Spectra of Decaying Turbulence in a Soap Film

Abstract

Grid turbulence in a flowing soap film is investigated with ambient pressure $P$ as one of the control parameters. Reducing $P$ significantly decreases air drag thus minimizing three-dimensional effects on the flowing film. It was found that while the total kinetic energy $\frac{1}{2}〈{v}^{2}〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\int}E(k)\mathrm{dk}$ of velocity fluctuations increased noticeably as $P$ was reduced, the energy spectrum $E(k)$ for wave numbers greater than the injection scale was remarkably insensitive to the pressure change, and obeyed a power law $E(k)\ensuremath{\sim}{k}^{\ensuremath{-}3.3\ifmmode\pm\else\textpm\fi{}0.3}$.