Ideal Incompressible Fluid Research Articles

Plasmas with a single sign of charge (an overview)

This paper presents a brief overview of recent theory and experiment for plasmas with a single sign of charge. In principle these plasmas can be confined forever in a state of thermal equilibrium that is guaranteed to be stable and quiescent. In practice confinement times of hours are routinely obtained. The plasmas can be cooled to the cryogenic temperature range where liquid and crystal-like states are predicted and observed. The plasmas provide experimental access to the parameter regime of strong magnetization where a many particle adiabatic invariant constrains the collisional dynamics. Also, the plasmas can be used to model the 2D vortex dynamics and turbulence of an ideal (incompressible and inviscid) fluid

Impact of a circular disk and washer on a fluid in a cylindrical vessel

The solution of the problem of the axisymmetric motion of an ideal incompressible fluid in a cylindrical vessel of finite depth is obtained for small vibrations of a flexible circular disk and washer (disk with centered hole) on the surface of the fluid. On the basis of this solution the virtual mass is determined as a function of the dimensions of the vessel, disk and washer for the special case of a rigid nondeformable disk and washer.

Hydraulic jump in the shear flow of an ideal incompressible fluid

Hydraulic jump in the shear flow of an ideal incompressible fluid

The conditions for the non-linear stability of plane and helical mhd flows

The stability of the steady flows of an ideal incompressible fluid of uniform density in a magnetic field is investigated. Only those MHD flows are considered which possess one of the types of symmetry (translational, axial, rotational or helical). The sufficient conditions for non-linear stability of the flows in question with respect to perturbations of this symmetry are obtained. These conditions are proved by the method of coupling the integrals of motion [1, 21 in the form [3–81, based on constructing functionals having absolute minima on specified steady solutions. Each of the functionals constructed is the sum of the kinetic energy, the integral of an arbitrary function of the Lagrangian coordinate and another integral, specific for the flows being investigated. The use of Lagrangian ooordinate fields leads to a whole family of new definitions of stability. According to these definitions, deviations of the perturbed flows from the unperturbed ones are measured by the integrals of the squares of the velocity-field and Lagrangiancoordinate perturbations. The stability conditions obtained are extended to existing results [5–7, 9] on new types of flows. These conditions are of an a priori nature since the corresponding theorems of existence of the solutions are not proved.

On the Instability of Certain Motions of an Ideal Incompressible Fluid

Short-wave instabilities in the general three-dimensional time-dependent flows of an ideal incompressible fluid are considered. A new geometrical optics equation for the perturbed vorticity amplitude is derived. It is shown that under certain conditions this equation can be solved explicitly. Using this observation a number of known instability conditions are obtained and some new ones are derived.

Unseparated uniform rotational flow past a plate in a channel

The plane problem of a uniform rotational stream of ideal incompressible fluid flowing past a plate in channel with parallel walls is solved analytically. It is found that there is a unique position of the plate in which in experiences the same lift from rotational and potential streams. In an unbounded rotational stream this statement is valid when the ordinates of the plate's mid-point and the point at infinity where the characteristic velocity of the incoming stream is specified are equal.

Some notes on the Clebsch representation for incompressible fluids

We show that an arbitrary periodic flow of ideal incompressible fluids can be represented by means of three pairs of periodic Clebsch variables.

The inclined entry of a thin wedge into an incompressible fluid

The self-similar problem of the inclined entry of a thin wedge into a half-space filled with an ideal incompressible fluid is considered in a linear formulation. The different modes of fluid motion whose existence has been previously demonstrated [1]are investigated. A criterion for non-separated flow is obtained in the form of a relation between three angles, defining the angle of the wedge, the direction of the entry velocity and the angle of attack. If this relation is not satisfied, modes of motion are possible in which a cavity is adjacent to one of the faces of the wedge. If the pressure in the cavity is less than the pressure at the surface of the fluid half-space, then only two of these modes exist and both faces are always wetted by the fluid, even in the case when the angle of the wedge is zero. If the pressure in the cavity is equal to the pressure at the surface of the half-space, another mode of motion exists: one of the faces of the wedge is not wetted by the fluid A criterion is obtained for the transition from this mode to the mode with a cavity. The dependence of the size of the cavity and the force acting on the faces of the wedge on the parameters of the problem is investigated numerically.

