Structure and detection of Kelvin-Helmholtz vortices in the ... - GPSM
Structure and detection of Kelvin-Helmholtz vortices in the ... - GPSM
Structure and detection of Kelvin-Helmholtz vortices in the ... - GPSM
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How can <strong>the</strong> secondary velocity shear be<br />
produced<br />
v<br />
1<br />
2<br />
1<br />
M<br />
1v<br />
r<br />
⎧<br />
⎪v1<br />
=<br />
⎪<br />
⎨<br />
⎪<br />
⎪<br />
v2<br />
=<br />
⎩<br />
∴<br />
− v<br />
2<br />
M<br />
2v2<br />
= = ≅<br />
a r<br />
M<br />
M<br />
2<br />
1<br />
a r<br />
2<br />
r<br />
= a r<br />
a<br />
1<br />
M<br />
1<br />
leads to,<br />
1<br />
−<br />
M<br />
2<br />
r<br />
=<br />
M1<br />
a r<br />
M<br />
1<br />
v2<br />
M2<br />
v1<br />
1−<br />
M<br />
M<br />
1<br />
2<br />
⎛ ∆ VSEC<br />
∝ rSEC<br />
⎜1<br />
− 1<br />
⎝ N<br />
RATIO<br />
r SEC = curvature radius <strong>of</strong> <strong>the</strong><br />
2nd velocity shear layer<br />
⎞<br />
⎟<br />
⎠<br />
At a certa<strong>in</strong> radial distance from <strong>the</strong> vortex center, <strong>the</strong> centrifugal<br />
force exert<strong>in</strong>g on <strong>the</strong> lighter <strong>and</strong> heavier fluids must be equal.<br />
↓<br />
Then, <strong>the</strong> shear velocity depends on <strong>the</strong> mass ratio <strong>and</strong> on <strong>the</strong><br />
curvature radius <strong>of</strong> <strong>the</strong> shear layer.
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