Vorticity evolution in liquids and gases

Марков, В. В.; Sizykh, G. B.

doi:10.1134/s0015462815020027

Cited by 12 publications

(6 citation statements)

References 6 publications

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“…In [22], a positive answer is given to the question of the existence of velocity U for an elementary vortex fragment which is a segment of the spatial vortex tube with nonzero vorticity. Moreover, in the same paper it is proved that there exist infinitely many Fridman velocities, and for a viscous incompressible fluid all of them are described by the following expression: where W is some scalar field that is constant along vortex lines, γ is an arbitrary scalar field, and f is some scalar function satisfying the condition…”

Section: On the Existence Of The Velocity Of Transfer Of Vortex Tubes...mentioning

confidence: 99%

“…Thus, the question of the existence of the Fridman velocity U for the flow region is linked to the question of the existence of a potential f that would satisfy condition (5.3). The authors of [22] conclude that such a function f exists for any elementary vortex fragment and can be obtained by integrating Eq. (5.3) along vortex lines.…”

Section: On the Existence Of The Velocity Of Transfer Of Vortex Tubes...mentioning

confidence: 99%

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Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments

Kotsur¹,

Shcheglov²,

Marchevsky³

2022

Nelin. Dinam.

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This paper is concerned with the equation for the evolution of vorticity in a viscous incompressible fluid, for which approximate weak solutions are sought in the class of vortex filaments. In accordance with the Helmholtz theorem, a system of vortex filaments that is transferred by the flow of an ideal barotropic fluid is an exact solution to the Euler equation. At the same time, for viscous incompressible flows described by the system of Navier – Stokes equations, the search for such generalized solutions in the finite time interval is generally difficult. In this paper, we propose a method for transforming the diffusion term in the vorticity evolution equation that makes it possible to construct its approximate solution in the class of vortex filaments under the assumption that there is no helicity of vorticity. Such an approach is useful in constructing vortex methods of computational hydrodynamics to model viscous incompressible flows.

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Section: On the Existence Of The Velocity Of Transfer Of Vortex Tubes...mentioning

confidence: 99%

Section: On the Existence Of The Velocity Of Transfer Of Vortex Tubes...mentioning

confidence: 99%

Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments

Kotsur¹,

Shcheglov²,

Marchevsky³

2022

Nelin. Dinam.

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“…In Ref. [4], it was shown that for any fluid or gas flow, along with the real flow velocity u, there is a speed U of some imagined environment whose particles transfer vortex tubes (that is vector tubes of the vorticity field) with maintaining their intensity. Classical theorems of Helmholtz [5] show that for barotropic ideal fluid fictitious speed U coincides with the real flow velocity u.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [4], the method of determination of the speed U for any flow is also suggested. But this approach is not local, because calculation of the velocity field U requires integration of hydrodynamic functions along vortex lines.…”

Section: Introductionmentioning

confidence: 99%

On the vorticity behind 3-D detached bow shock wave

Golubkin

Sizykh

2019

Adv. Aerodyn.

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For the general case of a spatial isoenergetic flow of ideal gas, Helmholtz's theorems are generalized and the speed with which vortex tubes move is found, keeping the intensity. It is shown that along the streamline without stagnation point, vorticity either is equal to zero everywhere, or it is non zero at all. The pattern of vortex lines behind the three-dimensional detached bow shock wave is specified.

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“…Later, other patterns of vortex movements were discovered. One group of laws is associated with the conservation of certain quantities (which depend on the flow parameters) along streamlines or vortex lines in the general 3D case in a non-barotropic gas [3][4][5][6]. These laws deal with "generalized" circulation or "generalized" velocity and vorticity fields (which makes it difficult to use them to verify numerical calculations).…”

mentioning

confidence: 99%

Closed vortex lines in fluid and gas

Sizykh

Борисович²

2019

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Исследуется непрерывное течение жидкости и газа с замкнутыми вихревыми трубками. Рассмотрена циркуляция вдоль вихревой линии отношения плотности равнодействующей всех сил (приложенных к жидкости или газу) к плотности жидкости или газа. Она совпадает с циркуляцией по той же вихревой линии частной производной вектора скорости по времени и поэтому для стационарных течений равна нулю на любой замкнутой вихревой линии. Для нестационарных течений рассмотрены вихревые трубки, которые остаются замкнутыми по крайней мере в течение некоторого интервала времени. Обнаружена неизвестная ранее закономерность, состоящая в том, что в каждый фиксированный момент времени такая циркуляция одинакова для всех замкнутых вихревых линий, составляющих вихревую трубку. Указанная закономерность верна для течений сжимаемых и несжимаемых, вязких (различных реологий) и невязких жидкостей в поле потенциальных и непотенциальных внешних массовых сил. Поскольку эта закономерность не заложена в современные численные алгоритмы, она может использоваться для верификации численных расчетов нестационарных течений с замкнутыми вихревыми трубками путем проверки равенства циркуляций на разных замкнутых вихревых линиях (в одной трубке). Выражение для плотности распределения равнодействующей всех сил, приложенных к жидкости или газу, может содержать производные высших порядков. В то же время выражение для частной производной вектора скорости по времени и выражение для вектора завихренности, который необходим для построения вихревой линии, содержат только первые производные, что позволяет использовать обнаруженную закономерность для верификации расчетов, проведенных методами не только высокого, но и низкого порядков.

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Vorticity evolution in liquids and gases

Cited by 12 publications

References 6 publications

Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments

Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments

On the vorticity behind 3-D detached bow shock wave

Closed vortex lines in fluid and gas

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