TY - JOUR
T1 - Free streamline flows with singularities
AU - Eggers, J.
AU - Smith, A. F.
PY - 2010/3/25
Y1 - 2010/3/25
N2 - We rederive and expand upon a method for finding solutions to the two-dimensional irrotational (inviscid) flow equations in the presence of a free surface, found by Hopkinson. This method allows the flow to be driven by placing singularities, like sources or vortices, in the interior of the flow domain. We then apply the method to find a number of novel solutions: separated flow driven by a source, vortices behind a plate and free-surface flow stirred by a double vortex. Free surfaces generically exhibit cusp singularities with a 2/3 power index, similar to those found in very viscous flow.
AB - We rederive and expand upon a method for finding solutions to the two-dimensional irrotational (inviscid) flow equations in the presence of a free surface, found by Hopkinson. This method allows the flow to be driven by placing singularities, like sources or vortices, in the interior of the flow domain. We then apply the method to find a number of novel solutions: separated flow driven by a source, vortices behind a plate and free-surface flow stirred by a double vortex. Free surfaces generically exhibit cusp singularities with a 2/3 power index, similar to those found in very viscous flow.
UR - http://www.scopus.com/inward/record.url?scp=77952389557&partnerID=8YFLogxK
U2 - 10.1017/S0022112009993624
DO - 10.1017/S0022112009993624
M3 - Article (Academic Journal)
AN - SCOPUS:77952389557
SN - 0022-1120
VL - 647
SP - 187
EP - 200
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -