Gradient Wind Balance Research Articles

Parameterization of Vertical Turbulent Transport in the Inner Core of Tropical Cyclones and Its Impact on Storm Intensification. Part II: Understanding TC Intensification in a Generalized Sawyer–Eliassen Diagnostic Framework

Abstract An analytical method for diagnosing the interaction between the primary and secondary circulations of a tropical cyclone (TC) and vortex intensification is developed. It includes a diagnostic equation describing the mean secondary circulation of a TC in an unbalanced framework by including the radial eddy forcing in the analytical system. It is an extension of the Sawyer–Eliassen equation (SEE) developed from the strict gradient-wind balance. This generalized SEE (GSEE) remediates some of the limitations of SEE and can be used to diagnose both balanced and unbalanced dynamical processes during the TC evolution. Using GSEE, this study investigates how the tangential and radial eddy forcing affects the TC intensification simulated by the Hurricane Weather Research and Forecasting Model (HWRF) with differently parameterized turbulent mixing. The diagnostic results show that the supergradient component of radial eddy forcing contributes positively to the acceleration of the peak tangential wind, whereas the subgradient component of the radial eddy forcing tends to lower the height of peak tangential wind. The relative importance of negative and positive effects of tangential eddy forcing on TC intensification varies depending on the details of turbulence parameterization. For a turbulent kinetic energy (TKE) scheme used in this study, a large sloping curvature of mixing length in the low troposphere causes the tangential eddy forcing to produce a net positive tangential wind tendency near the location of the peak tangential wind. In contrast, a small sloping curvature of mixing length generates a net negative tangential wind tendency at the peak tangential wind. Significance Statement The interaction between the primary and secondary circulations of a tropical cyclone (TC) plays a key role in TC evolution. Historically, the secondary circulation induced by turbulence and convection is often described by a so-called Sawyer–Eliassen equation (SEE). While SEE has provided much insight into the TC dynamics in the past, the assumption of gradient-wind balance used by SEE prevents it from understanding TC unbalanced dynamics. To remediate the limitation, we extended the analytical framework into the unbalanced regime by including radial eddy forcing in the analytical system and derived a generalized SEE (GSEE). Using GSEE, this study investigates how tangential and radial eddy forcing affects TC intensification. The result highlights the importance of multiple roles that turbulence plays in the intensification of TCs.

Topography-Generated Submesoscale Coherent Vortices in the Kuroshio–Oyashio Extension Region from High-Resolution Simulations

Abstract A variety of submesoscale coherent vortices (SCVs) in the Kuroshio Extension region have been reported by recent observational studies, and the preliminary understanding of their properties, spatial distribution, and possible origins has progressively improved. However, due to relatively sparse in situ observations, the generation mechanisms of these SCVs and associated dynamic processes remain unclear. In this study, we use high-resolution model simulations to fill the gaps of the in situ observations in terms of the three-dimensional structures and life cycles of SCVs. Vortex detection and tracking algorithms are adopted and the characteristics of warm-core and cold-core SCVs are revealed. These vortices have finite Rossby numbers (0.25–0.4), and their horizontal structures can be well described by the Taylor vortex model in terms of the gradient wind balance. The vertical velocity field is characterized by a distinct dipole pattern with upwelling and downwelling cells at the vortex edge. It is very likely that both types of SCVs are generated along the eastern Japan coast through flow–topography interactions, and the Izu–Ogasawara Ridge and Hokkaido slope are found to be two important generation sites where topography friction produces extremely low potential vorticity. After leaving the boundary, SCVs can propagate over long distances and trap a water volume of ∼1011 m3.

