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Asymptotics of solutions to the problem of fluid outflow from a rectangular duct. / Ostapenko, Vladimir V.
в: Physics of Fluids, Том 33, № 4, 047106, 01.04.2021.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Asymptotics of solutions to the problem of fluid outflow from a rectangular duct
AU - Ostapenko, Vladimir V.
N1 - Publisher Copyright: © 2021 Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
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