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摘要
En 中文
We consider pairs of self-similar two-dimensional vortex sheets forming cusps, equivalently single sheets merging into slip condition walls, as in classical Mach reflection at wedges. We derive from the Birkhoff-Rott equation a reduced model yielding formulas for cusp exponents and other quantities as functions of the similarity exponent and strain coefficient. Comparison to numerics shows that the piecewise quadratic and higher approximation of vortex sheets agree with each other and with the model. In contrast, piecewise linear schemes produce spurious results and violate conservation of mass, a problem that may have been undetected in prior work for other vortical flows. We find that vortex cusps only exist if the similarity exponent is sufficiently large and if the circulation on the sheet is counterclockwise (for a sheet above the wall with cusp opening to the right), unless a sufficiently positive strain coefficient compensates. Whenever a cusp cannot exist a spiral-ended jet forms instead; we find many jets are so narrow that they appear as false cusps.
Keyword:
contour dynamics
contact lines
jets
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期刊
IF:
3.9
论文数:
2.0W
被引数:
9.4W
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