Potential Vorticity Minimum Research Articles

Winter Weakening of Titan's Stratospheric Polar Vortices

Abstract Polar vortices are a prominent feature in Titan's stratosphere. The Cassini mission has provided a detailed view of the breakdown of the northern polar vortex and formation of the southern vortex, but the mission did not observe the full annual cycle of the evolution of the vortices. Here we use a TitanWRF general circulation model simulation of an entire Titan year to examine the full annual cycle of the polar vortices. The simulation reveals a winter weakening of the vortices, with a clear minimum in polar potential vorticity and midlatitude zonal winds between winter solstice and spring equinox. The simulation also produces the observed postfall equinox cooling followed by rapid warming in the upper stratosphere. This warming is due to strong descent and adiabatic heating, which also leads to the formation of an annular potential vorticity structure. The seasonal evolution of the polar vortices is very similar in the two hemispheres, with only small quantitative differences that are much smaller than the seasonal variations, which can be related to Titan's orbital eccentricity. This suggests that any differences between observations of the northern hemisphere vortex in late northern winter and the southern hemisphere vortex in early winter are likely due to the different observation times with respect to solstice, rather than fundamental differences in the polar vortices.

Variability of the Subantarctic Mode Water Volume in the South Indian Ocean During 2004–2018

AbstractAn analysis of Argo data reveals that the subantarctic mode water (SAMW) in the South Indian Ocean (SIO), characterized by a vertical potential vorticity (PV) minimum, decreases by 10% in volume from 2004 to 2018. Most of this decrease occurs at the 26.8–26.9 kg m−3 density range which forms southwest of Australia, while a slight volume increase occurs at 26.6–26.8 kg m−3. Further analysis indicates that the weakening of the Mascarene High and westerly winds in the SIO reduces the evaporation‐precipitation, surface heat flux, and Ekman pumping and shoals the mixed layer southwest of Australia, which leads to a volume decrease at 26.8–26.9 kg m−3 in approximately 3 years. West of 90°E, the parameters exhibit the opposite change, leading to a volume increase at 26.6–26.8 kg m−3. This result suggests that surface winds play an important role in the variability of the SIO SAMW volume during the Argo period.

Forcing of the Martian polar annulus by Hadley cell transport and latent heating

AbstractA hierarchy of idealized models is used to investigate the roles of Hadley cell forcing and latent heat release from carbon dioxide condensation in determining the annular potential vorticity structure of the Martian winter polar vortex. The angular momentum conserving the Hadley cell model of Lindzen and Hou with summer hemisphere heating maximum of appropriate strength and latitude produces a strong westerly jet near 60°N, which is similar in strength to the winter polar night jet on Mars. Although the corresponding potential vorticity profile in the angular momentum conserving and thermal wind regions has no annular structure resembling the Martian one, there is an implied δ‐function at the discontinuity in zonal wind. This δ‐function is smoothed out by explicit diffusion in full axisymmetric model integrations forming a partial annular structure, though a local maximum in potential vorticity at the pole persists and is further enhanced when cooling representing the polar night is included. A distinct polar minimum and clear annular potential vorticity structure are obtained, however, when an additional representation of polar latent heating is also included. Full eddy‐permitting shallow‐water model integrations confirm the basic structure obtained by the axisymmetric model and suggest a nominal value of viscosity appropriate as a representation of the effects of eddy mixing. Instability of the polar annulus leads to vacillation‐type behaviour involving eddy growth and annulus disruption, followed by re‐formation under the influence of radiative relaxation. The degree of transience and mean eddy activity both show an increase with stronger latent heating and the resulting deeper polar potential vorticity minimum, showing that mixing in polar regions may be dependent on details of polar carbon dioxide condensation. Vacillation time‐scales are also shown to vary with radiative time‐scales, but through a modification of instability growth rate rather than as a result of direct radiative restoration.

