Flow Around a Slender Circular Cylinder: A Case Study on Distributed Hopf Bifurcation

<table>Strouhal number St  = <svg height="14.7125" id="M164" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 119.5625 14.7125" width="119.5625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.66,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="6.6515961" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="10.12743" y="0">𝑈</tspan>
<tspan style="font-size: 12.50px; " x="18.942045" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="23.105543" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-30.62,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-22.79,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">𝜔</tspan>
</text>
<text transform="matrix(1,0,0,-1,-2.24,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,2.11,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">𝜋</tspan>
<tspan style="font-size: 12.50px; " x="17.316654" y="0">)</tspan>
</text>
</g>
</g>
</svg> as a function of Re.          (Bifurcations points <svg height="14.8625" id="M165" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 114.2125 14.8625" width="114.2125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8625)">
<g transform="translate(72,-60.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐑</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.92,60.28)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐶</tspan>
<tspan style="font-size: 8.75px; " x="5.872592" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-52.18,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">;</tspan>
<tspan style="font-size: 12.50px; " x="5.551332" y="0">𝐑</tspan>
</text>
<text transform="matrix(1,0,0,-1,-37.59,60.28)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐶</tspan>
<tspan style="font-size: 8.75px; " x="5.872592" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-22.67,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">a</tspan>
<tspan style="font-size: 12.50px; " x="5.551332" y="0">n</tspan>
<tspan style="font-size: 12.50px; " x="11.802832" y="0">d</tspan>
<tspan style="font-size: 12.50px; " x="22.217831" y="0">𝐑</tspan>
</text>
<text transform="matrix(1,0,0,-1,8.58,60.28)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐶</tspan>
<tspan style="font-size: 8.75px; " x="5.872592" y="0">3</tspan>
</text>
</g>
</g>
</svg>—source: Henderson [<a href="/journals/mpe/2009/526945/#B7">4</a>].)</table>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Flow Around a Slender Circular Cylinder: A Case Study on Distributed Hopf Bifurcation 