共查询到20条相似文献,搜索用时 10 毫秒
1.
Abdel Raouf F. Elhefnawy 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1995,46(2):239-254
The nonlinear evolution of interfacial waves separating two magnetic fluids subjected to an oblique magnetic field is studied in two dimensions, with the use of the method of multiple scales. It is shown that the evolution of the envelope is governed by two partial differential equations. These equations can be combined to yield two alternate Schrödinger equations with cubic nonlinearity; one of them leads to the determination of the cutoff wave number separating stable from unstable deformations while the other Schrödinger equation is used to analyze the stability of the system. The stability of the system is discussed both theoretically and computationally, and the stability diagrams are obtained. It is found in the linear theory that the oblique magnetic field has a stabilizing influence if 0 1 + 2 < /2, or 3/2 < 1 + 2 2 and a destabilizing influence if /2 < 1 + 2 < 3/2, where 0 j
, (j=1, 2) and , is the angle between the field and the horizontal axis.In the nonlinear theory, the stability analysis reveals that there exist different regions of stability and instability. It is reported that the oblique magnetic field plays a dual role in the stability criterion and the angles 1 and 2 play a distinctive role in this analysis besides the effect of the variation of the magnetic permeabilities. 相似文献
2.
B M Sharma 《Proceedings Mathematical Sciences》1979,88(1):55-68
The character of the equilibrium of a non-viscous, compressible finitely conducting rotating fluid in the presence of a vertical
magnetic field along the direction of gravitational field has been investigated. It is shown that the solution is characterised
by a variational principle. Based on the existence of variational principle, an approximate solution has been derived for
the case of a fluid having exponentially varying density in the vertical direction. Due to finite resistivity of the medium
it is found that potentially stable or unstable configuration retains its character. Further the growth rate of disturbance
has been obtained corresponding to short and long wavelengths and it is found that electrical resistivity suppresses the growth
rate for large wavelengths but it increases the same for small wavelengths. It is further shown that magnetic field has a
destabilizing influence for large wavelengths and a stabilizing influence for small wavelengths. 相似文献
3.
A study of the Rayleigh instability of a compressible plasma, density stratified in horizontal planes and subjected to a horizontal magnetic field, is made. It is found that in the presence of the compressibility effects the magnetic field continues to affect the development of the Rayleigh instability even for disturbances that propagate across the magnetic field (taken perpendicular to gravity), contrary to the result for the case of an incompressible plasma. The special case of a plane interface separating two superposed uniform plasmas of different densities is treated as an example to illustrate the compressibility effects on the hydromagnetic Rayleigh instability. It is found that the compressibility effects have a stabilising nature.
Zusammenfassung Es wird die Rayleigh-Instabilität eines kompressiblen Plasmas untersucht, mit Dichte-Schichtung in horizontalen Ebenen, in Gegenwart eines horizontalen Magnetfeldes. Es wird gezeigt, daß bei Kompressibilität das Magnetfeld auch die Instabilitätsentwicklung derjenigen Störungen beeinflußt, die sich quer zum Magnetfeld (welches senkrecht zur Gravitationsrichtung angenommen wurde) fortpflanzen; dies ist im kompressiblen Plasma nicht der Fall. Der Spezialfall einer ebenen Trennfläche zwischen zwei Plasmas mit verschiedenen gleichförmigen Dichten wird behandelt, um den Kompressibilitätseffekt auf die hydromagnetische Rayleigh-Instabilität zu zeigen; dieser erweist sich als stabilisierend.相似文献
4.
5.
6.
The linear and nonlinear evolution of perturbations is investigated in a magnetohydrodynamic channel flow with electrically insulating walls. The applied magnetic field is parallel to the walls and orthogonal to the stream. Linear optimal perturbations and their maximum amplifications over finite time intervals are computed using a scheme based on the direct and adjoint governing equations. It is shown that dominant optimal perturbations are no more the classical streamwise modes and how the flow is two-dimenzionalized for high enough Hartmann numbers. For fixed Reynolds and Hartmann numbers, direct numerical simulations are applied to investigate how the transition to turbulence is affected by the magnetic field. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
8.
