scholarly journals ON THE PHYSICAL PROPERTIES OF SPHERICALLY SYMMETRIC SELF-SIMILAR SOLUTIONS

2005 ◽  
Vol 14 (01) ◽  
pp. 73-84 ◽  
Author(s):  
M. SHARIF ◽  
SEHAR AZIZ
Keyword(s):  
Physical Properties ◽  
Radial Direction ◽  
The Self ◽  
Spherically Symmetric ◽  
Self Similar ◽  
Similar Solutions ◽  
Kinematic Properties

In this paper, we are exploring some of the properties of the self-similar solutions of the first kind. In particular, we shall discuss the kinematic properties and also check the singularities of these solutions. We discuss these properties both in co-moving and also in non-co-moving (only in the radial direction) coordinates. Some interesting features of these solutions turn up.

scholarly journals ON PHYSICAL PROPERTIES OF CYLINDRICALLY SYMMETRIC SELF-SIMILAR SOLUTIONS

2005 ◽  
Vol 20 (32) ◽  
pp. 7579-7591 ◽  
Author(s):  
M. SHARIF ◽  
SEHAR AZIZ
Keyword(s):  
Physical Properties ◽  
Radial Direction ◽  
The Self ◽  
Expansion Rate ◽  
Cylindrically Symmetric ◽  
Self Similar ◽  
Similar Solutions

This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration, rotation, expansion, shear, shear invariant and expansion rate. These kinematical quantities are discussed both in comoving as well as in noncomoving coordinates (only in radial direction). Finally, we would discuss the singularity feature of these solutions. It is expected that these properties would help in exploring some interesting features of the self-similar solutions.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

Natural convection flow far from a horizontal plate

1999 ◽  
Vol 387 ◽  
pp. 227-254 ◽  
Author(s):  
VALOD NOSHADI ◽  
WILHELM SCHNEIDER
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
The Self ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Self Similar ◽  
Similar Solutions

Plane and axisymmetric (radial), horizontal laminar jet flows, produced by natural convection on a horizontal finite plate acting as a heat dipole, are considered at large distances from the plate. It is shown that physically acceptable self-similar solutions of the boundary-layer equations, which include buoyancy effects, exist in certain Prandtl-number regimes, i.e. 0.5<Pr[les ]1.470588 for plane, and Pr>1 for axisymmetric flow. In the plane flow case, the eigenvalues of the self-similar solutions are independent of the Prandtl number and can be determined from a momentum balance, whereas in the axisymmetric case the eigenvalues depend on the Prandtl number and are to be determined as part of the solution of the eigenvalue problem. For Prandtl numbers equal to, or smaller than, the lower limiting values of 0.5 and 1 for plane and axisymmetric flow, respectively, the far flow field is a non-buoyant jet, for which self-similar solutions of the boundary-layer equations are also provided. Furthermore it is shown that self-similar solutions of the full Navier–Stokes equations for axisymmetric flow, with the velocity varying as 1/r, exist for arbitrary values of the Prandtl number.Comparisons with finite-element solutions of the full Navier–Stokes equations show that the self-similar boundary-layer solutions are asymptotically approached as the plate Grashof number tends to infinity, whereas the self-similar solution to the full Navier–Stokes equations is applicable, for a given value of the Prandtl number, only to one particular, finite value of the Grashof number.In the Appendices second-order boundary-layer solutions are given, and uniformly valid composite expansions are constructed; asymptotic expansions for large values of the lateral coordinate are performed to study the decay of the self-similar boundary-layer flows; and the stability of the jets is investigated using transient numerical solutions of the Navier–Stokes equations.

scholarly journals Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

2001 ◽  
Vol 7 (3) ◽  
pp. 253-282 ◽  
Author(s):  
Ch. Srinivasa Rao ◽  
P. L. Sachdev ◽  
Mythily Ramaswamy
Keyword(s):  
Initial Conditions ◽  
Nonlinear Damping ◽  
Nonlinear Ordinary Differential Equation ◽  
The Self ◽  
Similar Reduction ◽  
Generalized Burgers Equation ◽  
Different Types ◽  
Self Similar ◽  
Parameter Ranges ◽  
Similar Solutions

The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.

scholarly journals Theoretical interpretation of fetch limited wind-drivensea observations

2005 ◽  
Vol 12 (6) ◽  
pp. 1011-1020 ◽  
Author(s):  
V. E. Zakharov
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Field Studies ◽  
The Self ◽  
Theoretical Interpretation ◽  
Simple Analytical Model ◽  
Surface Gravity Waves ◽  
Interaction Terms ◽  
Self Similar ◽  
Similar Solutions

