### Abstract

The modeling system of equations is obtained that describes the two-dimensional long-wave modes of flows of the film for moderate flow rates in which the free boundary problem is solved in a certain sense. The transformation of coordinates is introduced and a variable that enables us to exclude explicitly the velocity of light from the space metrics is considered. We can restrict ourselves to the zero approximation and define the convective term in energy-momentum tensor. Projecting the viscous-stress tensor to the vector of the normal, the long-wave approximation is obtained. The divergent system of equations describing the evolution of long-wave disturbances of the free surface of the fluid film flowing down a vertical wall is derived. In its derivation, the transformation of coordinates converting the unsteady and beforehand unknown region of flow into a constant-width band is made. The tensor approach based on the system of equations of relativistic hydrodynamics used in this case can be efficiently used in various problems with free surfaces.

Original language | English |
---|---|

Pages (from-to) | 22-25 |

Number of pages | 4 |

Journal | Doklady Physics |

Volume | 56 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)

### Cite this

*Doklady Physics*,

*56*(1), 22-25. https://doi.org/10.1134/S1028335811010022

**Divergent system of equations for a fluid film flowing down a vertical wall.** / Alekseenko, S. V.; Arkhipov, D. G.; Tsvelodub, O. Yu.

Research output: Contribution to journal › Article

*Doklady Physics*, vol. 56, no. 1, pp. 22-25. https://doi.org/10.1134/S1028335811010022

}

TY - JOUR

T1 - Divergent system of equations for a fluid film flowing down a vertical wall

AU - Alekseenko, S. V.

AU - Arkhipov, D. G.

AU - Tsvelodub, O. Yu

PY - 2011/1/1

Y1 - 2011/1/1

N2 - The modeling system of equations is obtained that describes the two-dimensional long-wave modes of flows of the film for moderate flow rates in which the free boundary problem is solved in a certain sense. The transformation of coordinates is introduced and a variable that enables us to exclude explicitly the velocity of light from the space metrics is considered. We can restrict ourselves to the zero approximation and define the convective term in energy-momentum tensor. Projecting the viscous-stress tensor to the vector of the normal, the long-wave approximation is obtained. The divergent system of equations describing the evolution of long-wave disturbances of the free surface of the fluid film flowing down a vertical wall is derived. In its derivation, the transformation of coordinates converting the unsteady and beforehand unknown region of flow into a constant-width band is made. The tensor approach based on the system of equations of relativistic hydrodynamics used in this case can be efficiently used in various problems with free surfaces.

AB - The modeling system of equations is obtained that describes the two-dimensional long-wave modes of flows of the film for moderate flow rates in which the free boundary problem is solved in a certain sense. The transformation of coordinates is introduced and a variable that enables us to exclude explicitly the velocity of light from the space metrics is considered. We can restrict ourselves to the zero approximation and define the convective term in energy-momentum tensor. Projecting the viscous-stress tensor to the vector of the normal, the long-wave approximation is obtained. The divergent system of equations describing the evolution of long-wave disturbances of the free surface of the fluid film flowing down a vertical wall is derived. In its derivation, the transformation of coordinates converting the unsteady and beforehand unknown region of flow into a constant-width band is made. The tensor approach based on the system of equations of relativistic hydrodynamics used in this case can be efficiently used in various problems with free surfaces.

UR - http://www.scopus.com/inward/record.url?scp=79952645862&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952645862&partnerID=8YFLogxK

U2 - 10.1134/S1028335811010022

DO - 10.1134/S1028335811010022

M3 - Article

VL - 56

SP - 22

EP - 25

JO - Doklady Physics

JF - Doklady Physics

SN - 1028-3358

IS - 1

ER -