Water Lifting and Outflow Gain of Kinetic Energy in Tropical Cyclones

Abstract While water lifting plays a recognized role in the global atmospheric power budget, estimates for this role in tropical cyclones vary from no effect to a major reduction in storm intensity. To better assess this impact, here we consider the work output of an infinitely narrow thermodynamic cycle with two streamlines connecting the top of the boundary layer in the vicinity of maximum wind (without assuming gradient-wind balance) to an arbitrary level in the inviscid free troposphere. The reduction of a storm’s maximum wind speed due to water lifting is found to decline with increasing efficiency of the cycle and is about 5% for maximum observed Carnot efficiencies. In the steady-state cycle, there is an extra heat input associated with the warming of precipitating water. The corresponding positive extra work is of an opposite sign and several times smaller than that due to water lifting. We also estimate the gain of kinetic energy in the outflow region. Contrary to previous assessments, this term is found to be large when the outflow radius is small (comparable to the radius of maximum wind). Using our framework, we show that Emanuel’s maximum potential intensity (E-PI) corresponds to a cycle where total work equals work performed at the top of the boundary layer (net work in the free troposphere is zero). This constrains a dependence between the outflow temperature and heat input at the point of maximum wind, but does not constrain the radial pressure gradient. We outline the implications of the established patterns for assessing real storms.

A proposal of a semi-empirical method for modifying the atmospheric pressure and wind fields of tropical cyclones

ABSTRACT The actions of wind and atmospheric pressure associated with tropical cyclones (e.g. typhoons) are considered the primary factors behind the generation of storm surges, though the fields used in meteorological models can sometimes deviate from observations. To improve these, the direct modification method (DMM) has been previously proposed, though this only modifies the wind field of a typhoon, and further development is necessary for applying it to storm surge hindcasts. The present work describes the development of a semi-empirical gradient wind balance-based method (GWB-M) for modifying both the wind and pressure fields in meteorological models, based on the dynamic relationship between the wind and pressure in typhoons (i.e. gradient wind balance). The applicability of GWB-M was assessed through a storm surge hindcast based on Typhoon Faxai in 2019, which generated powerful waves and a storm surge at Tokyo Bay. GWB-M improved the time series of 10 m wind speed and sea level pressure, with their spatial distributions being more realistic than those in DMM and blending parametric typhoon models (BM), which cannot take into account the influence of the complex topography around Tokyo Bay. Further, the maximum sea level anomalies after the typhoon made landfall were also captured by GWB-M with a higher accuracy than DMM.

Ballooning of Surface‐Advected Freshwater Bulge in a Rotating Frame

AbstractThis research delves into the intrinsic dynamics of an anticyclonic circulation that involves a ballooning bulge generated by a generalized river plume over an idealized shelf topography. The circulation features a strong jet‐stream overshooting the estuary mouth, curving toward the coast, and a returning flow along the shoreside edge. Our study focuses on the ballooning process, which involves the jet‐stream’s expansion and the freshwaters’ downstream movement. We demonstrate that the negative curvature vorticity, generated by flow inertia, sustains this process by amplifying the jet‐stream through anticyclonic gradient wind balance. Our research presents new insights into the origin of the negative curvature vorticity associated with the anticyclonic bending of the jet‐stream. The negative curvature vorticity regulates the ration between streamline’s and trajectory's radius, promoting the freshwaters’ escape from the jet‐stream and facilitating the bulge’s ballooning. The negative shear vorticity over the downshelf coast near the estuary mouth is the source of the curvature vorticity. The banking and curvature‐acceleration processes, which stand for the cross‐stream variation of the downstream component of the pressure force and the turning of the jet‐stream, respectively, trade‐off this shear vorticity to form the negative curvature vorticity.

Does Extended Sawyer–Eliassen Equation Effectively Capture the Secondary Circulation of a Simulated Tropical Cyclone?

Abstract The validity of the gradient wind balance in a tropical cyclone (TC) remains controversial, especially for the boundary layer and the upper outflow layer, even though this balance is assumed in the derivation of the Sawyer–Eliassen (SE) equation. This study derives an extended SE equation with the relaxation of the gradient wind and hydrostatic balance in cylindrical r–z coordinates, and then we diagnose the secondary circulation using this unbalanced SE equation and the azimuthally averaged tangential wind and thermodynamical fields from a three-dimensional numerical simulation of an intensifying TC. The gradient wind and hydrostatic imbalance produce two additional time-dependent forcing terms on the right-hand side (rhs) of SE equation, which are proved to be negligible for diagnosing the secondary circulation, even as the storm evolves rapidly. The use of the unbalanced basic state deforms the fields of coefficients that appear in the SE equation, and thus the forced secondary flows. The results indicate that the unbalanced solution captures the boundary layer inflow better than the balanced solution described by Bui et al. and the pseudobalanced solution described by Heng et al. The unbalanced solution is closer to the simulation because more unbalanced components are included. Many previous studies always employ the thermal wind balance relation to simplify the SE equation, which is invalid in an unbalanced vortex and result in an overestimation of the boundary layer inflow. These unbalanced dynamics could provide a reliable diagnosis of the secondary flow near the boundary layer.

