Application of the Poor Man's Navier-Stokes Equations to Real-Time Control of Fluid Flow

<table> (a) 2501 × 1251 regime map for <svg height="13.8" id="M120" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 65.512497 13.8" width="65.512497" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-60.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛾</tspan>
<tspan style="font-size: 12.50px; " x="9.8148546" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.855244" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="30.4198" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="36.671299" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="39.79705" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="46.04855" y="0">5</tspan>
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</svg> with <svg height="14.875" id="M121" style="vertical-align:-3.25792pt" version="1.1" viewbox="0 0 135.0125 14.875" width="135.0125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.875)">
<g transform="translate(72,-60.1)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">Δ</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">𝛽</tspan>
<tspan style="font-size: 12.50px; " x="19.467171" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="31.507561" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.75906" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="40.884811" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="47.136311" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="53.38781" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="59.639309" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="69.366646" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="81.407036" y="0">Δ</tspan>
<tspan style="font-size: 12.50px; " x="90.434196" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,24.76,60.27)">
<tspan style="font-size: 8.75px; " x="0" y="0">C</tspan>
<tspan style="font-size: 8.75px; " x="5.837584" y="0">F</tspan>
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</svg>, (b) legend of regime types.</table>

Journal of Applied Mathematics

fig1

Figure 1

Figure 1: Application of the Poor Man's Navier-Stokes Equations to Real-Time Control of Fluid Flow 