Lagrangian trajectories at the outflow of tropical cyclones

Abstract

Recent observations from the upper levels of tropical cyclones show the development of a Low engulfed by a larger High. The impact of such a geopotential map on the dynamics of the outflow is studied by analysing the Lagrangian trajectories of air parcels. The geopotential is modelled by the hydrostatic sum of two, oppositely signed, Gaussians: a warm core and a near‐surface low that together reproduce the relevant features of the observed tropical cyclones. Assuming a time‐independent and axisymmetric geopotential map, the dynamics is described by an integrable, two degrees‐of‐freedom, angular momentum conserving, Hamiltonian system with a single non‐dimensional parameter. The steady states of this system bifurcate when the geopotential amplitude increases above a threshold where the single elliptic fixed‐point becomes hyperbolic surrounded by a pair of elliptic fixed‐points. A gradient balance prevails near the elliptic points while an inertial balance occurs at the radius of maximum geopotential, where the hyperbolic (unstable) point is located. The divergence of trajectories around this hyperbolic point implies the existence of strong horizontal wind divergence. A gradient non‐balance region emerges in the steady state (radius, geopotential amplitude) map and this region expands with the increase of geopotential amplitude which implies that higher angular momentum values are required for trajectories to transition from high to low. A transformation of the (radius, radial velocity) variables to action‐angle variables yields an approximate expression for the tangential drift (long‐time average of the tangential speed) that estimates the tangential winds. The analysis is extended numerically to the case of warm core offset, where the two Gaussians have different centres.

Upper‐level trajectories in the prototype problem for tropical cyclone intensification

“…For a field of air parcels moving in a prescribed pressure field, the mass continuity constraint must, in general, be forfeited. On these grounds, we have reservations about the results of the Cohen and Paldor study.…”

“…A more recent article is that by Cohen and Paldor (2020). Whereas our trajectory calculations are based on a three‐dimensional numerical simulation and focus on trajectories that start within the inflow layer below the outflow layer, Cohen and Paldor consider only trajectories in the outflow layer within an axisymmetric configuration. Moreover, they prescribe the pressure gradient in this layer.…”

Characteristics of the upper-level outflow and its impact on the rapid intensification of Typhoon Roke (2011)

“…Both model simulations (Cohen et al, 2017) and observations (Cohen et al, 2019) suggested that the outflow layer may exhibit a lowpressure center surrounded by high pressure due to the strong outward-pointing centrifugal and pressure gradient forces that cannot be counterbalanced by the inward-pointing Coriolis force. Furthermore, Cohen and Paldor (2020) analyzed the Lagrangian trajectories of air parcels in the outflow layer and described the dynamics using an integrable, two degrees-offreedom and angular momentum conserving Hamiltonian system with a single non-dimensional parameter. Several studies focused on the characteristics of low Richardson number in the outflow layer (Emanuel and Rotunno, 2011;Emanuel, 2012;Duran and Molinari, 2016).…”