Comparative assessment of validity of gradient wind models for a translating tropical cyclone

Accurate and conservative evaluations of the gradient wind in the free atmosphere are needed to account for high-wind hazards when designing wind resistance for critical infrastructure. This paper compared the validity of three existing gradient wind models to select an appropriate evaluation model, which enables us to accurately compute the asymmetric gradient wind field of a translating tropical cyclone under the condition of a symmetric pressure distribution and a constant translation velocity. The validity of the three models was assessed by evaluating the residuals in momentum conservation equations for the gradient wind under a specific tropical cyclone condition. The magnitude of the residuals was considered to be the measure of error in the gradient wind derived from each model. The results showed that the most frequently used model yielded the largest magnitude of residuals with the lowest maximum wind speed among the three models. The wind characteristics of the three models were validated using archived observation data of hurricanes. The physical reason for the difference in maximum wind speed among the three models was explained by the difference in the streamline feature of the gradient wind field. It was also revealed that the differences in maximum wind speed and magnitude of residuals became more pronounced as the translation speed and the intensity of a tropical cyclone increased. The comparative assessment of the three gradient wind models allowed us to identify the best model for use in conservative wind-resistant design and high-wind risk estimates.

Study of ageostrophy during strong, nonlinear eddy-front interaction in the Gulf of Mexico

The Loop Current (LC) system has long been assumed to be close to geostrophic balance despite its strong flow and the development of large meanders and strong frontal eddies during unstable phases. The region between the LC meanders and its frontal eddies was shown to have high Rossby numbers indicating nonlinearity; however, the effect of the nonlinear term on the flow has not been studied so far. In this study, the ageostrophy of the LC meanders is assessed using a high-resolution numerical model and geostrophic velocities from altimetry. A formula to compute the radius of curvature of the flow from the velocity field is also presented. The results indicate that during strong meandering, especially before and during LC shedding and in the presence of frontal eddies, the centrifugal force becomes as important as the Coriolis force and the pressure-gradient force: LC meanders are in gradient-wind balance. The centrifugal force modulates the balance and modifies the flow speed, resulting in a subgeostrophic flow in the LC meander trough around the LCFE and supergeostrophic flow in the LC meander crest. The same pattern is found when correcting the geostrophic velocities from altimetry to account for the centrifugal force. The ageostrophic percentage in the cyclonic and anticyclonic meanders is 47% ± 1% and 78% ± 8% in the model and 31% ± 3% and 78% ± 29% in the altimetry dataset, respectively. Thus, the ageostrophic velocity is an important component of the LC flow and cannot be neglected when studying the LC system.

Evaluation of the Assumptions in the Steady-State Tropical Cyclone Self-Stratified Outflow Using Three-Dimensional Convection-Allowing Simulations

The criteria and assumptions that were used to derive the steady-state tropical cyclone intensity and structure theory of Emanuel and Rotunno are assessed using three-dimensional convection-allowing simulations using the Weather Research and Forecasting Model. One real-data case of Hurricane Patricia (2015) and two idealized simulations with and without vertical wind shear are examined. In all three simulations, the gradient wind balance is valid in the inner-core region above the boundary layer. The angular momentum M and saturation entropy surfaces s* near the top of the boundary layer, in the outflow region and along the angular momentum surface that passes the low-level radius of maximum wind MRMW are nearly congruent, satisfying the criterion of slantwise moist neutrality in the vicinity of MRMW. The theoretically derived maximum wind magnitude above the boundary layer compares well with the simulated maximum tangential wind and gradient wind using the azimuthally averaged pressure field during the intensification and quasi-steady state of the simulated storms. The Richardson number analysis of the simulated storms shows that small Richardson number (0 < Ri ≤1) exists in the outflow region, related to both large local shear and small static stability. This criticality of the Richardson number indicates the existence of small-scale turbulence in the outflow region. We also show that the stratification of temperature along the M surfaces at the outflow region for steady-state hurricanes is approximately applicable in these three-dimensional simulations, while the radial distribution of gradient wind is qualitatively comparable to the theoretical radial profiles. Some caveats regarding the theory are also discussed.

