Instability of the isothermal, hydrostatic equatorial atmosphere at rest under the full Coriolis acceleration

Abstract

The traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysical phenomena in the tropics have non-negligible cosine Coriolis terms. Such cases warrant investigations with the non-traditional setting, i.e., the full Coriolis acceleration. In this manuscript, we study the effect of the non-traditional setting on an isothermal, hydrostatic and compressible atmosphere assuming a meridionally homogeneous flow. Employing linear stability analysis, we show that, given appropriate boundary conditions, i.e. free-slip boundary at the surface and non-reflecting boundary at the top, the equatorial atmosphere at rest becomes unstable. Numerical experiments were conducted, and Rayleigh damping is used as a numerical approximation for the non-reflecting top boundary. Our two main results are as follows. 1) Experiments involving the full Coriolis terms exhibit exponentially growing instability while experiments subject to the same initial condition and the traditional approximation remain stable. 2) The experimental instability growth rate is close to the theoretical value. Despite the limitations of our investigations wherein only studies on the f-plane are conducted, and effects from the β-plane approximation are ignored, the presence of this instability may have physical and experimental implications for the non-traditional setting. A discussion of the limitations and implications of our study concludes our investigations. Specifically, the influence on numerical deep-atmosphere models and the validity of assuming meridionally homogeneous flow are discussed. Ray , Mark Schlutow, Rupert Klein