Asymptotics of solutions to the problem of fluid outflow from a rectangular duct

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Asymptotics of solutions to the problem of fluid outflow from a rectangular duct. / Ostapenko, Vladimir V.

In: Physics of Fluids, Vol. 33, No. 4, 047106, 01.04.2021.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c3748bc40a314dc4902b03bbddee5ee8,

title = "Asymptotics of solutions to the problem of fluid outflow from a rectangular duct",

abstract = "We investigated the asymptotics of two-dimensional steady solutions simulating the energy-conserving flow in a horizontal duct of finite depth in situations where the flow contains a region spanning the depth of the duct, and a region in which the fluid surface detaches from the ceiling of the duct as a free surface. These asymptotics are constructed using the local hydrostatic approximation, which generalizes the classical long-wave approximation. The initial (zero-order) asymptotics leading to the piecewise constant solutions are obtained from the mass, momentum, and energy conservation laws of the first approximation of shallow water theory. The first-order asymptotics for the liquid depth are constructed using the momentum conservation law of the Green-Nagdi model representing the second approximation of shallow water theory. It is shown that the continuous solution obtained from this asymptotics is in good agreement with the Wilkinson laboratory experiment [D. L. Wilkinson, {"}Motion of air cavities in long horizontal ducts,{"}J. Fluid Mech. 118, 109 (1982)] on modeling the energy-conserving steady flow predicted by the classical piecewise constant Benjamin solution [T. B. Benjamin, {"}Gravity currents and related phenomena,{"}J. Fluid Mech. 31, 209 (1968)].",

author = "Ostapenko, {Vladimir V.}",

year = "2021",

month = apr,

day = "1",

doi = "10.1063/5.0045260",

language = "English",

volume = "33",

journal = "Physics of Fluids",

issn = "1070-6631",

publisher = "American Institute of Physics",

number = "4",

}

RIS

TY - JOUR

T1 - Asymptotics of solutions to the problem of fluid outflow from a rectangular duct

AU - Ostapenko, Vladimir V.

PY - 2021/4/1

Y1 - 2021/4/1

N2 - We investigated the asymptotics of two-dimensional steady solutions simulating the energy-conserving flow in a horizontal duct of finite depth in situations where the flow contains a region spanning the depth of the duct, and a region in which the fluid surface detaches from the ceiling of the duct as a free surface. These asymptotics are constructed using the local hydrostatic approximation, which generalizes the classical long-wave approximation. The initial (zero-order) asymptotics leading to the piecewise constant solutions are obtained from the mass, momentum, and energy conservation laws of the first approximation of shallow water theory. The first-order asymptotics for the liquid depth are constructed using the momentum conservation law of the Green-Nagdi model representing the second approximation of shallow water theory. It is shown that the continuous solution obtained from this asymptotics is in good agreement with the Wilkinson laboratory experiment [D. L. Wilkinson, "Motion of air cavities in long horizontal ducts,"J. Fluid Mech. 118, 109 (1982)] on modeling the energy-conserving steady flow predicted by the classical piecewise constant Benjamin solution [T. B. Benjamin, "Gravity currents and related phenomena,"J. Fluid Mech. 31, 209 (1968)].

AB - We investigated the asymptotics of two-dimensional steady solutions simulating the energy-conserving flow in a horizontal duct of finite depth in situations where the flow contains a region spanning the depth of the duct, and a region in which the fluid surface detaches from the ceiling of the duct as a free surface. These asymptotics are constructed using the local hydrostatic approximation, which generalizes the classical long-wave approximation. The initial (zero-order) asymptotics leading to the piecewise constant solutions are obtained from the mass, momentum, and energy conservation laws of the first approximation of shallow water theory. The first-order asymptotics for the liquid depth are constructed using the momentum conservation law of the Green-Nagdi model representing the second approximation of shallow water theory. It is shown that the continuous solution obtained from this asymptotics is in good agreement with the Wilkinson laboratory experiment [D. L. Wilkinson, "Motion of air cavities in long horizontal ducts,"J. Fluid Mech. 118, 109 (1982)] on modeling the energy-conserving steady flow predicted by the classical piecewise constant Benjamin solution [T. B. Benjamin, "Gravity currents and related phenomena,"J. Fluid Mech. 31, 209 (1968)].

UR - http://www.scopus.com/inward/record.url?scp=85103873702&partnerID=8YFLogxK

U2 - 10.1063/5.0045260

DO - 10.1063/5.0045260

M3 - Article

AN - SCOPUS:85103873702

VL - 33

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 4

M1 - 047106

ER -

ID: 28317619