Abdel Raouf F. Elhefnawy 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1993,44(3):495-509
A weakly nonlinear evolution of two dimensional wave packets on the surface of a magnetic fluid in the presence of an uniform magnetic field is presented, taking into account the surface tension. The method used is that of multiple scales to derive two partial differential equations. These differential equations can be combined to yield two alternate nonlinear Schrödinger equations. The first equation is valid near the cutoff wavenumber while the second equation is used to show that stability of uniform wave trains depends on the wavenumber, the density, the surface tension and the magnetic field. At the critical point, a generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. From the latter equation, the various stability crteria are obtained. 相似文献
9.
Material– and flow properties of magnetic fluids can be influenced by applying an external magnetic field. In this work we will particularly consider the onset of convection in magnetic fluids which is influenced by a magnetic force. In a horizontal magnetic fluid layer the force arises if a temperature gradient and an external magnetic field is applied. The behaviour of the onset of convection is investigated for a static and a time–modulated magnetic field. For the case of a static magnetic field the onset of convection depends on the strength of the field and for a time–modulated magnetic field an additional dependence on the frequency of magnetic field variation is found. The experimental results presented here confirm in principle the theoretical predictions about the influence of static and time–modulated magnetic forces on the onset of convection. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
We study a triple singular limit for the scaled barotropic Navier–Stokes system modeling the motion of a rotating, compressible, and viscous fluid, where the Mach and Rossby numbers are proportional to a small parameter \(\varepsilon \) , while the Reynolds number becomes infinite for \(\varepsilon \rightarrow 0\) . If the fluid is confined to an infinite slab bounded above and below by two parallel planes, the limit behavior is identified as a purely horizontal motion of an incompressible inviscid fluid, the evolution of which is described by an analogue of the Euler system. 相似文献
11.
The problem of the equilibrium of a liquid enclosed in a vessel heated from below has been considered by Sorokin [1], Iudovich and Ukhovskii [2] and Velt [3]. It has been established that if the Rayleigh number λ exceeds a certain critical value λ0, then secondary steady flows arise in the liquid.
The stability of a conductive liquid heated from below has been studied by many authors. The most complete and general studies are those of Sorokin and Sushkin [4], whose paper contains the appropriate bibliography, and that of Shliomis [5]. The results of [4 and 5] make clear the physical picture of the phenomena associated with the heating of a conductive fluid and indicate the possible existence of secondary steady and periodic flows.
The existence of steady convective flows in a conductive liquid are proved below. Our study is based on the procedure set forth in [2]. 相似文献
12.
Harry Yserentant 《Numerische Mathematik》1997,76(1):111-142
Summary. Fluid mechanics describes the motion of mass in space under the influence of internal and external forces. The particle model
presented in this article is based on this fact. The fluid is subdivided into a finite number of small mass packets, the particles.
These mass packets have a finite extension and share all properties with the fluid, except for the restriction that they cannot
get deformed and can perform only rigid body motions. The forces acting upon the particles are identical to those acting on
a part of a fluid. The exact conservation of mass and, for the case of adiabatic flows, also of entropy is automatically guaranteed
by the approach. When the particle size tends to zero, the mean local displacement of the particles converges in the weak
sense. In the inviscid case, the resulting flows can be regarded as solutions of the Euler equations.
Received February 17, 1995 / Revised version received December 28, 1995 相似文献
13.
We present a method for solving the optimal shape problems for profiles surrounded by viscous compressible fluids in two space dimensions. The class of admissible profiles is quite general including the minimal volume condition and a constraint on the thickness of the boundary. The fluid flow is modelled by the Navier-Stokes system for a general viscous barotropic fluid with the pressure satisfying p(o) = aQlog^d(o) for large Q. Here d 〉 1 and a 〉 0. 相似文献
14.
We consider a model of flow of two compressible and immiscible phases in a three-dimensional porous media. The equations are obtained by the conservation of the mass of each phase. This model is treated in its general form with the whole nonlinear terms. The only assumption concerns the dependence of densities on a global pressure. We obtain the existence of weak solutions under different kinds of degeneracies of the capillary terms. 相似文献
15.
Summary The authors consider the case of two compressible, non-viscous fluids, one above the other, and investigate the stability
of their equilibrium under the action of gravity. It is found that the equilibrium is stable if and only if the density of
the upper fluid in the immediate vicinity of the interface is less than that of the lower.
To Mauro Picone on his 70th birthday.
Work was cosponsored by the Office of Naval Research and the U. S. Army under Contract No. N-7-ONR-38801 and Contract No.
