Surface singularities of ideal fluid

Кузнецов, Е. А.; Spector, M.D.; Захаров, В. Е.

doi:10.1016/0375-9601(93)90413-t

Cited by 41 publications

(45 citation statements)

References 4 publications

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“…On the whole, such behavior is similar to that of the velocity potential of an ideal liquid in the absence of external forces [10,11,12]. In Sec.…”

Section: Introductionmentioning

confidence: 61%

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Formation of singularities on the surface of a liquid metal in a strong electric field

Зубарев

1998

J. Exp. Theor. Phys.

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The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.

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“…On the whole, such behavior is similar to that of the velocity potential of an ideal liquid in the absence of external forces [10,11,12]. In Sec.…”

Section: Introductionmentioning

confidence: 61%

“…This means that, as in Refs. [10,11,12], the formation of singularities can be interpreted as the result of violation of the analyticity of the complex-valued potential due to the movement of the singularities of the potential to the boundary.…”

Section: Formation Of a Branch Point Of The Root Typementioning

confidence: 99%

Formation of singularities on the surface of a liquid metal in a strong electric field

Зубарев

1998

J. Exp. Theor. Phys.

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“…It should be mentioned that such a behavior of the charged surface is similar to the behavior of a free surface of an ideal fluid in the absence of external forces [5,6], though the singularities are of a different nature (in the latter case the singularity formation is connected with inertial forces).…”

mentioning

confidence: 82%

“…Kuznetsov for attracting my attention to Refs. [5,6]. This work was supported by Russian Foundation for Basic Research, Grant No.…”

mentioning

confidence: 99%

Formation of root singularities on the free surface of a conducting fluid in an electric field

Зубарев

1998

Physics Letters A

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The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.Electrohydrodynamic instability of a free surface of a conducting fluid in an external electric field [1,2] plays an essential role in a general problem of the electric strength. The interaction of strong electric field with induced charges at the surface of the fluid (liquid metal for applications) leads to the avalanche-like growth of surface perturbations and, as a consequence, to the formation of regions with high energy concentration which destruction can be accompanied by intensive emissive processes.In this Letter we will show that the nonlinear equations of motion of a conducting fluid can be effectively solved in the approximation of small perturbations of the boundary. This allows us to study the nonlinear dynamics of the electrohydrodynamic instability and, in particular, the most physically meaningful singular solutions.Let us consider an irrotational motion of a conducting ideal fluid with a free surface, z = η(x, y, t), that occupies the region −∞ < z ≤ η(x, y, t), in an external uniform electric field E. We will assume the influence of gravitational and capillary forces to be negligibly small, which corresponds to the conditionwhere g is the acceleration of gravity, α is the surface tension coefficient, and ρ is the mass density. The potential of the electric field ϕ satisfies the Laplace equation, ∆ϕ = 0, with the following boundary conditions, ϕ → −Ez, z → ∞,

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“…Canonical variables are used also for analytical study of the surface dynamics in the limit of small steepness. It was shown [15][16][17] that the simplest truncation of the series (2), namely:…”

Section: Introductionmentioning

confidence: 99%

On optimal canonical variables in the theory of ideal fluid with free surface

Lushnikov

Захаров

2005

Physica D: Nonlinear Phenomena

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Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transformation from original physical variables to new variables for which instability is absent.

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Surface singularities of ideal fluid

Cited by 41 publications

References 4 publications

Formation of singularities on the surface of a liquid metal in a strong electric field

Formation of singularities on the surface of a liquid metal in a strong electric field

Formation of root singularities on the free surface of a conducting fluid in an electric field

On optimal canonical variables in the theory of ideal fluid with free surface

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