Abstract. We show that the results of major fetch limited field studies of wind-generated surface gravity waves on deep water can be explained in the framework of simple analytical model. The spectra measured in these experiments are described by self-similar solutions of ``conservative" Hasselmann equation that includes only advective and nonlinear interaction terms. Interaction with the wind and dissipation due to the wave breaking indirectly defines parameters of the self-similar solutions.

scholarly journals ACCRETION AND PLASMA OUTFLOW FROM DISSIPATIONLESS DISCS

2010 ◽  
Vol 19 (03) ◽  
pp. 339-365 ◽  
Author(s):  
S. V. BOGOVALOV ◽  
S. R. KELNER
Keyword(s):  
Angular Momentum ◽  
Similar Case ◽  
Gravitational Energy ◽  
Accretion Disc ◽  
The Self ◽  
Low Viscosity ◽  
Variable Polarity ◽  
Self Similar ◽  
Similar Solutions ◽  
High Electric Conductivity

We consider the specific case of disc accretion for negligibly low viscosity and infinitely high electric conductivity. The key component in this model is the outflowing magnetized wind from the accretion disc, since this wind effectively carries away angular momentum of the accreting matter. Assuming magnetic field has variable polarity in the disc (to avoid magnetic flux and energy accumulation at the gravitational center), this leads to radiatively inefficient accretion of the disc matter onto the gravitational center. In such a case, the wind forms an outflow, which carries away all the energy and angular momentum of the accreted matter. Interestingly, in this framework, the basic properties of the outflow (as well as angular momentum and energy flux per particle in the outflow) do not depend on the structure of accretion disc. The self-similar solutions obtained prove the existence of such an accreting regime. In the self-similar case, the disc accretion rate (Ṁ) depends on the distance to the gravitational center, r, as [Formula: see text], where λ is the dimensionless Alfvenic radius. Thus, the outflow predominantly occurs from the very central part of the disc provided that λ ≫ 1 (it follows from the conservation of matter). The accretion/outflow mechanism provides transformation of the gravitational energy from the accreted matter into the energy of the outflowing wind with efficiency close to 100%. The flow velocity can essentially exceed the Kepler velocity at the site of the wind launch.

The importance of Hall effect on the magnetized thin accretion disc

2019 ◽  
Vol 492 (2) ◽  
pp. 1770-1777
Author(s):  
Maryam Ghasemnezhad
Keyword(s):  
Hall Effect ◽  
Equatorial Plane ◽  
Radial Direction ◽  
Vertical Structure ◽  
Accretion Rate ◽  
Accretion Disc ◽  
Mhd Equations ◽  
Self Similar ◽  
Similar Solutions

ABSTRACT To study the role of Hall effect on the structure of accretion disc, we have considered a toroidal magnetic field in our paper. To study the vertical structure of the disc, we have written a set of magnetohydrodynamic (MHD) equations in the spherical coordinates (r, θ, ϕ) based on the two assumptions of axisymmetric and steady state. Also, we employed the self-similar solutions in the radial direction to obtain the structure of the disc in the θ-direction. We have solved a set of ordinary differential equations in the θ-coordinate with symmetrical boundary conditions in the equatorial plane. In order to describe the behaviour of Hall effect, we introduced the ΛH parameter that was called the dimensionless Hall Elsasser number. The strength of the Hall effect is measured by the inverse of dimensionless Hall Elsasser number. We have shown that the strong Hall effect decreases the accretion rate or infall velocity and size of inflow part. It has also been found the Hall effect is maximum in the equatorial plane and gets the value close to zero near the boundary, and it has the antidiffusive nature. The results display that the strong Hall effect makes the standard accretion sub-Keplerian disc becomes thinner. Our solutions have shown the Hall effect leads to transport magnetic flux outward in the upper layer of the disc and it produces outflows in the surface of the disc.

On the correctness of a model for phase transitions in binary alloys

1990 ◽  
Vol 1 (4) ◽  
pp. 327-338 ◽  
Author(s):  
I. G. Götz
Keyword(s):  
Phase Transitions ◽  
Heat Conduction ◽  
Stability Criterion ◽  
Binary Alloys ◽  
The Self ◽  
Self Similar Solution ◽  
Self Similar ◽  
The Stability ◽  
Similar Solutions ◽  
And Diffusion

The main result of this paper is a non-uniqueness theorem for the self-similar solutions of a model for phase transitions in binary alloys. The reason for this non-uniqueness is the discontinuity in the coefficients of heat conduction and diffusion at the inter-phase. Also the existence of a self-similar solution and the stability criterion are discussed.

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