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htab01=Join[htab,htab1];
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Dimensions[htab01]
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{2002,2}
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lhinterp=Interpolation@Log[htab01];
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LogLogPlot[Exp[lhinterp[Log[k]]],{k,0.1,1000},PlotLabel->"H(κ)",AxesLabel->{κ,H}]
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Dv2[r_]:=NIntegrate[1/Pi^2(1-Sin[kr]/(kr))Exp[lhinterp[Log[k]]],{k,0.1,1000}];
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rD[(1-Sin[kr]/(kr)),r]//Simplify
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-Cos[kr]+
Sin[kr]
kr
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DDv2[r_]:=NIntegrate1Pi^2-Cos[kr]+Exp[lhinterp[Log[k]]],{k,0.1,1000};
Sin[kr]
kr
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DDv2[1.]
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0.00560144
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vtab=ParallelTable[{r,Dv2[r]},{r,0.01,10,0.01}];
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ListLinePlot[vtab]
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PTh=LogLogPlot[Dv2[r],{r,0.001,100},PlotLegends->{"Theory"}]
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PTh0=LogLogPlot[Dv2[r],{r,0.00001,0.001},PlotLegends->{"Theory"},PlotStyle->{Green}]
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Pas=LogLogPlot[Dv2[0.001](r/0.001)^2,{r,0.00001,0.001},PlotStyle->{Red,Dashed},PlotLegends->{ρ^2}]
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Show[{PTh0,PTh,Pas},PlotRange->All,PlotLabel->"Velocity second moment",AxesLabel->{ρ,νtΔv^2}]
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24864
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20736
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Subscript[ξ,2][r]
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ξ
2
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ξ2[r_]:=DDv2[r]/Dv2[r];
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ξ2[1]
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0.0562551
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X2=Plot[ξ2[10^t],{t,-3,2.5},PlotRange->All,PlotStyle->{Blue,Thick},AxesLabel->{"Log[r/L[t]]","r D[Log[Δ v^2],r]"},PlotLabel->"Effective index vs Log[r/L[t]]"]
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X1=Plot[ξ2[10^t],{t,1,2.5},PlotRange->All,PlotStyle->{Blue,Thin},AxesLabel->{"Log[r/L[t]]","r D[Log[Δ v^2],r]"},PlotLabel->"Oscillations of effective index at large r"]
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ArrayReshape[{X2,X1},{2,1}]//TableForm