Beta mode-coupling kernel
= Beta mode-coupling kernel
{title2=$\beta(\mathbf k_1,\mathbf k_2)$}
The Euler-equation kernel is the symmetric function
$$
\beta(\mathbf k_1,\mathbf k_2)
=\frac{|\mathbf k_1+\mathbf k_2|^2
(\mathbf k_1\mathbin\cdot\mathbf k_2)}{2k_1^2k_2^2}.
$$