6,573 research outputs found
The Navier-Stokes-alpha model of fluid turbulence
We review the properties of the nonlinearly dispersive Navier-Stokes-alpha
(NS-alpha) model of incompressible fluid turbulence -- also called the viscous
Camassa-Holm equations and the LANS equations in the literature. We first
re-derive the NS-alpha model by filtering the velocity of the fluid loop in
Kelvin's circulation theorem for the Navier-Stokes equations. Then we show that
this filtering causes the wavenumber spectrum of the translational kinetic
energy for the NS-alpha model to roll off as k^{-3} for k \alpha > 1 in three
dimensions, instead of continuing along the slower Kolmogorov scaling law,
k^{-5/3}, that it follows for k \alpha < 1. This rolloff at higher wavenumbers
shortens the inertial range for the NS-alpha model and thereby makes it more
computable. We also explain how the NS-alpha model is related to large eddy
simulation (LES) turbulence modeling and to the stress tensor for second-grade
fluids. We close by surveying recent results in the literature for the NS-alpha
model and its inviscid limit (the Euler-alpha model).Comment: 22 pages, 1 figure. Dedicated to V. E. Zakharov on the occasion of
his 60th birthday. To appear in Physica
The vortex blob method as a second-grade non-Newtonian fluid
We show that a certain class of vortex blob approximations for ideal
hydrodynamics in two dimensions can be rigorously understood as solutions to
the equations of second-grade non-Newtonian fluids with zero viscosity, and
initial data in the space of Radon measures . The
solutions of this regularized PDE, also known as the averaged Euler or
Euler- equations, are geodesics on the volume preserving diffeomorphism
group with respect to a new weak right invariant metric. We prove global
existence of unique weak solutions (geodesics) for initial vorticity in
such as point-vortex data, and show that the
associated coadjoint orbit is preserved by the flow. Moreover, solutions of
this particular vortex blob method converge to solutions of the Euler equations
with bounded initial vorticity, provided that the initial data is approximated
weakly in measure, and the total variation of the approximation also converges.
In particular, this includes grid-based approximation schemes of the type that
are usually used for vortex methods
Einstein and Beyond: A Critical Perspective on General Relativity
An alternative approach to Einstein's theory of General Relativity (GR) is
reviewed, which is motivated by a range of serious theoretical issues
inflicting the theory, such as the cosmological constant problem, presence of
non-Machian solutions, problems related with the energy-stress tensor
and unphysical solutions.
The new approach emanates from a critical analysis of these problems,
providing a novel insight that the matter fields, together with the ensuing
gravitational field, are already present inherently in the spacetime without
taking recourse to . Supported by numerous evidences, the new insight
revolutionizes our views on the representation of the source of gravitation and
establishes the spacetime itself as the source, which becomes crucial for
understanding the unresolved issues in a unified manner. This leads to a new
paradigm in GR by establishing equation as the field equation of
gravitation plus inertia in the very presence of matter.Comment: An invited review accepted for publication by `Universe' in its
Special Issue "100 Years of Chronogeometrodynamics: the Status of the
Einstein's Theory of Gravitation in Its Centennial Year
Unsteady Flows of a Generalized Fractional Burgers’ Fluid between Two Side Walls Perpendicular to a Plate
The unsteady flows of a generalized fractional Burgers’ fluid between two side walls perpendicular to a plate are studied for the case of Rayleigh-Stokes’ first and second problems. Exact solutions of the velocity fields are derived in terms of the generalized Mittag-Leffler function by using the double Fourier transform and discrete Laplace transform of sequential fractional derivatives. The solution for Rayleigh-Stokes’ first problem is represented as the sum of the Newtonian solutions and the non-Newtonian contributions, based on which the solution for Rayleigh-Stokes’ second problem is constructed by the Duhamel’s principle. The solutions for generalized second-grade fluid, generalized Maxwell fluid, and generalized Oldroyd-B fluid performing the same motions appear as limiting cases of the present solutions. Furthermore, the influences of fractional parameters and material parameters on the unsteady flows are discussed by graphical illustrations
The effect of boundary slip on transient non-Newtonian blood flows under pulsatile pressure
In this work, we investigate the influence of boundary slip for two pulsatile flow problems. The first problem is considered with the transient axially symmetric flows of fluids through vessels taking into account the Fahraeus-Lindqvist effect. The second problem is on general three-dimensional blood flows in the human right coronary artery. Both analytical and numerical results are presented to show the flow phenomena and the influence of the slip parameter on the flow behaviour
The Stokes boundary layer for a thixotropic or antithixotropic fluid
We present a mathematical investigation of the oscillatory boundary layer (‘Stokes layer’) in a semi-infinite fluid bounded by an oscillating wall (the socalled ‘Stokes problem’), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid. For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall
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