Open AccessThe Golden Radius in Balanced Atmospheric Flows
Author(s) -
H. E. Willoughby
Publication year - 2011
Publication title -
monthly weather review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.862
H-Index - 179
eISSN - 1520-0493
pISSN - 0027-0644
DOI - 10.1175/2010mwr3579.1
Subject(s) - geostrophic wind , pressure gradient , radius , rossby number , physics , zonal flow (plasma) , anticyclone , balanced flow , thermal wind , mechanics , wind shear , geology , meteorology , atmospheric sciences , wind speed , turbulence , quantum mechanics , plasma , computer security , computer science , tokamak
In gradient-balanced, cyclonic flow around low pressure systems, a golden radius exists where RG, the gradient-wind Rossby number, is φ−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 φ−1. In anomalous (anticyclonic) flow around a low, the golden radius falls where RG = −φ = −1.618 034, and the magnitude of the ratio of the anomalous wind to any of the two-term approximations is φ. 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 φ−2 and φ−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 = −φ−3 plays a role somewhat like that of the golden radius, but it is much less interesting.