Spatial power spectrum of natural water turbulence with any average temperature, salinity concentration, and light wavelength
Jin-Ren Yao, Mohammed Elamassie, Olga Korotkova
Abstract
The power spectrum of water optical turbulence is shown to vary with its average temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>T</mml:mi> <mml:mo fence="false" stretchy="false">⟩</mml:mo> </mml:math> and average salinity concentration <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>S</mml:mi> <mml:mo fence="false" stretchy="false">⟩</mml:mo> </mml:math> , as well as with light wavelength <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> </mml:math> . This study explores such variations for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>T</mml:mi> <mml:mo fence="false" stretchy="false">⟩</mml:mo> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi/> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>30</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi/> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">]</mml:mo> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo fence="false" stretchy="false">⟨</mml:mo> <mml:mi>S</mml:mi> <mml:mo fence="false" stretchy="false">⟩</mml:mo> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>40</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">]</mml:mo> </mml:math> covering most of the possible natural water conditions within the Earth’s boundary layer and for visible electromagnetic spectrum, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>400</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>700</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">]</mml:mo> </mml:math> . For illustration of the effects of these parameters on propagating light, we apply the developed power spectrum model for estimation of the scintillation index of a plane wave (the Rytov variance) and the threshold between weak and strong turbulence regimes.