A Possible Three-Dimensional Mechanism for Oscillating Wobbles in Tropical Cyclone–Like Vortices with Concentric Eyewalls

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.

Structure and Maintenance Mechanism of Long-Lived Concentric Eyewalls Associated with Simulated Typhoon Bolaven (2012)

Typhoons with long-lived concentric eyewalls (CEs) are more intense than those with short-lived CEs. It is important for more accurate prediction of typhoon intensity to understand the maintenance mechanism of the long-lived CEs. To study the mechanism of the long-term maintenance of CEs, a numerical experiment of Typhoon Bolaven (2012) is performed using a nonhydrostatic model with full physics. Two aspects of the maintenance of simulated CEs are investigated: the maintenance of the inner eyewall and the contraction of the outer eyewall. To examine the maintenance of the inner eyewall, the equivalent potential temperature budget and air parcel trajectories of the simulated inner eyewall are calculated. The results show that the entropy supply to the inner eyewall is sufficient to maintain the inner eyewall after secondary eyewall formation (SEF). During the early period after SEF, entropy is supplied by an axisymmetric inflow, and later it is supplied by nonaxisymmetric flows of the outer eyewall. To examine the contraction of the outer eyewall, the potential vorticity (PV) budget of the outer eyewall is diagnosed. The result reveals that the negative contribution to the contraction of the outer PV peak (i.e., the outer eyewall) in the early period is the negative PV generation due to axisymmetric advection and diabatic heating just inside of the outer PV peak. In the later period, the negative PV generation due to nonaxisymmetric structure is important for the prevention of contraction. The present study reveals that the structure of the outer eyewall plays important roles in the maintenance of long-lived CEs.

Concentric Eyewall Asymmetries in Hurricane Gonzalo (2014) Observed by Airborne Radar

Two eyewall replacement cycles were observed in Hurricane Gonzalo by the NOAA P3 Tail (TA) radar and the recently developed NASA High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar. These observations captured detailed precipitation and kinematic features of Gonzalo’s concentric eyewalls both before and after the outer eyewall’s winds became the vortex maximum winds. The data were analyzed relative to the deep-layer environmental wind shear vector. During the beginning eyewall replacement cycle stages, the inner and outer eyewalls exhibited different asymmetries. The inner eyewall asymmetry exhibited significant low-level inflow, updrafts, and positive tangential acceleration in the downshear quadrants, consistent with observational and theoretical studies. The outer eyewall asymmetry exhibited these features in the left-of-shear quadrants, further downwind from those of the inner eyewall. It is suggested that the low-level inflow occurring at the outer but not at the inner eyewall in the downwind regions signals a barrier effect that contributes to the eventual decay of the inner eyewall. Toward the later eyewall replacement stages, the outer eyewall asymmetry shifts upwind, becoming more aligned with the asymmetry of the earlier inner eyewall. This upwind shift is consistent with the structural evolution of eyewall replacement as the outer eyewall transitions into the primary eyewall of the storm.

Doppler Radar Analysis of Triple Eyewalls in Typhoon Usagi (2013)

Strong tropical cyclones often undergo eyewall replacement cycles that are accompanied by concentric eyewalls and/or rapid intensity changes while the secondary eyewall contracts radially inward and eventually replaces the inner eyewall. To the best of our knowledge, the only documented partial/incomplete tertiary eyewall has been mostly inferred from two-dimensional satellite images or one-dimensional aircraft flight-level measurements that can be regarded as indirect and tangential. This study presents the first high spatial and temporal resolution Doppler radar observations of a tertiary eyewall formation event in Typhoon Usagi (2013) over a 14-h time period before it makes landfall. The primary (tangential) and secondary (radial) circulations of Usagi deduced from the Ground-Based Velocity Track Display (GBVTD) methodology clearly portrayed three distinct axisymmetric maxima of radar reflectivity, tangential wind, vertical velocity, and vertical vorticity. Usagi’s central pressure steadily deepened during the contraction of the secondary and tertiary eyewalls until the tertiary eyewall hit the coast of southeast China, which erminated the intensification of the storm.

Relationship between Typhoons with Concentric Eyewalls and ENSO in the Western North Pacific Basin

The typhoons with concentric eyewalls (CE) over the western North Pacific in different phases of the El Niño–Southern Oscillation (ENSO) between 1997 and 2012 are studied. They find a good correlation (0.72) between the annual CE typhoon number and the oceanic Niño index (ONI), with most of the CE typhoons occurring in the warm and neutral episodes. In the warm (neutral) episode, 55% (50%) of the typhoons possessed a CE structure. In contrast, only 25% of the typhoons possessed a CE structure in the cold episode. The CE formation frequency is also significantly different with 0.9 (0.2) CEs per month in the warm (cold) episode. There are more long-lived CE cases (CE structure maintained more than 20 h) and typhoons with multiple CE formations in the warm episodes. There are no typhoons with multiple CE formations in the cold episode. The warm episode CE typhoons generally have a larger size, stronger intensity, and smaller variation in convective activity and intensity. This may be due to the fact that the CE formation location is farther east in the warm episodes. Shifts in CE typhoon location with favorable conditions thus produce long-lived CE typhoons and multiple CE formations. The multiple CE formations may lead to expansion of the typhoon size.

Long-Lived Concentric Eyewalls in Typhoon Soulik (2013)

The authors report on western North Pacific Typhoon Soulik (2013), which had two anomalously long-lived concentric eyewall (CE) episodes, as identified from microwave satellite data, radar data, and total precipitable water data. The first period was 25 h long and occurred while Soulik was at category 4 intensity. The second period was 34 h long and occurred when Soulik was at category 2 intensity. A large moat and outer eyewall width were present in both CE periods, and there was a significant contraction of the inner eyewall radius from the first period to the second period. The typhoon intensity decrease was partially due to encountering unfavorable environmental conditions of low ocean heat content and dry air, even though inner eyewall contraction would generally support intensification. The T–Vmax diagram (where T is the brightness temperature and Vmax is the best track–estimated intensity) is used to analyze the time sequence of the intensity and convective activity. The convective activity (and thus the integrated kinetic energy) increased during the CE periods despite the weakening of intensity.

How Does the Boundary Layer Contribute to Eyewall Replacement Cycles in Axisymmetric Tropical Cyclones?

Three diagnostic models of the axisymmetric tropical cyclone boundary layer, with different levels of approximation, are applied to the problem of tropical cyclones with concentric eyewalls. The outer eyewall is shown to have an inherently stronger frictional updraft than the inner because it is in an environment of lower vorticity. Similarly, a relatively weak local enhancement of the radial vorticity gradient outside the primary radius of maximum winds can produce a significant frictional updraft, even if there is no outer wind maximum. Based on these results, it is proposed that the boundary layer contributes to the formation of outer eyewalls through a positive feedback among the local enhancement of the radial vorticity gradient, the frictional updraft, and convection. The friction-induced secondary circulation associated with the inner eyewall is shown to weaken as the outer wind maximum strengthens and/or contracts, so boundary layer processes will contribute, along with the heating-induced secondary circulation, to the weakening of the inner eyewall during an eyewall replacement cycle. An integral mass constraint on the friction-induced secondary circulation is derived and used to examine the oft-stated proposition that “the outer eyewall uses up the inflowing energy-rich boundary layer air.” Using the integral constraint, the author argues that formation of a secondary eyewall will tend to increase the total friction-induced secondary circulation and that, if the moat between the two eyewalls has a local vorticity minimum, then sufficient subsidence may occur there to maintain the primary eyewall's updraft. It is noted, however, that the enthalpy of the updraft is important as well as its mass.