Wavelet Decomposition of Forced Turbulence: Applicability of the Iterative Donoho-Johnstone Threshold

We examine the decomposition of forced Taylor-Green and Arn’old-Beltrami- Childress (ABC) flows into coherent and incoherent components using an orthonormal wavelet decomposition. We ask whether wavelet coefficient thresh- olding based on the Donoho-Johnstone criterion can extract a coherent vortex signal while leaving behind Gaussian random noise. We find that no threshold yields a strictly Gaussian incoherent component, and that the most Gaussian incoherent flow is found for data compression lower than that achieved with the fully iterated Donoho-Johnstone threshold. Moreover, even at such low compression, the incoherent component shows clear signs of large-scale spatial correlations that are signatures of the forcings used to drive the flows