Contribution of mean and eddy momentum processes to tropical cyclone intensification
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Abstract An idealized, three‐dimensional, 1 km horizontal grid spacing numerical simulation of a rapidly intensifying tropical cyclone is used to extend basic knowledge on the role of mean and eddy momentum transfer on the dynamics of the intensification process. Examination of terms in the tangential and radial velocity tendency equations provides an improved quantitative understanding of the dynamics of the spin‐up process within the inner‐core boundary layer and eyewall regions of the system‐scale vortex. Unbalanced and non‐axisymmetric processes are prominent features of the rapid spin‐up process. In particular, the wind asymmetries, associated in part with the asymmetric deep convection, make a substantive contribution ( ∼ 30%) to the maximum wind speed inside the radius of this maximum. The analysis provides a novel explanation for inflow jets sandwiching the upper‐tropospheric outflow layer which are frequently found in numerical model simulations. In addition, it provides an opportunity to assess the applicability of generalized Ekman balance during rapid vortex spin‐up. The maximum tangential wind occurs within and near the top of the frictional inflow layer and as much as 10 km inside the maximum gradient wind. Spin‐up in the friction layer is accompanied by supergradient winds that exceed the gradient wind by up to 20%. Overall, the results affirm prior work pointing to significant limitations of a purely axisymmetric balance description, for example, gradient balance/Ekman balance, when applied to a rapidly intensifying tropical cyclone.Keywords:
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Inflow
Ekman layer
Ekman number
Thermal wind
Rainband
Outflow
Large-Eddy Simulation
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Abstract The low‐level cold pool just under a tropical cyclone eyewall and its effect on the formation of inner rainbands are studied, through idealized convection‐permitting simulations. Analysis of the potential temperature budget indicates that the formation of the eyewall cold pool (ECP) results from the evaporation of eyewall rainfall. The ECP is a barrier to boundary layer inflow, which results in clear convergence and vertical updraft at its outer edge. A budget analysis of the vertical motion tendency also indicates that the sum of the buoyancy and vertical pressure gradient terms makes a large contribution to the vertical updraft at the outer edge of the ECP. This then promotes the formation of convection cells and an inner rainband. Two sensitivity experiments further verify that the intensity of the ECP‐triggered inner rainbands is positively correlated with the magnitude of the radial gradient of potential temperature at the outer edge of the ECP.
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Rainband
Inflow
Leading edge
Pressure-gradient force
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A new hourly rainfall dataset is formed using variational method, based on raingauge and radar-retrieved rainfall intensity. The new data are used to investigate temporal and spatial variations of precipitation structure within 111-km radius centered the typhoon, especially the evolution of rainfall structure during the concentric eyewalls cycle before Saomai landfall. The authors find that typhoon Saomai had concentric eyewalls before it landed, and the mean radii of the inner and outer eyewalls were 24 km and 59 km, respectively. The radius of the outer eyewall did not minish due to the rapid landfall of typhoon Saomai after the concentric eyewalls combination. During concentric eyewalls circulation, the precipitation in the inner and outer eyewalls and rainband regions was very heavy. In the outer eyewall region, the time series of mean rainfall rate was more variable than that in the inner eyewall and rainband regions. And in the inner and outer eyewalls regions, the mean rainfall rate increased with time, but in the rainband region it decreased. The precipitation in the inner-core and outer regions was also heavy, and the mean rainfall rate in the inner-core region increased abruptly about the three hours before Saomai landed, and then it decreased, accompanied with the reduction of the typhoon intensity after Saomai landed. The distribution of precipitation of typhoon Saomai was asymmetric. Before Saomai landfall, the maximum rainfall rates in the inner eyewall, outer eyewall, and rainband regions occurred in the right quadrant relative to the storm moving track, and the azimuth in the rainband region was always to the right of those in the inner and outer eyewalls regions. The azimuth of the maximum precipitation in outer eyewall and rainband regions varied with time during the concentric circulation. After typhoon Saomai landfall more precipitation in the inner-core and outer regions appeared in the back quadrant relative to the storm track.