Crescent-Shaped Low-Temperature Distribution along the Convex Topography in the Southeastern Edge of Taiwan Bank in Summer

Abstract Various physical mechanisms of ocean upwelling usually occur near or along coastal regions worldwide. Five upwelling zones of unequal intensity are found around the Taiwan Strait, and the Taiwan Bank (TB) upwelling zone has the most prominent characteristics of low temperature. In this study, satellite images, shipboard ADCPs (acoustic Doppler current profilers), and CTDs (conductivity–temperature–depth measures) were analyzed to investigate the processes of cold water upwelling around the TB shoaling zone. In addition, the MITgcm numerical model and the flexible cubic spline technique were also employed, allowing us to better understand those processes. The model results suggested that a combination of Ekman transport and the centrifugal force, driven by the geostrophic South China Sea Warm Current (SCSWC), constitutes a physical mechanism to contribute the vigorous upwelling in the TB shoal zone. The upwelling is largely driven by Ekman transport. However, the centrifugal force may explain why the upwelling with a crescent-shaped distribution of low temperatures along the convex topography of the southeastern edge of the TB shoaling zone is more prominent than expected, as it tends toward the so-called gradient wind balance. Sudden relaxation of the friction force occurred because of the very sharp shelf break (20–60 m) and steep slope topography; a discontinuous velocity zone around the shelf break could also lead to vigorous cold water upwelling. Significance Statement Extensive data concerning the Taiwan Bank (TB) shoaling zone have been collected in the past decade in an attempt to improve understanding of the process of cold water upwelling in the area. Because the Kuroshio invades the South China Sea from the east, and the South China Sea Warm Current flows northeastward around the southeastern edge of the TB, water circulation in and around the sandbar is very complicated. Thus, we expanded our model range from small to large scale to avoid the open boundary settings of small-scale model (including the temperature and salinity fields, wind stress, and the model driving forces), which were not easy to set up. Thus, we used a large-scale, high-resolution circulation model to study a small-scale ocean region. Physical processes of this upwelling can finally be verified in the small-scale region. To compensate for the insufficient resolution of the large-scale numerical model, our strategy was to utilize the flexible cubic spline technique to resolve the curvature of the markedly meandering currents. In light of scale analysis, the results showed that in addition to the critical contribution of Ekman transport to the upwelling, the effects of centrifugal forces on upwelling in the TB shoal zone need to be considered.

Multiple convective storms within a single cyclone on Saturn

Here we describe a cyclone at 50∘N in the atmosphere of Saturn that was the source of eight separate convective storms. The storm clouds that appeared bright in scattered sunlight were identified using images from the Cassini Imaging Science Subsystem (ISS) and ground-based telescopes. The Cassini Radio and Plasma Wave Science (RPWS) instrument detected Saturn Electric Discharge (SED) signals from the lightning within the storms, which were correlated to the sudden appearance of bright storm clouds in and surrounding the cyclone. Using the number and flash rate of SEDs we infer the duration and intensity of the storms. Although previous storms have been observed to erupt from within cyclones, the cyclone studied here is unusual in that it survived six storms before being disrupted by the seventh and strongest storm. An eighth storm occurred in the remnant of the disrupted cyclone. We conjecture that the anticyclonic circulation generated by the seventh storm was enough to overwhelm the cyclone’s gradient wind balance.

