Research output: Contribution to journal › Conference article › peer-review
On modeling of undular bores based on the second approximation of the shallow water theory. / Ostapenko, V. V.
In: Journal of Physics: Conference Series, Vol. 1268, No. 1, 012052, 16.07.2019.Research output: Contribution to journal › Conference article › peer-review
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TY - JOUR
T1 - On modeling of undular bores based on the second approximation of the shallow water theory
AU - Ostapenko, V. V.
PY - 2019/7/16
Y1 - 2019/7/16
N2 - It is studied the possibility of modeling of undular bores on the basis of the second approximation of the shallow water theory. The classical differential Green-Naghdi model cannot be used for correct numerical simulation of wave flows with undular bores. The reason for this is that this model is derived within the framework of the long-wave approximation, by virtue of which the characteristic depth of the stream is much less than the characteristic length of the surface waves, which is not performed in the undular bore front. An integro-differential Green-Naghdi model is proposed for numerical simulation of undular bores. In this model we used the divergent differential form of the continuity equation and the integral conservation law of horizontal momentum. This model is derived from two-dimensional integral conservation laws of mass and momentum, describing a plane-parallel flow of an ideal incompressible fluid over a horizontal bottom. The basis of this conclusion is the concept of a local hydrostatic approximation, which generalizes the concept of the long-wave approximation and is used to justify the applicability of shallow water models to describe wave flows with the hydraulic bores.
AB - It is studied the possibility of modeling of undular bores on the basis of the second approximation of the shallow water theory. The classical differential Green-Naghdi model cannot be used for correct numerical simulation of wave flows with undular bores. The reason for this is that this model is derived within the framework of the long-wave approximation, by virtue of which the characteristic depth of the stream is much less than the characteristic length of the surface waves, which is not performed in the undular bore front. An integro-differential Green-Naghdi model is proposed for numerical simulation of undular bores. In this model we used the divergent differential form of the continuity equation and the integral conservation law of horizontal momentum. This model is derived from two-dimensional integral conservation laws of mass and momentum, describing a plane-parallel flow of an ideal incompressible fluid over a horizontal bottom. The basis of this conclusion is the concept of a local hydrostatic approximation, which generalizes the concept of the long-wave approximation and is used to justify the applicability of shallow water models to describe wave flows with the hydraulic bores.
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KW - EQUATIONS
KW - SCHEME
UR - http://www.scopus.com/inward/record.url?scp=85073888873&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/1268/1/012052
DO - 10.1088/1742-6596/1268/1/012052
M3 - Conference article
AN - SCOPUS:85073888873
VL - 1268
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012052
T2 - All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019
Y2 - 13 May 2019 through 17 May 2019
ER -
ID: 22036677