implementations rely on matrix representations expressed in user-selected bases. When these bases are non-Cartesian and non-orthonormal, additional…
In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
The motion of a two-dimensional buoyant vortex patch, i.e. a vortex patch with a uniform density different from the uniform density of the surrounding fluid, is analyzed in terms of evolution equations for the motion of its centroid,…
In this paper, we examine the recently developed skew-symmetric couple stress theory and demonstrate its inner consistency, natural simplicity and fundamental connection to classical mechanics. This hopefully will help the scientific…
We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e. fluid particles, that initially form a regular tetrahedron. We report results from…
In this paper we aim to construct a very weak solution to the steady two-dimensional Navier-Stokes equations which is affected by an external force induced by a point vortex on the unit disk. Such a solution is also the form of…
A four component decomposition of the local instantaneous velocity is proposed. It brings out more readily the terms in the Navier-Stokes equations associated with different events and fluid structures of turbulent flows than the classic…
In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes…