The Golden Radius in Balanced Atmospheric Flows

Abstract

n gradient-balanced, cyclonic flow around low pressure systems, a golden radius exists where RG, the gradient-wind Rossby number, is ??1 = 0.618 034, the inverse golden ratio. There, the geostrophic, cyclostrophic, and inertia-circle approximations to the wind all produce equal magnitudes. The ratio of the gradient wind to any of these approximations is ??1. In anomalous (anticyclonic) flow around a low, the golden radius falls where RG = ?? = ?1.618 034, and the magnitude of the ratio of the anomalous wind to any of the two-term approximations is ?. In normal flow, the golden radius marks the transition between more-nearly cyclostrophic and more-nearly geostrophic regimes. In anomalous flow, it marks the transition between more-nearly cyclostrophic (anticyclonic) and inertia-circle regimes. Over a large neighborhood surrounding the golden radius, averages of the geostrophic and cyclostrophic winds weighted as ??2 and ??3 are good approximations to the gradient wind. In high pressure systems Rg, the geostrophic Rossby number, must be in the range 0 > Rg ≥ ?¼, and the pressure gradient cannot produce inward centripetal accelerations. An analogous radius where Rg = ???3 plays a role somewhat like that of the golden radius, but it is much less interesting.