Abstract
It is known that concentric eyewalls can influence tropical cyclone (TC) intensity. However, they can also influence TC track. Observations indicate that TCs with concentric eyewalls are often accompanied by wobbling of the inner eyewall, a motion that gives rise to cycloidal tracks. Currently, there is no general consensus of what might constitute the dominant triggering mechanism of these wobbles. In this paper we revisit the fundamentals. The control case constitutes a TC with symmetric concentric eyewalls embedded in a quiescent environment. Two sets of experiments are conducted: one using a two-dimensional nondivergent nonlinear model and the other using a three-dimensional nonlinear model. It is found that when the system is two-dimensional, no wobbling of the inner eyewall is triggered. On the other hand, when the third dimension is introduced, an amplifying wobble is evident. This result contradicts the previous suggestion that wobbles occur only in asymmetric concentric eyewalls. It also contradicts the suggestion that environmental wind shear can be the main trigger. Examination of the dynamics along with complementary linear eigenmode analysis revealed the triggering mechanism to be the excitation of a three-dimensional exponentially growing azimuthal wavenumber-1 instability. This instability is induced by the coupling of two baroclinic vortex Rossby waves across the moat region. Additional sensitivity analyses involving reasonable modifications to vortex shape parameters, perturbation vertical length scale, and Rossby number reveal that this instability can be systematically the most excited. The growth rates are shown to peak for perturbations characterized by realistic vertical length scales, suggesting that this mechanism can be potentially relevant to actual TCs.
A nonlinear model for inextensible rods as a low energy Γ -limit of three-dimensional nonlinear elasticity
