Roles of Barotropic Instability across the Moat in Inner Eyewall Decay and Outer Eyewall Intensification: Three-Dimensional Numerical Experiments

2020 ◽  
Author(s):  
Tsz-Kin Lai ◽  
Eric A. Hendricks ◽  
Konstantinos Menelaou ◽  
M. K. Yau
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclones ◽  
Numerical Experiments ◽  
Radial Flow ◽  
Three Dimensional ◽  
Barotropic Instability ◽  
Radar Imagery ◽  
Eyewall Replacement Cycles ◽  
Significant Intensification

AbstractRadar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls became elliptical prior to their dissipation during the eyewall replacement cycles, indicating that the barotropic instability (BI) across the moat (a.k.a. type-2 BI) may play a role. To further examine the physics of inner eyewall decay and outer eyewall intensification under the influence of the type-2 instability, three-dimensional numerical experiments are performed. In the moist full-physics run, the simulated vortex exhibits the type-2 instability and the associated azimuthal wavenumber-2 radial flow pattern. The absolute angular momentum (AAM) budget calculation indicates, after the excitation of the type-2 instability, a significant intensification in the negative radial advection of AAM at the inner eyewall. It is further shown that the changes in radial AAM advection largely result from the eddy processes associated with the type-2 instability, and contribute significantly to the inner eyewall decay. The budget calculation also suggests that the type-2 instability can accelerate the inner eyewall decay in concert with the boundary layer cut-off effect. Another dry no-physics idealised experiment is conducted and the result shows that the type-2 instability alone is able to weaken the inner eyewall and also strengthen the outer eyewall with non-negligible effect.

Roles of Barotropic Instability across the Moat in Inner Eyewall Decay and Outer Eyewall Intensification: Essential Dynamics

2021 ◽  
Vol 78 (5) ◽  
pp. 1411-1428
Author(s):  
Tsz-Kin Lai ◽  
Eric A. Hendricks ◽  
M. K. Yau ◽  
Konstantinos Menelaou
Keyword(s):  
Angular Momentum ◽  
Unstable Mode ◽  
Numerical Study ◽  
Three Dimensional ◽  
Barotropic Instability ◽  
Radial Transport ◽  
Radar Imagery ◽  
Case Simulation ◽  
Eyewall Replacement Cycles

AbstractIntense tropical cyclones (TCs) often experience secondary eyewall formations and the ensuing eyewall replacement cycles. Better understanding of the underlying dynamics is crucial to make improvements to the TC intensity and structure forecasting. Radar imagery of some double-eyewall TCs and a real-case simulation study indicated that the barotropic instability (BI) across the moat (aka type-2 BI) may play a role in inner eyewall decay. A three-dimensional numerical study accompanying this paper pointed out that type-2 BI is able to withdraw the inner eyewall absolute angular momentum (AAM) and increase the outer eyewall AAM through the eddy radial transport of eddy AAM. This paper explores the reason why the eddy radial transport of eddy AAM is intrinsically nonzero. Linear and nonlinear shallow water experiments are performed and they produce expected evolutions under type-2 BI. It will be shown that only nonlinear experiments have changes in AAM over the inner and outer eyewalls, and the changes solely originate from the eddy radial transport of eddy AAM. This result highlights the importance of nonlinearity of type-2 BI. Based on the distribution of vorticity perturbations and the balanced-waves arguments, it will be demonstrated that the nonzero eddy radial transport of eddy AAM is an essential outcome from the intrinsic interaction between the mutually growing vortex Rossby waves across the moat under type-2 BI. The analyses of the most unstable mode support the findings and will further attribute the inner eyewall decay and outer eyewall intensification to the divergence and convergence of the eddy angular momentum flux, respectively.

scholarly journals Barotropic Instability across the Moat and Inner Eyewall Dissipation: A Numerical Study of Hurricane Wilma (2005)

2019 ◽  
Vol 76 (4) ◽  
pp. 989-1013
Author(s):  
Tsz-Kin Lai ◽  
Konstantinos Menelaou ◽  
M. K. Yau
Keyword(s):  
Growth Rate ◽  
Tropical Cyclones ◽  
Potential Role ◽  
Radial Flow ◽  
Numerical Study ◽  
Barotropic Instability ◽  
Hurricane Wilma ◽  
Radar Imagery ◽  
Barotropic Vorticity

Abstract Radar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls become elliptical prior to their dissipation. These elliptical features indicate that the barotropic instability (BI) across the moat (aka, type-2 BI) may play a role in the process. To investigate the mechanism for dissipation, a WRF simulation of Hurricane Wilma (2005) is performed. The results reveal an elliptical elongation of the inner eyewall and a change in the structure of the radial flow from wavenumber (WN) 1 to WN 2 at the lower levels. A linear stability analysis as well as idealized nonlinear experiments using a nondivergent barotropic vorticity model initialized with the vorticity fields before the change in the dominant wavenumber of the radial flow are presented with the results supporting the presence of a type-2 BI at the lower levels. The accompanying WN-2 radial flow is also found to dilute the vorticity within the inner eyewall and the eye. However, this dilution is not seen at higher levels as the type-2 BI becomes weak and short lived at the middle levels and reaches its weakest strength at the upper levels. This phenomenon is traced to the fact that a higher growth rate comes with a narrower moat for type-2 BI. As the outward slope of the outer eyewall is larger than that of the inner eyewall, the moat width increases with height so that the growth rate decreases with height. The results presented here thus highlight the potential role played by the barotropic instability across the moat in inner eyewall dissipation.

scholarly journals A Triggering Mechanism for Rapid Intensification of Tropical Cyclones

2015 ◽  
Vol 72 (7) ◽  
pp. 2666-2681 ◽  
Author(s):  
Yoshiaki Miyamoto ◽  
Tetsuya Takemi
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Convective Cell ◽  
Rapid Intensification ◽  
Rotating Fluid ◽  
Coriolis Parameter ◽  
Maximum Tangential Velocity

Triggering processes for the rapidly intensifying phase of a tropical cyclone (TC) were investigated on the basis of numerical experiments using a three-dimensional nonhydrostatic model. The results revealed that the rapid intensification of the simulated TC commenced following the formation of a circular cloud, which occurred about 12 h after the TC became essentially axisymmetric. The circular cloud (eyewall) evolved from a cloudy convective cell that was originally generated near the radius of maximum wind speed (RMW). The development of the convective cell in the eyewall was closely related to the radial location of the strong boundary layer convergence of axisymmetric flow. The radius of maximum convergence (RMC) was small relative to the RMW when the TC vortex was weak, which is consistent with the boundary layer theory for a rotating fluid system on a frictional surface. As the TC intensified, the RMC approached the RMW. An eyewall was very likely to form in the simulated TC when the RMC approached the RMW. Because the RMC is theoretically determined by a Rossby number defined by the maximum tangential velocity, RMW, and Coriolis parameter, a series of numerical experiments was conducted by changing the three parameters. The results were consistent with the hypothesis that intensification occurs earlier for larger Rossby numbers. This finding indicates that initial TC vortices with larger Rossby numbers are more likely to experience rapid intensification and, hence, to evolve into strong hurricanes.

scholarly journals Why Do Model Tropical Cyclones Intensify More Rapidly at Low Latitudes?

2015 ◽  
Vol 72 (5) ◽  
pp. 1783-1804 ◽  
Author(s):  
Roger K. Smith ◽  
Gerard Kilroy ◽  
Michael T. Montgomery
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclones ◽  
Three Dimensional ◽  
Feedback Mechanism ◽  
Meridional Overturning Circulation ◽  
Time Dependent ◽  
Lower Latitude ◽  
Tangential Wind ◽  
Low Latitudes ◽  
Diabatic Forcing

Abstract The authors examine the problem of why model tropical cyclones intensify more rapidly at low latitudes. The answer to this question touches on practically all facets of the dynamics and thermodynamics of tropical cyclones. The answer invokes the conventional spin-up mechanism, as articulated in classical and recent work, together with a boundary layer feedback mechanism linking the strength of the boundary layer inflow to that of the diabatic forcing of the meridional overturning circulation. The specific role of the frictional boundary layer in regulating the dependence of the intensification rate on latitude is discussed. It is shown that, even if the tangential wind profile at the top of the boundary layer is held fixed, a simple, steady boundary layer model produces stronger low-level inflow and stronger, more confined ascent out of the boundary layer as the latitude is decreased, similar to the behavior found in a time-dependent, three-dimensional numerical model. In an azimuthally averaged view of the problem, the most prominent quantitative differences between the time-dependent simulations at 10° and 30°N are the stronger boundary layer inflow and the stronger ascent of air exiting the boundary layer, together with the much larger diabatic heating rate and its radial gradient above the boundary layer at the lower latitude. These differences, in conjunction with the convectively induced convergence of absolute angular momentum, greatly surpass the effects of rotational stiffness (inertial stability) and evaporative-wind feedback that have been proposed in some prior explanations.

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

2013 ◽  
Vol 70 (9) ◽  
pp. 2808-2830 ◽  
Author(s):  
Jeffrey D. Kepert
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclones ◽  
Secondary Circulation ◽  
Local Enhancement ◽  
Wind Maximum ◽  
Boundary Layer Processes ◽  
Mass Constraint ◽  
Concentric Eyewalls ◽  
Eyewall Replacement Cycles ◽  
Tropical Cyclone Boundary Layer

Abstract 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.

