Related papers: Helical shell models for three dimensional turbule…
Three-dimensional (3D) turbulence has both energy and helicity as inviscid constants of motion. In contrast to two-dimensional (2D) turbulence, where a second inviscid invariant--the enstrophy--blocks the energy cascade to small scales, in…
From the definition of a generalized conformable spatial derivative, an exponential conformable function with three parameters $(a,b,\alpha)$ is proposed for a viscous and an inertial-viscous steady-state Navier-Stokes 1D models, obtaining…
The Exergetic Port-Hamiltonian Systems modeling language combines a graphical syntax inspired by bond graphs with a port-Hamiltonian semantics akin to the GENERIC formalism. The syntax enables the modular and hierarchical specification of…
We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by…
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the…
The equations for strands of rigid charge configurations interacting nonlocally are formulated on the special Euclidean group, SE(3), which naturally generates helical conformations. Helical stationary shapes are found by minimizing the…
Subcritical transition to turbulence, in which the laminar state is linearly stable yet finite-amplitude perturbations develop into turbulence, is ubiquitous but lacks a simple analytical framework. We demonstrate such a framework using a…
The basic entity of nonlinear interaction in Navier-Stokes and the Magnetohydrodynamic (MHD) equations is a wavenumber triad ({\bf k,p,q}) satisfying ${\bf k+p+q=0}$. The expression for the combined energy transfer from two of these…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the…
Disordered hyperuniform structures are locally random while uniform like crystals at large length scales. Recently, an exotic hyperuniform fluid state was found in several non-equilibrium systems, while the underlying physics remains…
Applications of the shell model of turbulence to the case of rapidly rotating bodies are considered. Starting from the classical GOY model we introduce the Coriolis force and obtain a $\sim k^{-2}$ spectrum for 3D hydrodynamical turbulence…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like…
The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic…
Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for…
Using direct numerical simulation of hydrodynamic turbulence with helicity forcing applied at all scales, a near-maximum helical turbulent state is obtained, with an inverse energy cascade at scales larger than the energy forcing scale and…
A recent theoretical development in the understanding of the small-scale structure of Navier-Stokes turbulence has been the proposition that the scales $\eta_n(R)$ that separate inertial from viscous behavior of many-point correlation…
In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…