Kinematic dynamo and intermittence in a turbulent flow

Abstract The large time asymptotics of a magnetic field in a turbulent δ-correlated (in time) flow of an ideal incompressible fluid are studied. It is shown that the magnetic field exhibits the dynamo effect (exponential stretching) unless the Lagrangian flow generated by the velocity field is (almost surely) distance preserving; and it is intermittent unless the Lagrangian flow associated to the turbulent component of the velocity is (almost surely) distance preserving.

The spectrum of the second variation of the energy for an ideal incompressible fluid

The Arnold theory of hydrodynamic stability suggests the study of the second variation of the energy on the submanifold of isovorticial vector fields. We show that, in three or more dimensions, the spectrum of the associated Hermitian operator generally ranges from -∞ to ∞. The sole exceptional case is where the velocity field is harmonic (solenoidal and irrotational) in which case the Hessian is identically zero.

On the curvature of the diffeomorphisms group

An expression for the sectional curvature ofSDIFF(M) (the group of diffeomorphism preserving Riemannian density on a closed manifoldM) is obtained. In the case of a locally Euclidean manifoldM, the negativeness of curvature that implies the instability of solutions of Euler equations of ideal incompressible fluids onM is established.

Construction of the velocity potential of a fluid in an infinite cylindrical container, containing a vibrating rigid spherical body

In this paper we solve, on the basis of the approach presented in [7], the problem of the construction of the velocity potential of a fluid for an infinite circular cylindrical container, filled with an ideal incompressible fluid and containing a rigid spherical body, vibrating according to a given law. The solution of such a problem is based on the re-expansion of the particular solutions of the Laplace equation, written in cylindrical (spherical) coordinates with respect to spherical (cylindrical) harmonic functions, respectively, giving the possibility, applying also the addition theorems of cylindrical functions, to represent the combined potential of the velocities of the fluid both in spherical and cylindrical systems of coordinates. Satisfying the boundary conditions on the spherical and cylindrical surfaces, the solving of the problem of the construction of the velocity potential of the fluid reduces to the solving of an infinite system of algebraic equations with respect to the coefficients of the expansions of the spherical and cylindrical components of the desired potential.

The forces acting on an obstacle in stratified flow

The three-dimensional steady flow of a heavy incompressible ideal fluid past an obstacle with a rigid boundary with general restrictions on the density and velocity distributions of the incident flow is considered. A set of two non-linear second-order equations which describe the flow pattern is derived. Formulation of the boundary-value problem is discussed. Formulae for calculating the forces acting on the obstacle are derived. The simplifying assumptions associated with approximating the obstacle by a system of dipoles distributed over the barrier surface are investigated. As an example, the flow of an unbounded exponentially stratified fluid around a sphere is considered. Assuming the stratification parameter to be small, the main term in the asymptotic formula which expresses the dependence of the resistance on the sphere radius and the stratification parameters is calculated.

Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars

Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):

Evolution of flexure-gravitational stimulated vibrations of a floating nonuniformly compressed elastic plate

We consider the evolution of vibrations of a thin nonuniformly compressed elastic plate that floats on a surface of a homogeneous ideal incompressible fluid of finite depth, by using the method of integral transformations. Waves are caused by pressures of the type of traveling waves on the surface of the plate, which is harmonic in one of the directions. An analysis of conditions of perturbations of waves that form oscillations of the plate and the wave motion of the fluid is given. A study is given of the dependence of the structure and the number of waves from stressing forces and characteristics of perturbed pressures.

Impact of a rectangular plate on a liquid half-space

The potential flow of an ideal incompressible fluid occupying a half-space resulting from the impact of a rectangular plate on its surface is considered. Outside the plate the surface of the fluid is free. An integral equation of the first kind is obtained for the impulsive pressure beneath a flexible plate. It is solved on a computer by the power series method for the particular case of a rigid nondeformable plate. The accuracy of the method is estimated. The theoretical dependence of the virtual mass and virtual moment of inertia coefficients of a rigid nondeformable plate on the plate geometry is constructed and compared with the experimental data and with empirical formulas [1-3] not directly related with the solution of the Laplace equation.

