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

<table>Wavenumber spectrum for several points in the dispersion plane <svg height="14.75" id="M236" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 42.637501 14.75" width="42.637501" xmlns="http://www.w3.org/2000/svg">
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</svg>. <svg height="13.6125" id="M237" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 92.737503 13.6125" width="92.737503" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
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<tspan style="font-size: 12.50px; " x="22.842981" y="0">𝛾</tspan>
<tspan style="font-size: 12.50px; " x="32.670338" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="44.710728" y="0">𝜇</tspan>
<tspan style="font-size: 12.50px; " x="55.788387" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="67.828773" y="0">1</tspan>
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</svg>: (a) <svg height="14.6" id="M238" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 39.900002 14.6" width="39.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.76,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
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<text transform="matrix(1,0,0,-1,-58.41,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
</text>
</g>
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</svg>; (b) <svg height="14.6" id="M239" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 39.900002 14.6" width="39.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.76,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-58.41,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">4</tspan>
</text>
</g>
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</svg>. (Burr (2007)—NDF)</table>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Flow Around a Slender Circular Cylinder: A Case Study on Distributed Hopf Bifurcation 