Related papers: Observable Divergence Theorem: Evolution Equations…
The Navier-Stokes equation describes the deterministic evolution of incompressible fluids. The effects of random initial conditions on solutions of this equation are studied. It is shown that there is an infrared stable fixed point…
The new proposed "energy gradient theory," which physically explains the phenomena of flow instability and turbulent transition in shear flows and has been shown to be valid for parallel flows, is extended to curved flows in this study.…
We study steady vortex sheet solutions of the Navier-Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a…
In this study, we propose a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on the extended Navier-Stokes (N-S) equations. With some phenomenological observations and H. J. Kreuer's…
We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…
Dissipation anomaly, a phenomenon predicted by Kolmogorov's theory of turbulence, is the persistence of a non-vanishing energy dissipation for solutions of the Navier-Stokes equations as the viscosity goes to zero. Anomalous dissipation,…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
The turbulence field is stacked on the laminar flow. In this research, the laminar flow is described as a macro deformation which forms an instant curvature space. On such a curvature space, the turbulence is viewed as a micro deformation.…
Elastic turbulence can lead to to increased flow resistance, mixing and heat transfer. Its control -- either suppression or promotion -- has significant potential, and there is a concerted ongoing effort by the community to improve our…
Through the Ginzburg-Landau and the Navier-Stokes equations, we study turbulence phenomena for viscous incompressible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of…
A derivation of the "exact" two-point equations analogous to those used as a basis for one-point Reynolds-Averaged Navier-Stokes turbulence model for variable density, incompressible turbulence. The purpose is to present the statistical…
The circulation around any closed loop is a Lagrangian invariant for classical, smooth solutions of the incompressible Euler equations in any number of space dimensions. However, singular solutions relevant to turbulent flows need not…
The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple,…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…
In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
A theory for the evolution of a metric $g$ driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an evolving three-dimensional Riemannian manifold immersed in…
A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then…
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…
The Navier-Stokes equations in the primitive formulation for incompressible flow describe the evolution of velocity and pressure, without recourse to vorticity. We show that, beyond the finite Leray-Hopf regularity interval, every…