  We consider turbulence in a stratified 'Kolmogorov' flow, driven by
horizontal shear in the form of sinusoidal body forcing in the presence of an
imposed background linear stable stratification in the third direction. This
flow configuration allows the controlled investigation of the formation of
coherent structures, which here organise the flow into horizontal layers by
inclining the background shear as the strength of the stratifica- tion is
increased. By numerically converging exact steady states from direct numerical
simulations of chaotic flow, we show, for the first time, a robust connection
between linear theory predicting instabilities from infinitesimal perturbations
to the robust finite amplitude nonlinear layered state observed in the
turbulence. We investigate how the observed vertical length scales are related
to the primary linear instabilities and compare to previously considered
examples of shear instability leading to layer formation in other horizontally
sheared flows.