DA-36-034-ORD-1646, respectively.
On leave from the Weizmann Institute of Science, Rehovoth, Israel. 相似文献
16.
Paolo Secchi 《Annali dell'Universita di Ferrara》2000,46(1):21-33
We consider the Euler equations of barotropic inviscid compressible fluids in a bounded domain. It is well known that, as
the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible
fluids. Here we discuss, for the boundary case, the different kinds of convergence under various assumptions on the data,
in particular the weak convergence in the case of uniformly bounded initial data and the strong convergence in the norm of
the data space.
Sunto Nel presente lavoro consideriamo le equazioni di Eulero per un fluido inviscido comprimibile barotropico in un dominio limitato. è ben noto che, quando il numero di Mach tende a zero, i moti comprimibili approssimano le soluzioni delle equazioni del moto relative ad un fluido inviscido incomprimibile. Qui discutiamo, per il problema al contorno, i diversi tipi di convergenza sotto differenti ipotesi sui dati, in particolare la convergenza debole nel caso di dati iniziali uniformemente limitati e la convergenza forte nella norma dello spazio dei dati.相似文献
17.
J. R. Gupta S. K. Sood U. D. Bhardwaj 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1984,35(2):252-256
A sufficient condition for the validity of the principle of exchange of stabilities in the Rayleigh-Bénard convection problem under the simultaneous action of a uniform vertical rotation and magnetic field is derived. Furthermore the complex growth rate of an arbitrary oscillatory perturbation, neutral or unstable, is shown to lie inside a semicircle in the right half of the complexp-plane. These results are uniformly valid for all combinations of free insulating, rigid perfectly conducting and rigid insulating boundaries.
Zusammenfassung Für die Gültigkeit des Prinzipes der Vertauschung der Stabilitäten im Rayleigh-Bénard-Konvektionsproblem mit simultanen Wirkungen einer gleichförmigen vertikalen Rotation und eines Magnetfeldes wird eine hinreichende Bedingung hergeleitet. Weiterhin wird gezeigt, daß die komplexe Anfachungsrate für eine beliebige oszillatorische Störung innerhalb eines Halbkreises in der rechten Hälfte der komplexenp-Ebene liegt. Diese Resultate sind gleichermaßen gültig für alle Kombinationen von freien isolierten, starren vollkommen leitenden und starren isolierten Begrenzungen.相似文献
18.
Nurlan S. Dairbekov Gabriel P. Paternain Gunther Uhlmann 《Advances in Mathematics》2007,216(2):535-609
For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Mañé action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of α.For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on α. We also show injectivity and stability for g and α in a generic class G including real analytic ones.For the nonlinear problem, we show rigidity for real analytic simple (g,α), rigidity for metrics in a given conformal class, and locally, near any (g,α)∈G. We also show that simple magnetic systems on two-dimensional manifolds are always rigid. 相似文献
19.
Somaraju Vempaty Prakki Satyamurty 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(5):800-825
Following Hollerbachs work (Geophys. Astrophys.Fluid Dynam., 1996) we investigate the hydromagnetic flow in a region x 0, – < y < , 0 < z < 1 bounded by three electrically insulating rigid walls. The rotation vector is in the z-direction while the applied uniform magnetic field B0 is in the x-direction. Antisymmetric and symmetric cases are considered and analytical solutions are obtained for all the field variables for both the transition field regime (E1/2 E1/3) and strong magnetic field regime ( E1/3) where (= B2/) is Elsasser number. Emphasis is put on the physical aspects of the problem and the meridional cir-culation pattern of electric currents. Unlike the case where a separate magnetic boundary layer exists to close the meridional electric current flux when the rotation vector and applied magnetic field are aligned, it is found that no such layer exists in the present problem; the electric currents generated in the interior and in the boundary layer regions have to be closed through interior region only. The transition field regime is characterized by the Stewartsons double layer structure with the noted exception that the outer Stewartson layer O(E/)1/2 is weak. In addition, sub-boundary layers with an axial scale equal to the corresponding boundary layer scale develop at z=0,1 for each layer. In the large magnetic field regime, while the layer which replaces the inner Stewartson layer O(E1/3) satisfies the boundary condition on u-field, the thin (E/)1/2 layer is necessary to satisfy the boundary condition on v and w fields. 相似文献