= White-noise vertical shear gives an Ornstein-Uhlenbeck inclination
{title2=$d\beta=-c\beta\,dt-g\,dW$}
In the long-time growing horizontal-gradient branch, independent vertical shear noises combine as $\cos\phi\,dW_1+\sin\phi\,dW_2=dW$. The signed inclination $\beta=k_3e^{-ct}/k_0$ satisfies the displayed <Ornstein-Uhlenbeck stochastic differential equation>. For $c>0$ its stationary density is $\sqrt{c/(\pi g^2)}e^{-cB^2/g^2}$, with variance $g^2/(2c)$. The <Fokker-Planck probability current> vanishes at infinity and gives this Gaussian by one integration. At $c=0$ and nonzero noise there is no normalizable stationary density.
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