An Evaluation of Hurricane Superintensity in Axisymmetric Numerical Models

Potential intensity (PI) is an analytical bound on steady, inviscid, axisymmetric hurricane wind speed. Studies have shown that simulated hurricane azimuthal wind speed can greatly exceed a PI bound on the maximum gradient wind. This disparity is called superintensity (SI) and has been attributed to the contribution of the unbalanced flow to the azimuthal wind. The goals of this study are 1) to introduce a new surface wind PI (PIs), based on a differential Carnot cycle and bounding the magnitude of the surface winds; 2) to evaluate SI in numerical simulations with respect to diagnostic PI bounds on gradient wind (PIg), azimuthal wind (PIa), and surface wind (PIs); and 3) to evaluate the validity of each PI bound based on the SI computations. Here, we define superintensity as the normalized amount by which each version of PI is exceeded by the quantity it bounds. Axisymmetric tropical cyclone simulations are performed while varying the parameterized turbulent mixing as a way of estimating SI in the inviscid limit. As the mixing length decreases, all three bounded wind speeds increase similarly from a sub-PI state to a marginally superintense state. This shows that all three forms of PI evaluated here are good approximations to their respective metrics in numerical simulations.

Trajectory optimization and control of stratospheric airship in cruising

Stratospheric airships are important platforms for near-space enduring cruising capability for several applications. Since energy shortage is one of major limiting factors in stratospheric airship, it is crucial to develop novel methods to reduce the requirement on energy systems. In this article, optimal trajectory of stratospheric airship in gradient wind fields is investigated in order to reduce energy consumption. First, polynomial expressions for wind gradients are assumed, and three-dimensional point mass airship equations of motion are used. Then the variety characters of energy for stratospheric airship are studied, the minimum power output of power system is taken as the optimizing target, and collocation approach is used to convert the trajectory optimization problem into parameters optimization. The characters of stratospheric airship’s cruising in three typical wind field are analyzed, including control and state parameters time histories, power changes for airship system, and so on. This research work shows that the greater the wind gradient, the more favorable to reduce energy consumptions, but the speed of the gradient wind cannot be too high.

Evaluation of a Time-Dependent Model for the Intensification of Tropical Cyclones

Axisymmetric and three-dimensional simulations are used to evaluate the theory of tropical cyclone (TC) intensification proposed by K. A. Emanuel, which is based on gradient wind balance and moist-neutral ascent along angular momentum (M) surfaces. According to the numerical model results, the intensification of the TC can be divided into two periods, phase I and phase II. During phase I, the TC intensifies while the M and saturation entropy (s*) surfaces evolve from nearly orthogonal to almost congruent. During phase II, the M and s* surfaces in the eyewall and outflow are congruent as the TC intensifies, which is consistent with Emanuel’s study. Therefore, the condition of moist slantwise neutrality in Emanuel’s study is sufficiently satisfied throughout the intensification in phase II. It is also found that the sensitivity of the intensification rates to the surface exchange coefficient for entropy Ck matches Emanuel’s theoretical result, which is that the intensification rate is proportional to Ck. However, the intensification rate varies in proportion to the surface exchange coefficient for momentum Cd, while the Emanuel model growth rate is insensitive to Cd. Furthermore, although the tendency diagnosed by Emanuel is qualitatively similar to the numerical model result during phase II, it is not quantitatively similar. The present analysis finds the inclusion of non–gradient wind effects in the theoretical framework of Emanuel’s study produces an intensification rate that is quantitatively similar to the numerical model results. The neglect of non–gradient wind effects in Emanuel’s study may be the reason for the different dependence of its intensification rate on Cd compared to that of the numerical model. Other aspects of Emanuel’s study in the context of recent research on TC intensification are discussed.