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Using a fine resolution numerical model (4000<sup>2</sup> × 2 grid-points) of the two-layer shallow-water equations of the mid-latitude β-plane dynamics, it is shown that there is no sudden breakdown of balance in the turbulent enstrophy cascade but a faint and continuous emission of inertia–gravity waves. The wave energy accumulates in the equator-ward region of the domain due to the Coriolis parameter depending on the latitude and dispersion relation of inertia–gravity waves.