The effect of cross flow on one-dimensional spectra measured using hot wires

Abstract

Expressions were developed to estimate the cross-flow error that occurs in the one-dimensional velocity spectra determined by applying Taylor’s frozen field hypothesis to measurements with single- and cross-wire probes. The cross-flow error and the error caused by the unsteady convection of the small-scale motions were evaluated for typical measurements. It was found that the cross-flow error could be significant in inertial range of the measured one-dimensional spectra, and was much larger than the error caused by the unsteady convection of the small-scale motions in the one-dimensional spectra of the cross-stream velocity components, $F^{2}_{{22}} {\left( {k_{1} } \right)}$ and $F^{1}_{{33}} {\left( {k_{1} } \right)}$. The results indicate that the one-dimensional spectra of the streamwise velocity component $F^{1}_{{11}} {\left( {k_{1} } \right)}$ measured with a single-wire probe should be significantly more accurate than the spectra measured with a cross-wire probe. The cross-flow error in the one-dimensional spectra also becomes much less important in the dissipation range of the measured spectra.