TY - JOUR

T1 - Hierarchy of nonlinear models of the hydrodynamics of long surface waves

AU - Shokin, Yu I.

AU - Fedotova, Z. I.

AU - Khakimzyanov, G. S.

PY - 2015

Y1 - 2015

N2 - The derivation of shallow-water models taking into account the dispersion is based on the Euler equations for an ideal incompressible fluid on a rotating sphere, the mobility of the bottom surface being taken into account, while further passage along the hierarchy from completely nonlinear equations with dispersion towards simplifications proceeds with inheritance of the most important properties, in particular, the laws of conservation. It should be noted that the presence of the consistent balance equation of total energy makes it possible to carry out an additional control of calculations using the numerical methods of the solution instead of only confirming the physical validity of the NLD model.

AB - The derivation of shallow-water models taking into account the dispersion is based on the Euler equations for an ideal incompressible fluid on a rotating sphere, the mobility of the bottom surface being taken into account, while further passage along the hierarchy from completely nonlinear equations with dispersion towards simplifications proceeds with inheritance of the most important properties, in particular, the laws of conservation. It should be noted that the presence of the consistent balance equation of total energy makes it possible to carry out an additional control of calculations using the numerical methods of the solution instead of only confirming the physical validity of the NLD model.

UR - http://www.scopus.com/inward/record.url?scp=84931273602&partnerID=8YFLogxK

U2 - 10.1134/S1028335815050079

DO - 10.1134/S1028335815050079

M3 - Article

AN - SCOPUS:84931273602

VL - 60

SP - 224

EP - 228

JO - Doklady Physics

JF - Doklady Physics

SN - 1028-3358

IS - 5

ER -