Characteristics of the Intraseasonal Oscillation in the Equatorial Mesosphere and Lower Thermosphere Region Revealed by Satellite Observation and Global Analysis by the JAGUAR Data Assimilation System

AbstractClimatological features of the intraseasonal oscillation (ISO) in the equatorial mesosphere and lower thermosphere were analyzed using temperature data from the Aura Microwave Limb Sounder (MLS) and global analysis data from a data assimilation using satellite observations, including the MLS, over 15 years. Based on spectral analyses, fluctuations with a period of 15–90 days were extracted as the ISO component. First, an empirical orthogonal function (EOF) analysis was performed for the ISO components of the zonal mean temperature from the MLS in the region of 10°S–10°N, 68–85 km, where the ISO amplitudes are found to be maximized. The global structure of the ISO anomalies of temperature and zonal winds estimated assuming a gradient wind balance was examined by a regression analysis using the first and second principal EOFs. It is shown that the ISO phases propagate downward with a vertical wavelength of 25–30 km above a height of 60 km and that the ISO signal synchronized with the equatorial ISO is observed even in the middle and high latitude regions of both hemispheres. Second, the global analysis data were used to examine the driving mechanism of the ISO. It was confirmed that the time series of the equatorial ISO zonal mean zonal wind in the analysis agreed well with radar observations, which were not used for assimilation. Results suggest small‐scale phenomena, such as gravity waves not necessarily represented in the parameterization and the meridional advection of angular momentum, mainly contribute to drive the ISO.

Dynamics of a Standing Meander of the Subantarctic Front Diagnosed from Satellite Altimetry and Along-Stream Anomalies of Temperature and Salinity

Abstract Meanders formed where the Antarctic Circumpolar Current (ACC) interacts with topography have been identified as dynamical hot spots, characterized by enhanced eddy energy, momentum transfer, and cross-front exchange. However, few studies have used observations to diagnose the dynamics of ACC standing meanders. We use a synoptic hydrographic survey and satellite altimetry to explore the momentum and vorticity balance of a Subantarctic Front standing meander, downstream of the Southeast Indian Ridge. Along-stream anomalies of temperature in the upper ocean (150–600 m) show along-stream cooling entering the surface trough and along-stream warming entering the surface crest, while warming is observed from trough to crest in the deeper ocean (600–1500 m). Advection of relative vorticity is balanced by vortex stretching, as found in model studies of meandering currents. Meander curvature is sufficiently large that the flow is in gradient wind balance, resulting in ageostrophic horizontal divergence. This drives downwelling of cooler water along isopycnals entering the surface trough and upwelling of warmer water entering the surface crest, consistent with the observed evolution of temperature anomalies in the upper ocean. Progressive along-stream warming observed between 600 and 1500 m likely reflects cyclogenesis in the deep ocean. Vortex stretching couples the upper and lower water column, producing a low pressure at depth between surface trough and crest and cyclonic flow that carries cold water equatorward in the surface trough and warm water poleward in the surface crest (poleward heat flux). The results highlight gradient–wind balance and cyclogenesis as central to dynamics of standing meanders and their critical role in the ACC momentum and vorticity balance. Significance Statement The Antarctic Circumpolar Current (ACC) in the Southern Ocean is a nearly zonal current that encircles Antarctica. It acts as a barrier between warmer water equatorward and colder water poleward. In a few regions where the current encounters strong topographic changes, the current meanders and opens a pathway for heat to travel across the ACC toward Antarctica. We surveyed a meander in the ACC and examined the along-stream change of temperature. In the upper ocean, temperature changes are caused by a vertical circulation, bringing cool water down when entering the surface trough (the part of the meander closest to the equator), and warm water up when exiting the surface trough and entering the surface crest. At depth, cold water is transported equatorward in the surface trough and warm water poleward in the surface crest, leading to a net transport of heat poleward. This study highlights the importance of the secondary circulation within a meander for generating cross-ACC flows and moving heat toward Antarctica.

数値シミュレーションで得られた上陸前の台風Faxai (1915)の強度・構造変化

A numerical simulation of Typhoon Faxai (1915), which made landfall with a central pressure of 960 hPa in the Kanto region of Japan, was conducted using a nonhydrostatic numerical model with a 1-km grid spacing. Faxai sustained a symmetric structure until the landfall and caused severe damage due to strong winds. The simulation successfully simulated the realistic track and intensity of Faxai for 48 h around landfall. The simulated intensity was strong until the time of landfall, and the spatial size of the vortex was small. The structure of the simulated Faxai, identified as having an axisymmetric flow field and eyewall, was similar to that of a welldeveloped tropical cyclone (TC) in the tropics. Around the TC center, the surface latent heat flux was over 300 W m−2 until landfall, and the vertical wind shear was less than 9 m s−1 between the 1.5- and 12.0-km altitudes, which is relatively weak at midlatitudes. The maximum potential intensity (MPI) was calculated using environmental parameters around the simulated TC. The simulated and best track TC intensities exceeded the MPI for approximately 12 h before landfall, that is, the TC was in a superintense state. The superintensity was mainly caused by the presence of supergradient wind, which, in turn, resulted from the strong intensity and axisymmetric structure of the typhoon. The simulated TC satisfies the assumptions for the formulation of the MPI during the quasi-steady state, except for the gradient wind balance, implying that the structure of a TC is similar to that of a developed TC in the tropics. The present analyses suggest that the strong intensity of Faxai results from favorable environmental conditions and vortex structure.