On the instability of three-dimensional flows of an ideal incompressible fluid

In a recent paper Lifschitz and Hameiri [Phys. Fluids A 34 (1991) 2644] demonstrated how the stability of general three-dimensional steady flows of an ideal incompressible fluid with respect to short wavelength perturbations can be studied via the geometrical optics method. The flow is unstable if for some stream line the transport equation associated with the wave which is advected by the fluid has a sufficiently rapidly growing solution. In the present paper we show that under certain conditions this equation can be solved explicitly. Using this fact we demonstrate that all axisymmetric flows such that the corresponding poloidal velocity has a point of stagnation, particularly all axisymmetric vortex rings, are unstable. We also describe explicitly exponentially growing solutions of the transport equation for three-dimensional flows with stretching.

Stationary arrays of vortical patches near linear boundaries

This paper addresses the problem of plane stationary currents generated in an ideal incompressible fluid by an infinite array of identical areas of constant vorticity located near a linear boundary. Eddy shapes are constructed analytically and numerically for diverse vortical areas and ranges off the boundary. The limits of applicability of the asymptotic solution derived are given. The results are matched within situ observations.

Resonant structures within incompressible ideal MHD

The resonant characteristics of an incompressible ideal MHD fluid are highly structured. To help expose this structure, an equivalent electrical analogue of the MHD system is developed. The model, in the form of a transmission line, makes it possible to identify a number of new and important concepts, one of which is the effective impedance. This in turn enables entire regions of MHD fluid to be replaced with equivalent impedances. When fully exploited, the model also provides a more consistent interpretation of the spectrum of ideal MHD. The discrete Alfvén modes are found to be highly degenerate, while the transition to a discontinuous profile is accompanied by a redistribution of an uncountably infinite number of ‘poles’ from the continuous spectrum and onto the Alfvén modes. In addition, the electrical analogue shows that within a continuously structured fluid the characteristic behaviour is not necessarily dominated by the ‘surface mode’ alone. This view is also supported by the results of a numerical simulation of the linear MHD equations. Depending on the initial conditions, the collective behaviour can have any frequency within the range spanned by the transition zone. The energy itself is monitored using a new pair of energy and flux expressions derived from a variational (Lagrangian) description of the MHD system. Again the electrical model is used to provide a physical interpretation of the individual terms within these expressions. In particular, it allows a partition of the total energy into separate kinetic- and potential-energy terms.

Equations of motion of ball lightning in a rocket airstream

In the literature we often encounter descriptions of the motion of ball lightning of large radius in aircraft airstreams. There are well-known cases of the motion of ball lightning in the airstream created by the engines of a multiengined aircraft, when the lightning, whose dimensions are comparable with those of the aircraft, is captured by the engines and pursues the aircraft persistently, traveling at speeds of 150--200 m/sec while preserving its spherical shape and a constant distance from the tail [1, 2]. I f lightning with a radius o f 5 m were replaced by a rigid sphere o f the same radius, then for it to pursue the aircraft a force of the order o f several tons would have to be applied [3]. Obviously, in this case there can be no question o f the pursuit of the aircraft under the influence of hydrodynamic forces. However, numerous observations o f the motion of ball lightning of large radius in aircraft airstreams give reason to suppose that because of its special internal structure it behaves in a viscous air medium like a rigid sphere in an ideal incompressible fluid [4]. Without concerning ourselves with the physical causes of this behavior, we will accept this property as a finding of numerous experiments [5, 6]. In this case it is possible to investigate the laws of motion of ball lightning in the airstreams created by various flying bodies. We will consider the hydrodynamic interaction between ball lightning and a rocket traveling along a certain trajectory under its own engine power, which can be simulated in the first approximation by a moving point source of variable intensity. Since the lightning undergoes hydrodynamic interaction with a source moving relative to the stationary air medium, it is possible to assume that the stationary source and the lightning moving relative to it are located in a translational airstream variable in magnitude and direction, whose velocity components v x, Vy, and v z are determined by the kinematic equation of motion of the rocket. Bearing this in mind, we will describe the position of the center M of ball lightning of radius a by means of the spherical coordinates s, or, /3 of a fixed system, at whose center lies a point source of intensity 3' per unit solid angle. We make the center of the moving coordinate system xyz coincide with the point M, directing the z axis towards the source, .the y axis in the direction of the unit vector et3, and the x axis in the direction opposite to that of the unit vector ecc The motion of the airstream is described by the equation [7] 27 5L= ~i(r-s),5(cos 0-1) (1) $2