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 -