TY - JOUR

T1 - Shock waves in Stokes flows down an inclined plate

AU - Benilov, E. S.

AU - Lapin, V. N.

PY - 2011/6/29

Y1 - 2011/6/29

N2 - We consider a viscous flow on an inclined plate, such that the liquid's depth far upstream is larger than that far downstream, resulting in a "smoothed-shock wave" steadily propagating downstream. Our numerical simulations show that in a large section of the problem's parameter space all initial conditions overturn (i.e., the liquid's surface becomes vertical at some point) and thus no steady solution exists. The overturning can only be stopped by a sufficiently strong surface tension.

AB - We consider a viscous flow on an inclined plate, such that the liquid's depth far upstream is larger than that far downstream, resulting in a "smoothed-shock wave" steadily propagating downstream. Our numerical simulations show that in a large section of the problem's parameter space all initial conditions overturn (i.e., the liquid's surface becomes vertical at some point) and thus no steady solution exists. The overturning can only be stopped by a sufficiently strong surface tension.

UR - http://www.scopus.com/inward/record.url?scp=79961051101&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.83.066321

DO - 10.1103/PhysRevE.83.066321

M3 - Article

AN - SCOPUS:79961051101

SN - 1539-3755

VL - 83

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 6

M1 - 066321

ER -