Related papers: On the shock change equations
The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular we establish rigorous bounds between solutions of the Whitham and KdV equations and provide…
Supersonic vortex plane and axisymmetric flows of non-viscous non-heatconductive gas with arbitrary thermodynamic properties in the vicinity of a steady shock wave are studied. The differential equations describing the gas flow exterior to…
We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes, and naturally live on a…
We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct…
We describe the physical hypotheses underlying the derivation of an approximate model of water waves. For unidirectional surface shallow water waves moving over an irrotational flow as well as over a non-zero vorticity flow, we derive the…
We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of…
Starting from coupled fluid-kinetic equations for the modeling of laden flows, we derive relevant viscous corrections to be added to asymptotic hydrodynamic systems, by means of Chapman-Enskog expansions and analyse the shock profile…
Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
Diffusive acceleration at collisionless shock waves remains one of the most promising acceleration mechanisms for the description of the origin of cosmic rays at all energies. A crucial ingredient to be taken into account is the reaction of…
A generalized physics-based expression for the drag coefficient of spherical particles moving in a fluid is derived. The proposed correlation incorporates essential rarefied physics, low-speed hydrodynamics, and shock-wave physics to…
We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel flows with steady mean. Analytical…
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispersive} solution when singularities give rise to a graph of…
We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids and the hydrodynamic equations are reduced to a set of ordinary differential equations for the…
A global equilibrium state of a spin polarized fluid that undergoes constant acceleration along the stream lines is described as a solution of recently introduced perfect-fluid hydrodynamic equations with spin 1/2.
We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory…
The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution…
We address the shocks from acoustic pulses and wave trains in general one-dimensional flows, with an emphasis on the application to super-Eddington outbursts in massive stars. Using approximate adiabatic invariants, we generalize the…
Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the…
These notes are intended as an elementary introduction to the concept of absolute instability. The transition from convective instability to absolute instability is an important issue when the stability of stationary flow solutions is…