Pressure Fluctuations in Two-dimensional Turbulence

We investigate pressure fluctuations in two-dimensional (2D) turbulence driven electromagnetically in a freely suspended soap film. The reduced probability distribution function (PDF), $P(p/\sigma_{p})$, is found to be universal for different Reynolds numbers and consists of asymmetrical exponential wings, where $\sigma_{p}\equiv\langle p^{2}\rangle^ {1/2}$ is the standard deviation. The calculated pressure skewness $S_{p}=\langle p^{3}\rangle/\sigma_{p}^{3}\simeq-0.5$ is significantly smaller than predictions by simple 2D models (Holzer and Siggia, Phys. Fluids A5, 2525 (1993)) but surprisingly close to 3D calculations using a random velocity field with a Kolmogorov energy spectrum $E(k)\propto k^{-5/3}$. The pressure spectrum $E_{pp}(k)$ scales approximately as $E_ {pp}(k)\propto k^{-7/3}$ in the energy inverse-cascade subrange and $k^{-5}$ in the enstrophy cascade subrange. These observations suggest that pressure fluctuations is essentially a large-scale phenomenon and the presence of an enstrophy cascade has no effect on the tails of $P(p/\sigma_{p})$.