A Numerical Study of Cirrus Bands and Low Static-stability Layers associated with Tropical Cyclone Outflow

AbstractProminent cirrus cloud banding occurred episodically within a northern cirrus canopy of Typhoon Talim (2017) during its recurvature. The generation mechanisms of the cirrus bands and low static-stability layers that support the bands are investigated using a numerical simulation with the Advanced Research Weather Research and Forecasting Model. Inspection of model output reveals that thin layers of near-neutral to weakly unstable static stability are persistently present in the upper and lower parts of the upper-level outflow, and shallow convection aligned along the vertical shear vector is prevalent in these layers. The cirrus banding occurs as the lowered outflow from the weakening storm ascends slantwise over a midlatitude baroclinic zone, and updrafts of the preexisting shallow convection in the upper part of the outflow layer become saturated. It is shown that the strong outflow resulting from violation of gradient-wind balance in the core region, by itself, creates the low static-stability layers. Analyses of potential temperature and static stability budgets show that the low static-stability layers are created mainly by the differential radial advection of radial thermal gradients on the vertical edges of the outflow. The radial thermal gradients occur in response to the outward air parcel acceleration in the core region and deceleration in the outer region, which, by inducing compensating vertical mass transport into and out of the outflow, act to tilt the isentropes within the shear layers. The effects of environmental flow and cloud radiative forcing on the cirrus banding are also addressed.

Study of Ageostrophy during Strong, Nonlinear Eddy-Front Interaction in the Gulf of Mexico

AbstractThe 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 LC frontal eddies 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.

Filaments, Fronts and Eddies in the Cabo Frio Coastal Upwelling System, Brazil

We investigate the dynamics of meso- and submesoscale features of the northern South Brazil Bight shelf region with a 500-m horizontal resolution regional model. We focus on the Cabo Frio upwelling center, where nutrient-rich, coastal waters are transported into the mid- and outer shelf, because of its importance for local and remote productivity. The Cabo Frio upwelling center undergoes an upwelling phase, from late September to March, and a relaxation phase, from April to early September. During the upwelling phase, an intense front around 200 km long and 20 km wide with horizontal temperature gradients as large as 8 ∘C over less than 10 km develops. A surface-intensified frontal jet of 0.7 ms−1 in the upper 20 m and velocities of around 0.3 ms−1 reaching down to 65 m depth makes this front a preferential cross-shelf transport pathway. Large vertical mixing and vertical velocities are observed within the frontal region. The front is associated with strong cyclonic vorticity and strong variance in relative vorticity, frequently with O(1) Rossby numbers. The dynamical balance within the front is between the pressure gradient, Coriolis and vertical mixing terms, which are induced both by the winds, during the upwelling season, and by the geostrophic frontal jet. Therefore, the frontal dynamics may be largely described as sum of Ekman and turbulent thermal wind balances. During the upwelling phase, a mix of barotropic and baroclinic instabilities dominates in the upwelling center. However, these instabilities do not lead to the local formation of coherent eddies when the front is strong. In the relaxation phase, the front vanishes, and the water column becomes less stratified. The interaction between eastward coastal currents generated by sea level variability, coastal intrusions of the Brazil Current, and sporadic wind-driven, coastal upwelling events induce the formation of cyclonic eddies with diameters of, approximately, 20 km. They are in gradient-wind balance and propagate along the 100-m isobath on the shelf. During this phase baroclinic instability dominates. Cold filaments with widths of 2 km are formed due to straining and stretching of cold, coastal temperature anomalies. They last for a few days and are characterized by downwelling as large as 1 cms−1. The turbulent thermal wind balance provides a good first order estimate of the dynamical balance within the filament, but vertical and horizontal advection are shown to be important. To our knowledge, this is the first account of these smaller scale features in the region. Because these meso- and submesoscale features on the shelf heavily affect the water properties crucial to productivity of the South Brazil Bight, it is important to take these features into account for a better understanding of the functioning of this ecosystem and its resilience to both direct human activities as well as to climate change.

