Nonlinear Vertical Scale Selection in Equatorial Inertial Instability

The zonal flows of the earth's equatorial stratosphere and mesosphere are prone to inertial instability when the horizontal shear Λ ≠ 0 at the equator. However, it is not clear why the vertical wavelength of the observed structures is much greater than that predicted by the simple linear theory, based on a vertical scale selection by molecular diffusion. Here, a nonlinear mechanism is described that can lead to upscaling from structures with short vertical wavelengths to long vertical wavelengths. The mechanism is dependent upon a secondary Kelvin–Helmholtz instability that develops as the inertial instability grows. Numerical simulations on an equatorial β plane, employing a simple parameterization of the vertical transport of horizontal momentum due to the secondary instability, are used to assess the likely degree of upscaling in a zonally symmetric system. For a fluid with buoyancy frequency N, it is shown that upscaling toward the buoyancy cutoff wavenumber 4Nβ/Λ2 can occur, even when diffusion is so weak that the wavelength of the most unstable linear mode is much smaller than the buoyancy cutoff wavelength. Thus, the simulated latitudinal and vertical structure of the instability in the nonlinear regime is significantly different from that predicted by the linear theory, and can explain the scales of the structures observed near the equatorial stratopause.