TY - JOUR
T1 - A nonlinear approximation for vortex sheet evolution and singularity formation
AU - Caflisch, Russel E.
AU - Semmes, Stephen
N1 - Funding Information:
1Research supported in part by the Air Force Office of Scientific Research under U.RI grant 86-0352 and grant 90-0003 and by the National Science Foundation under grant NSF-MCS-83-01260. Current address: Mathematics Department, UCLA, Los Angeles, CA 90024, USA. 2 Research supported by the National Science Foundation and the Alfred P. Sloan Foundation.
PY - 1990/3
Y1 - 1990/3
N2 - The evolution of a vortex sheet in two-dimensional, incompressible, inviscid flow is governed by the integro-differential equation of Birkhoff-Rott. We derive a simple approximation for vortex sheet evolution, consisting of a system of four first-order differential equations. This approximate system has the advantage of involving only local operators. The errors in the approximation are shown to be relatively small even if the sheet has infinite curvature at a point. For the approximate equations, exact similarity solutions exhibiting singularity formation are constructed.
AB - The evolution of a vortex sheet in two-dimensional, incompressible, inviscid flow is governed by the integro-differential equation of Birkhoff-Rott. We derive a simple approximation for vortex sheet evolution, consisting of a system of four first-order differential equations. This approximate system has the advantage of involving only local operators. The errors in the approximation are shown to be relatively small even if the sheet has infinite curvature at a point. For the approximate equations, exact similarity solutions exhibiting singularity formation are constructed.
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U2 - 10.1016/0167-2789(90)90122-6
DO - 10.1016/0167-2789(90)90122-6
M3 - Article
AN - SCOPUS:0013277711
SN - 0167-2789
VL - 41
SP - 197
EP - 207
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 2
ER -