Revisiting the Dynamics of Eyewall Contraction of Tropical Cyclones

2019 ◽  
Vol 76 (10) ◽  
pp. 3229-3245 ◽  
Author(s):  
Yuanlong Li ◽  
Yuqing Wang ◽  
Yanluan Lin
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclones ◽  
Directional Derivative ◽  
Three Dimensional ◽  
Lower Boundary ◽  
Lower Troposphere ◽  
Surface Friction ◽  
Three Dimensions ◽  
Tangential Wind ◽  
Lower Boundary Layer

Abstract The dynamics of eyewall contraction of tropical cyclones (TCs) has been revisited in this study based on both three-dimensional and axisymmetric simulations and dynamical diagnostics. Because eyewall contraction is closely related to the contraction of the radius of maximum wind (RMW), its dynamics is thus often studied by examining the RMW tendency in previous studies. Recently, Kieu and Stern et al. proposed two different frameworks to diagnose the RMW tendency but had different conclusions. In this study, the two frameworks are evaluated first based on theoretical analysis and idealized numerical simulations. It is shown that the framework of Kieu is a special case of the earlier framework of Willoughby et al. if the directional derivative is applied. An extension of Stern et al.’s approach not only can reproduce but also can predict the RMW tendency. A budget of the azimuthal-mean tangential wind tendency indicates that the contributions by radial and vertical advections to the RMW tendency vary with height. Namely, radial advection dominates the RMW contraction in the lower boundary layer, and vertical advection favors the RMW contraction in the upper boundary layer and lower troposphere. In addition to the curvature, the increase of the radial gradient of horizontal mixing (including the resolved eddy mixing in three dimensions) near the eyewall prohibits eyewall contraction in the lower boundary layer. Besides, the vertical mixing including surface friction also plays an important role in the cessation of eyewall contraction in the lower boundary layer.

Numerical experiments in boundary-layer stability

1984 ◽  
Vol 392 (1803) ◽  
pp. 373-389 ◽  
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Boundary Layer Stability ◽  
Physical Processes ◽  
Navier Stokes Equations

Numerical solution of the three-dimensional incompressible Navier-Stokes equations is used to study the instability of a flat-plate boundary layer in a manner analogous to the vibrating-ribbon experiments. Flow field structures are observed which are very similar to those found in the vibrating-ribbon experiment to which computational initial conditions have been matched. Stream wise periodicity is assumed in the simulation so that the evolution occurs in time, but the events that constitute the instability are so similar to the spatially occurring ones of the laboratory that it seems clear the physical processes involved are the same. A spectral and finite difference numerical algorithm is employed in the simulation.

scholarly journals The Boundary Layer Dynamics of Tropical Cyclone Rainbands

2018 ◽  
Vol 75 (11) ◽  
pp. 3777-3795 ◽  
Author(s):  
Jeffrey D. Kepert
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Tropical Cyclone ◽  
Tropical Cyclones ◽  
Surface Wind ◽  
Three Dimensional ◽  
Surface Wind Speed ◽  
Wind Maximum ◽  
Boundary Layer Dynamics ◽  
Spiral Bands

Abstract Spiral bands are ubiquitous features in tropical cyclones and significantly affect boundary layer thermodynamics, yet knowledge of their boundary layer dynamics is lacking. Prompted by recent work that has shown that relatively weak axisymmetric vorticity perturbations outside of the radius of maximum winds in tropical cyclones can produce remarkably strong frictional convergence, and by the observation that most secondary eyewalls appear to form by the “wrapping up” of a spiral rainband, the effect of asymmetric vorticity features that mimic spiral bands is studied. The mass field corresponding to an axisymmetric vortex with added spiral vorticity band is constructed using the nonlinear balance equation, and supplied to a three-dimensional boundary layer model. The resulting flow has strong low-level convergence and a marked updraft extending along the vorticity band and some distance downwind. There is a marked along-band wind maximum in the upper boundary layer, similar to observations, which is up to about 20% stronger than the balanced flow. A marked gradient in the inflow-layer depth exists across the band and there is an increase in the surface wind factor (the ratio of surface wind speed to nonlinear-balanced wind speed) near the band. The boundary layer dynamics near a rainband therefore form a continuum with the flow near a secondary eyewall. None of these features are due to convective momentum transports, which are absent from the model. The sensitivities of the flow to band length, width, location, crossing angle, and amplitude are examined, and the possible contribution of boundary layer dynamics to the formation of the tropical cyclone rainbands discussed.

Comments on “How Does the Boundary Layer Contribute to Eyewall Replacement Cycles in Axisymmetric Tropical Cyclones?”

2014 ◽  
Vol 71 (12) ◽  
pp. 4682-4691 ◽  
Author(s):  
Michael T. Montgomery ◽  
Sergio F. Abarca ◽  
Roger K. Smith ◽  
Chun-Chieh Wu ◽  
Yi-Hsuan Huang
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclones ◽  
Eyewall Replacement Cycles
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