Revisiting gradient wind balance in tropical cyclones using dropsonde observations

AbstractThis study diagnoses the degree of gradient wind balance (GWB) in dropsonde observations of 30 tropical cyclones (TCs) divided into 91 intense observation periods. The diagnosed GWB in these observation periods are composited to investigate which characteristics of a TC are significantly related to departures from GWB. This analysis confirms that on average the flow above the boundary layer is approximately in GWB. Supergradient flow is more common near the radius of maximum wind (RMW) in the upper boundary layer than above in the free troposphere or outside the RMW and is also more common in strong storms than in weak storms. In contrast, the degree of GWB does not differ between intensifying, steady‐state and weakening storms. Storms with a peaked wind profile have a higher probability of showing supergradient winds than those with a flat wind profile. The comparison of two commonly used functions to fit observations shows that the diagnosing GWB from dropsonde observations is highly dependent on the analysis technique. The agradient wind magnitude and even sign is shown to depend on which of these functions is used to fit the observations. The use of a polynomial fit consistently diagnoses the presence of supergradient winds far more frequently than a piece‐wise function, and also shows a marked degree of imbalance above the boundary layer. Therefore, caution is warranted when determining the degree of GWB with a polynomial fit.

The Role of Curvature in Modifying Frontal Instabilities. Part I: Review of Theory and Presentation of a Nondimensional Instability Criterion

AbstractIn this study, we examine the role of curvature in modifying frontal stability. We first evaluate the classical criterion that the Coriolis parameter f multiplied by the Ertel potential vorticity (PV) q is positive for stable flow and that instability is possible when this quantity is negative. The first portion of this statement can be deduced from Ertel’s PV theorem, assuming an initially positive fq. Moreover, the full statement is implicit in the governing equation for the mean geostrophic flow, as the discriminant, fq, changes sign. However, for curved fronts in cyclogeostrophic or gradient wind balance (GWB), an additional term enters the discriminant owing to conservation of absolute angular momentum L. The resulting expression, (1 + Cu)fq < 0 or Lq < 0, where Cu is a nondimensional number quantifying the curvature of the flow, simultaneously generalizes Rayleigh’s criterion by accounting for baroclinicity and Hoskins’s criterion by accounting for centrifugal effects. In particular, changes in the front’s vertical shear and stratification owing to curvature tilt the absolute vorticity vector away from its thermal wind state; in an effort to conserve the product of absolute angular momentum and Ertel PV, this modifies gradient Rossby and Richardson numbers permitted for stable flow. This forms the basis of a nondimensional expression that is valid for inviscid, curved fronts on the f plane, which can be used to classify frontal instabilities. In conclusion, the classical criterion fq < 0 should be replaced by the more general criterion for studies involving gravitational, centrifugal, and symmetric instabilities at curved density fronts. In Part II of the study, we examine interesting outcomes of the criterion applied to low-Richardson-number fronts and vortices in GWB.

The Role of Curvature in Modifying Frontal Instabilities. Part II: Application of the Criterion to Curved Density Fronts at Low Richardson Numbers

AbstractWe continue our study of the role of curvature in modifying frontal stability. In Part I, we obtained an instability criterion valid for curved fronts and vortices in gradient wind balance (GWB): Φ′ = L′q′ < 0, where L′ and q′ are the nondimensional absolute angular momentum and Ertel potential vorticity (PV), respectively. In Part II, we investigate this criterion in a parameter space representative of low-Richardson-number fronts and vortices in GWB. An interesting outcome is that, for Richardson numbers near 1, anticyclonic flows increase in q′, while cyclonic flows decrease in q′, tending to stabilize anticyclonic and destabilize cyclonic flow. Although stability is marginal or weak for anticyclonic flow (owing to multiplication by L′), the destabilization of cyclonic flow is pronounced, and may help to explain an observed asymmetry in the distribution of small-scale, coherent vortices in the ocean interior. We are referring to midlatitude submesoscale and polar mesoscale vortices that are generated by friction and/or buoyancy forcing within boundary layers but that are often documented outside these layers. A comparison is made between several documented vortices and predicted stability maps, providing support for the proposed mechanism. A simple expression, which is a root of the stability discriminant Φ′, explains the observed asymmetry in the distribution of vorticity. In conclusion, the generalized criterion is consistent with theory, observations, and recent modeling studies and demonstrates that curvature in low-stratified environments can destabilize cyclonic and stabilize anticyclonic fronts and vortices to symmetric instability. The results may have implications for Earth system models.