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With the Ekman momentum approximation,the influence of atmospheric baroclinity on the dynamics of boundarylayer is studied.Some new results are obtained.These results show that the atmospheric baroclinity plays an importantrole in altering the horizontal velocity of Ekman boundary layer and its angle with the horizontal wind velocity compo-nent near the surface.There are three different physical factors affecting the nonlinear Ekman suction,the vertical mo-tion at the top of boundary layer:first,barotropic geostrophic relative vorticity at the ground;second,the thermal windvorticity induced by the baroclinity;and third,the nonlinear interaction between the barotropic geostrophic relativevorticity and the baroclinic thermal wind vorticity.These results may provide a better physical basis for theparameterization of boundary layer and the interpretation of the numerical modeling results.
Ekman layer
Barotropic fluid
Ekman transport
Thermal wind
Ekman number
Ocean dynamics
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Abstract Previous studies have demonstrated the importance of the downwind development of a rainband in secondary eyewall formation (SEF) in tropical cyclones. However, the details of the transition from rainbands to a secondary eyewall are not well understood. This study examined the convection onset in the early stage of SEF in the numerically simulated Typhoon Soudelor (2015). Results show that the convection onset in the SEF region was associated with the organization of a stationary band complex (SBC), which resulted from the outward propagation of inner rainbands and downwind propagation of secondary rainbands, with convection enhanced in the downwind sector of the SBC. The outward propagation of the inner rainbands involved the mesoscale pressure perturbations-induced unbalanced boundary layer dynamics, which were responsible for the radial outflow above the boundary layer inflow and the related secondary circulation on the inward side of the rainband. In the downwind propagation, secondary rainbands evolved into stratiform precipitation in the downshear-left quadrant, where mesoscale descending inflow continuously occurred and transported low equivalent potential temperature ( θ e ) and dry air downward and downwind, leading to a decrease in low-level θ e on the outward side of the rainband. A balanced state of the cold pool dynamics was finally reached in the downwind sector of the SBC between the supergradient-induced vertical wind shear and the low- θ e -induced cold pool, resulting in the convection enhancement. Our results strongly suggest that both the unbalanced dynamics and rainband processes were essential in the early stage of SEF. Significance Statement The purpose of this study is to better understand how spiral rainbands evolve into a stationary rainband complex (SBC), and the physical processes responsible for the convection enhancement in the downwind sector of the SBC. This is important because it is this downwind convective enhancement that leads to the secondary eyewall formation (SEF). Our results provide the details of the transition from rainbands to a secondary eyewall and suggest that both the unbalanced boundary layer dynamics and rainband processes are essential in the early stage of SEF.
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Microphysical characteristics of the raindrop size distribution(RSD)in Typhoon Morakot(2009) have been studied through the PARSIVEL disdrometer measurements at one site in Fujian province,China during the passage of the storm from 7 to 10 August 2009.The time evolution of the RSD reveals different segments of the storm.Significant difference was observed in the microphysical characteristics between the outer rainband and the eyewall;the eyewall precipitation had a broader size distribution(a smaller slope) than the outer rainband and eye region.The outer rainband and the eye region produced stratiform rains while the eyewall precipitation was convective or mixed stratiform-convective.The RSD was typically characterized by a single peak distribution and well represented by the gamma distribution.The relations between the shape(μ)and slope(Λ)of the gamma distribution and between the reflectivity(Z)and rainfall rate(R)have been investigated.Based on the NW–Dm relationships,we suggest that the stratiform rain for the outer rainband and the eye region was formed by the melting of graupel or rimed ice particles,which likely originated from the eyewall clouds.
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Abstract Ocean currents in the surface boundary layer are sensitive to a variety of parameters not included in classic Ekman theory, including the vertical structure of eddy viscosity, finite boundary layer depth, baroclinic pressure gradients, and surface waves. These parameters can modify the horizontal and vertical flow in the near-surface ocean, making them of first-order significance to a wide range of phenomena of broad practical and scientific import. In this work, an approximate Green’s function solution is found for a model of the frictional ocean surface boundary layer, termed the generalized Ekman (or turbulent thermal wind) balance. The solution admits consideration of general, more physically realistic forms of parameters than previously possible, offering improved physical insight into the underlying dynamics. Closed form solutions are given for the wind-driven flow in the presence of Coriolis–Stokes shear, a result of the surface wave field, and thermal wind shear, arising from a baroclinic pressure gradient, revealing the common underlying physical mechanisms through which they modify currents in the ocean boundary layer. These dynamics are further illustrated by a case study of an idealized two-dimensional front. The solutions, and estimates of the global distribution of the relative influence of surface waves and baroclinic pressure gradients on near-surface ocean currents, emphasize the broad importance of considering ocean sources of shear and physically realistic parameters in the Ekman problem.
