Barotropic instability of a time-dependent parallel flow. (English) Zbl 1493.76048
Summary: This study examines the long-wavelength instabilities of an inviscid parallel time-dependent current on the beta-plane. The basic flow is represented by the Kolmogorov pattern, the amplitude of which is modulated in time. Particular attention is given to the regime in which the corresponding steady flows are stable according to the Rayleigh-Kuo criterion. It is shown that the presence of a fluctuating component, regardless of how weak it may be, always renders the basic current linearly unstable. The destabilization is attributed to the resonant forcing of large-scale Rossby waves. The analysis is based on the asymptotic multiscale model, which is validated by numerical simulations. Since most geophysical flows are inherently time-dependent, the associated shear instabilities could represent a significant and ubiquitous source of barotropic turbulence.
MSC:
| 76E20 | Stability and instability of geophysical and astrophysical flows |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
Keywords:
inviscid geophysical flow; long-wavelength instability; beta-plane; Kolmogorov flow; Rayleigh-Kuo stability criterion; large-scale Rossby wave; asymptotic multiscale modelReferences:
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