My jet turbulence intensities (at 8D, D being inlet nozzle diameter) are as high as 30% and 50%. Is the Taylor's hypothesis valid in this case? Can I use the hypothesis for converting the time derivative into space derivative? If not what are the corrections needed?
The Taylor hypothesis is probably not valid in your case. The high turbulence levels in a jet shear layer are caused by the instability waves (pressure waves) that are generated in the shear layer. The wave propagation speed of the instability waves may be different from the local mean flow velocity. The radial position of your probe is important. On the jet axis the mean flow speed has a maximum but the convection velocity of the flow unsteadiness caused by the instability waves in the shear layer is much smaller, about 60% of the flow velocity. The Taylor hypothesis assumes that the unsteadiness is convected with the flow speed.
The two contributions (i) turbulence convected with the mean flow speed and (ii) turbulence induced by the vortices in the shear layer can be separated in the potential core of the jet, where the axial flow speed is constant, by using a microphone and a hot wire probe. A microphone will sense the pressure fluctuations only, the hot wires sense the velocity fluctuations due to convected vorticity and due to pressure waves.
You may read: Michel, U.; Froebel. E. 1988: Lower limit for the velocity fluctuation level in wind tunnels. Experiments in Fluids 6, 49-54 (1988)
How did you measure your velocity? Is it with a single probe at 8D? In grid turbulence with u'/U
The Taylor hypothesis is probably not valid in your case. The high turbulence levels in a jet shear layer are caused by the instability waves (pressure waves) that are generated in the shear layer. The wave propagation speed of the instability waves may be different from the local mean flow velocity. The radial position of your probe is important. On the jet axis the mean flow speed has a maximum but the convection velocity of the flow unsteadiness caused by the instability waves in the shear layer is much smaller, about 60% of the flow velocity. The Taylor hypothesis assumes that the unsteadiness is convected with the flow speed.
The two contributions (i) turbulence convected with the mean flow speed and (ii) turbulence induced by the vortices in the shear layer can be separated in the potential core of the jet, where the axial flow speed is constant, by using a microphone and a hot wire probe. A microphone will sense the pressure fluctuations only, the hot wires sense the velocity fluctuations due to convected vorticity and due to pressure waves.
You may read: Michel, U.; Froebel. E. 1988: Lower limit for the velocity fluctuation level in wind tunnels. Experiments in Fluids 6, 49-54 (1988)
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