a summary of key terms defined in this paper for later reference.

In the following, we assume that there is no preferred horizontal direction in the data. In this case, the bispectrum of the divergence field is real. The expectation value $\EE[X(\bk) X(\bl) X^*(\bmm) ]$ is zero if $\bmm\neq\bk+\bl$ because of the assumed translation invariance. Therefore, the triadic relation $\bmm=\bk+\bl$ is implicitly understood in the following and the third variable is omitted in bispectrum-related quantities.

Estimating the bispectrum {#secEstB}
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In principle, the bispectrum can be estimated using Equation  by simply averaging over [independent]{} realizations $X^{(i)}(\bk)$ of the data [e.g., @Kim1979]. See Appendix \[appBispecEst\] for a formal definition of the estimator $\hat B$, which is obtained this way. We take this approach although it may not be optimal; @Nikias1987 discuss other possible approaches.

In order to assess the significance of the estimated bispectrum, it is necessary to consider the bispectral coherence (also known as the bicoherence) $b$, which is a normalized bispectrum [e.g., @Kim1979], $$\begin{aligned}
b(\bk,\bl) 
&= \frac{\EE[X(\bk) X(\bl) X^*(\bmm) ]}{\sqrt{\EE[|X(\bk)X(\bl)|^2] \EE[|X(\bmm)|^2]}}. \label{eqbDef}\end{aligned}$$ The definition of $b$ is independent of the convention used to define the Fourier transform because it is normalized and because the bispectrum is real in our 