TY - JOUR

T1 - Roll waves structure in two-layer Hele–Shaw flows

AU - Chesnokov, Alexander

AU - Liapidevskii, Valery

AU - Stepanova, Irina

N1 - Publisher Copyright: © 2017 Elsevier B.V.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provided. It is shown that small perturbations of the interface in the inlet section of the channel lead to the roll waves for certain parameters of the flow. Two-parametric class of exact solutions corresponding to the roll waves regime is obtained. Diagrams of critical depths of roll waves development are constructed.

AB - The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provided. It is shown that small perturbations of the interface in the inlet section of the channel lead to the roll waves for certain parameters of the flow. Two-parametric class of exact solutions corresponding to the roll waves regime is obtained. Diagrams of critical depths of roll waves development are constructed.

KW - Hyperbolic equations

KW - Roll waves

KW - Two-layer Hele–Shaw flow

KW - CHANNEL

KW - STABILITY

KW - POROUS-MEDIA

KW - MODEL

KW - Two-layer Hele-Shaw flow

KW - CELL

UR - http://www.scopus.com/inward/record.url?scp=85019841842&partnerID=8YFLogxK

U2 - 10.1016/j.wavemoti.2017.05.001

DO - 10.1016/j.wavemoti.2017.05.001

M3 - Article

AN - SCOPUS:85019841842

VL - 73

SP - 1

EP - 10

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

ER -