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Context. The spatial power spectrum of supergranulation does not fullycharacterize the underlying physics of turbulent convection. For example, itdoes not describe the non-Gaussianity in the horizontal flow divergence.  Aims. Our aim is to statistically characterize the spatial pattern of solarsupergranulation beyond the power spectrum. The next-order statistic is thebispectrum. It measures correlations of three Fourier components and is relatedto the nonlinearities in the underlying physics.  Methods. We estimated the bispectrum of supergranular horizontal surfacedivergence maps that were obtained using local correlation tracking (LCT) andtime-distance helioseismology (TD) from one year of data from the Helioseismicand Magnetic Imager on-board the Solar Dynamics Observatory starting in May2010.  Results. We find significantly nonzero and consistent estimates for thebispectrum. The strongest nonlinearity is present when the three coupling wavevectors are at the supergranular scale. These are the same wave vectors thatare present in regular hexagons, which were used in analytical studies of solarconvection. At these Fourier components, the bispectrum is positive, consistentwith the positive skewness in the data and with supergranules preferentiallyconsisting of outflows surrounded by a network of inflows. We use thebispectrum to generate synthetic divergence maps that are very similar to thedata by a model that consists of a Gaussian term and a weaker quadraticnonlinear component. Thereby, we estimate the fraction of the variance in thedivergence maps from the nonlinear component to be of the order of 4-6%.  Conclusions. We propose that bispectral analysis is useful for understandingsolar turbulent convection, for example for comparing observations andnumerical models of supergranular flows. This analysis may also be useful togenerate synthetic flow fields.

Characterizing the spatial pattern of solar supergranulation using the bispectrum