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

<table>Amplitude <svg height="14.55" id="M38" style="vertical-align:-3.20526pt" version="1.1" viewbox="0 0 17.387501 14.55" width="17.387501" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.36)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐴</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
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</svg>(Re) = <svg height="14.7125" id="M39" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 148.8 14.7125" width="148.8" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">m</tspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">a</tspan>
<tspan style="font-size: 12.50px; " x="27.306553" y="0">x</tspan>
<tspan style="font-size: 12.50px; " x="33.558052" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="36.058651" y="0">𝑢</tspan>
</text>
<text transform="matrix(1,0,0,-1,-29.96,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
</text>
<text transform="matrix(1,0,0,-1,-25.11,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝐱</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="14.578498" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="17.079098" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="20.554932" y="0">m</tspan>
<tspan style="font-size: 12.50px; " x="30.282267" y="0">a</tspan>
<tspan style="font-size: 12.50px; " x="35.833599" y="0">x</tspan>
<tspan style="font-size: 12.50px; " x="42.085098" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="44.585697" y="0">𝑢</tspan>
</text>
<text transform="matrix(1,0,0,-1,25.41,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
</text>
<text transform="matrix(1,0,0,-1,29.91,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝐱</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="14.578498" y="0">|</tspan>
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</svg> of the <svg height="7.1374998" id="M40" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
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</svg>th  mode.  Numerical computation (for Re = 100, also shown PIV computation)  (source: Barbeiro &amp; Korkischko (2008)—NDF).</table>

Mathematical Problems in Engineering

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Figure 3

Figure 3: Flow Around a Slender Circular Cylinder: A Case Study on Distributed Hopf Bifurcation 