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Turbulence Modeling
Ekman number
Thermal wind
Ekman transport
Pressure gradient
Ocean dynamics
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Eyewall replacement cycles (ERCs) are frequently observed during the evolution of intensifying tropical cyclones (TCs). Although intensely studied in recent years, the underlying mechanisms of ERCs are still not well understood, and a timely accurate forecast of ERCs remains to be a challenge. To advance our understanding of ERCs and provide insights into the improvement of numerical forecast of ERCs, a series of three-dimensional full physics simulations is performed using the Weather Research and Forecasting (WRF) model to investigate ERCs in TC-like vortices on an f plane. The simulated ERC in the control experiment possesses key features similar to those observed in real TCs including the formation and development of a secondary tangential wind maximum associated with the outer eyewall. The Sawyer-Eliassen diagnoses and tangential momentum budget analyses are performed to investigate the mechanisms underlying the secondary eyewall formation (SEF) and ERC. The simulations show the crucial roles of outer rainband heating in governing the formation and development of the secondary tangential wind maximum and demonstrate that the outer rainband convection must reach a critical strength relative to the eyewall convection before SEF and ERC can occur. The diagnoses reveal a positive feedback among low-level convection, acceleration of tangential winds and convergence of radial flow in the upper boundary layer, and surface evaporation that leads to the development of outer rainband convection and formation of secondary eyewall, and a mechanism for the demise of inner eyewall that involves the interaction between the transverse circulations induced by eyewall and outer rainband convection.
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Numerical simulations of three-dimensional rapidly rotating Rayleigh–Bénard convection are performed by employing an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parametrized Ekman pumping boundary conditions and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier–Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations (DNS) and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for Prandtl number $Pr\approx 1$ when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman number ( $E\approx 10^{-7}$ ); good qualitative agreement is achieved for $Pr>1$ . Similar to studies with stress-free boundaries, four spatially distinct flow morphologies exists. Despite the presence of frictional drag at the upper and/or lower boundaries, a strong non-local inverse cascade of barotropic (i.e. depth-independent) kinetic energy persists in the final regime of geostrophic turbulence and is dominant at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries, Ekman friction is found to attenuate the efficiency of the upscale energy transport and, unlike the case of stress-free boundaries, rapidly saturates the barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is strong enough to prevent the development of a coherent dipole vortex condensate. Instead, vortex pairs are found to be intermittent, varying in both time and strength. For all combinations of boundary conditions, a Nastrom–Gage type of spectrum of kinetic energy is found, where the power-law exponent changes from ${\approx}-3$ to ${\approx}-5/3$ , i.e. from steep to shallow, as the spectral wavenumber increases.
Ekman number
Ekman transport
Ekman layer
Thermal wind
Barotropic fluid
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Microphysical characteristics of the raindrop size distribution(RSD)in Typhoon Morakot(2009) have been studied through the PARSIVEL disdrometer measurements at one site in Fujian province,China during the passage of the storm from 7 to 10 August 2009.The time evolution of the RSD reveals different segments of the storm.Significant difference was observed in the microphysical characteristics between the outer rainband and the eyewall;the eyewall precipitation had a broader size distribution(a smaller slope) than the outer rainband and eye region.The outer rainband and the eye region produced stratiform rains while the eyewall precipitation was convective or mixed stratiform-convective.The RSD was typically characterized by a single peak distribution and well represented by the gamma distribution.The relations between the shape(μ)and slope(Λ)of the gamma distribution and between the reflectivity(Z)and rainfall rate(R)have been investigated.Based on the NW-Dm relationships,we suggest that the stratiform rain for the outer rainband and the eye region was formed by the melting of graupel or rimed ice particles,which likely originated from the eyewall clouds.
Rainband
Eye
Typhoon
Graupel
Disdrometer
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