  In this paper, we derive a four-mode model for the Kolmogorov flow by
employing Galerkin truncation and Craya-Herring basis for the decomposition of
velocity field. After this, we perform a bifurcation analysis of the model.
Though our low-dimensional model has fewer modes than the past models, it
captures the essential features of the primary bifurcation of the Kolmogorov
flow. For example, it reproduces the critical Reynolds number for the
supercritical pitchfork bifurcation and the flow structures of the past works.
We also demonstrate energy transfers from intermediate scales to large scales.
We perform direct numerical simulations of the Kolmogorov flow and show that
our model predictions match with the numerical simulations very well.