Relating Observations of Gradient Nonbalance at the Top of Hurricanes With Their Warm Core Structures

AbstractRecent analysis of Weather Research and Forecasting simulations shows that the flow around high‐pressure regions that often develop at the top of Hurricanes (15‐km altitude) violates the gradient wind balance, hence termed as “gradient nonbalance.” While observations at such high altitudes are rare, recently, NASA‐HS3 and the Office of Naval Research‐Tropical Cyclone Intensity campaigns deployed dropsondes from unprecedented levels around 18 km. In this work we use a wavenumber decomposition method to reproduce 2‐D slices and 3‐D structures from three storms from these campaigns: Edouard (2014), Joaquin (2015), and Patricia (2015). The analyzed data show that the development of high pressure at the hurricane's top leads to various degrees of gradient nonbalance. These highs are a hydrostatic reflection of the storm tilt, which offsets the warm core with respect to the near surface low and the slanted eyewall. The implications of these findings and the relations with recent reports of upper‐level wind field are discussed.

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

Abstract 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.

A numerical modelling investigation of the role of diabatic heating and cooling in the development of a mid-level vortex prior to tropical cyclogenesis – Part 1: The response to stratiform components of diabatic forcing

Abstract. Mid-tropospheric mesoscale convective vortices have been often observed to precede tropical cyclogenesis. Moreover, recent cloud-resolving numerical modelling studies that are initialized with a weak cyclonic mid-tropospheric vortex sometimes show a considerable intensification of the mid-level circulation prior to the development of the strong cyclonic surface winds that characterize tropical cyclogenesis. The objective of this two-part study is to determine the processes that lead to the development of a prominent mid-level vortex during a simulation of the transformation of a tropical disturbance into a tropical depression, in particular the role of diabatic heating and cooling. For simplicity simulations are initialized from a quiescent environment. In this first part, results of the numerical simulation are described and the response to stratiform components of the diabatic forcing is investigated. In the second part, the contribution of diabatic heating in convective cells to the development of the mid-level vortex is examined. Results show that after a period of intense convective activity, merging of anvils from numerous cells creates an expansive stratiform ice region in the upper troposphere, and at its base a mid-level inflow starts to develop. Subsequently conservation of angular momentum leads to strengthening of the mid-level circulation. A 12 h period of mid-level vortex intensification is examined during which the mid-level tangential winds become stronger than those at the surface. The main method employed to determine the role of diabatic forcing in causing the mid-level inflow is to diagnose it from the full physics simulation and then impose it in a simulation with hydrometeors removed and the microphysics scheme turned off. Removal of hydrometeors is achieved primarily through artificially increasing their fall speeds 3 h prior to the 12 h period. This results in a state that is in approximate gradient wind balance, with only a weak secondary circulation. Then, estimates of various components of the diabatic forcing are imposed as source terms in the thermodynamic equation in order to examine the circulations that they independently induce. Sublimation cooling at the base of the stratiform ice region is shown to be the main factor responsible for causing the strong mid-level vortex to develop, with smaller contributions from stratiform heating aloft and low-level melting and evaporation. This contrasts with the findings of previous studies of mid-latitude vortices that indicate sublimation plays a relatively minor role. An unanticipated result is that the central cool region that develops near the melting level is to a large degree due to compensating adiabatic ascent in response to descent driven by diabatic cooling adjacent to the central region, rather than in situ diabatic cooling. The mid-level inflow estimated from stratiform processes is notably weaker than for the full physics simulation, suggesting a moderate contribution from diabatic forcing in convective cells.