Wave Scattering by Small Undulation on the Porous Bottom of an Ocean in the Presence of Surface Tension

<table>     Reflection coefficient <svg height="14.6" id="M160" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 24.0375 14.6" width="24.0375" 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">|</tspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">𝑅</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.2,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-55.32,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">|</tspan>
</text>
</g>
</g>
</svg> against wave number <svg height="14.8625" id="M161" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 23.700001 14.8625" width="23.700001" 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">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,60.28)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.3,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
</text>
</g>
</g>
</svg> for <svg height="10.95" id="M162" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 41.3125 10.95" width="41.3125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑙</tspan>
<tspan style="font-size: 12.50px; " x="3.9759541" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="14.653516" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.693905" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="11.0125" id="M163" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 60.262501 11.0125" width="60.262501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0125)">
<g transform="translate(72,-63.19)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="6.2765059" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.7523403" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="20.429901" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="32.470291" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.72179" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="41.847542" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.3125" id="M164" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 62.487499 14.3125" width="62.487499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3125)">
<g transform="translate(72,-60.55)">
<text transform="matrix(1,0,0,-1,-71.95,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
<tspan style="font-size: 12.50px; " x="12.565515" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="16.041349" y="0">ℎ</tspan>
</text>
<text transform="matrix(1,0,0,-1,-48.69,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-40.35,60.78)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="11.0125" id="M165" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 59.537498 11.0125" width="59.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0125)">
<g transform="translate(72,-63.19)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐺</tspan>
<tspan style="font-size: 12.50px; " x="9.1772022" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="19.854765" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="31.895153" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.146652" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="41.272404" y="0">1</tspan>
</text>
</g>
</g>
</svg>.   </table>

International Scholarly Research Notices

fig3

Figure 3

Figure 3: Wave Scattering by Small Undulation on the Porous Bottom of an Ocean in the Presence of Surface Tension 