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The Effects of Probe-Induced Flow Distortion on Atmospheric Turbulence Measurements: Extension to Scalars

J. C. WyngaardNational Center for Atmospheric Research, Boulder, Colorado

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Abstract

I prove that in a steady velocity field the frequency spectrum of a conservative scalar is unaffected by flow distortion. This is a good approximation in turbulent flow if (qa1/3;/U1l1/3;) ≪ 1, where q and l are velocity and length scales of the energy-containing turbulence, a is the crosstream dimension of the body, and U1 is the mean flow speed. Rapid-distortion theory gives the same result under more restrictive conditions. Both sets of criteria seem easily met for scalar mixing ratio measurements in typical aircraft applications but are more difficult to satisfy on towers.

At aircraft speeds, crosstalk from air density fluctuations can seriously contaminate species density signals measured in regions of strong flow distortion. These errors can be very important in aircraft measurements of the vertical fluxes of CO2 and water vapor, whose sensors typically measure species density rather than mixing ratio. These errors can be minimized through boom design.

Temperature measurements from aircraft can also be seriously affected by flow distortion; an error in the fluctuating temperature signal is generated by the exchange of kinetic energy and enthalpy during the flow distortion process. Appearing in the temperature signal as crosstalk from velocity fluctuations, the error is proportional to the amount of flow distortion and the deviation of the sensor recovery factor from 1.0.

Abstract

I prove that in a steady velocity field the frequency spectrum of a conservative scalar is unaffected by flow distortion. This is a good approximation in turbulent flow if (qa1/3;/U1l1/3;) ≪ 1, where q and l are velocity and length scales of the energy-containing turbulence, a is the crosstream dimension of the body, and U1 is the mean flow speed. Rapid-distortion theory gives the same result under more restrictive conditions. Both sets of criteria seem easily met for scalar mixing ratio measurements in typical aircraft applications but are more difficult to satisfy on towers.

At aircraft speeds, crosstalk from air density fluctuations can seriously contaminate species density signals measured in regions of strong flow distortion. These errors can be very important in aircraft measurements of the vertical fluxes of CO2 and water vapor, whose sensors typically measure species density rather than mixing ratio. These errors can be minimized through boom design.

Temperature measurements from aircraft can also be seriously affected by flow distortion; an error in the fluctuating temperature signal is generated by the exchange of kinetic energy and enthalpy during the flow distortion process. Appearing in the temperature signal as crosstalk from velocity fluctuations, the error is proportional to the amount of flow distortion and the deviation of the sensor recovery factor from 1.0.

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