The Nature of Eddy Kinetic Energy in the Labrador Sea: Different Types of Mesoscale Eddies, Their Temporal Variability, and Impact on Deep Convection

AbstractOceanic eddies are an important component in preconditioning the central Labrador Sea (LS) for deep convection and in restratifying the convected water. This study investigates the different sources and impacts of eddy kinetic energy (EKE) and its temporal variability in the LS with the help of a 52-yr-long hindcast simulation of a 1/20° ocean model. Irminger Rings (IR) are generated in the West Greenland Current (WGC) between 60° and 62°N, mainly affect preconditioning, and limit the northward extent of the convection area. The IR exhibit a seasonal cycle and decadal variations linked to the WGC strength, varying with the circulation of the subpolar gyre. The mean and temporal variations of IR generation can be attributed to changes in deep ocean baroclinic and upper-ocean barotropic instabilities at comparable magnitudes. The main source of EKE and restratification in the central LS are convective eddies (CE). They are generated by baroclinic instabilities near the bottom of the mixed layer during and after convection. The CE have a middepth core and reflect the hydrographic properties of the convected water mass with a distinct minimum in potential vorticity. Their seasonal to decadal variability is tightly connected to the local atmospheric forcing and the associated air–sea heat fluxes. A third class of eddies in the LS are the boundary current eddies shed from the Labrador Current (LC). Since they are mostly confined to the vicinity of the LC, these eddies appear to exert only minor influence on preconditioning and restratification.

The Stability of Mars’s Annular Polar Vortex

Abstract The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising, since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here the stability of a Mars-like annular vortex is investigated using numerical integrations of the rotating shallow-water equations. The mode of instability and its growth rate is shown to depend upon the latitude and width of the annulus. By introducing thermal relaxation toward an annular equilibrium profile with a time scale similar to that of the instability, a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere can be simulated. This time scale, typically 0.5–2 sols, is similar to radiative relaxation time scales for Mars’s polar atmosphere. The persistence of an annular vortex is also shown to be robust to topographic forcing, as long as it is below a certain amplitude. It is therefore proposed that the persistence of this barotropically unstable annular vortex is permitted owing to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.

Variability of subduction rates of the subtropical North Pacific mode waters

The climatology subduction rate for the entire Pacific is known, but the mechanism of interannual to decadal variation remains unclear. In this study, we calculated the annual subduction rates of three types of North Pacific subtropical mode waters using a general circulation model (LICOM1.0) for the period of 1958–2001. The model experiments focused on interannual variations of ocean dynamical processes under daily wind forcings and seasonal heat fluxes. The mode water formation region was defined by a potential vorticity minimum at outcrop locations. The model results show that two subduction rate maxima (>100 m/a) were located in the Subtropical Mode Water (STMW) and the Central Mode Water (CMW) formation regions. These regions are consistent with a climatologically calculated value. The subduction rate in the Eastern Subtropical Mode Water (ESTMW) formation region was smaller at about 75 m/a. The subduction rate shows clear interannual and decadal variations associated with oceanic dynamic variabilities. The average subduction rate of the STMW was much smaller during the period of 1981–1990 compared with other periods, while that of the CMW had a negative anomaly before 1975 and a positive anomaly after 1978. The variability agreed with Ekman and geostrophic advections and mixed layer depths. The interannual variability of the subduction rate for the ESTMW was smallest during 1970–1990, as a result of a weak wind stress curl. This paper explores how interannual signals from the atmosphere are stored in different parts of the ocean, and thus may contribute to a better understanding of feedback mechanisms for the Pacific Decadal Oscillation (PDO) event.

“Eddy Resolving” Observation of the North Pacific Subtropical Mode Water

Abstract Hydrographic data obtained by high-resolution shipboard observations and Argo profiling floats have been analyzed to study the mesoscale structure and circulation of the North Pacific Subtropical Mode Water (STMW). The float data show that in the late winter of 2008, STMW having a temperature of approximately 18.8°, 17.7°, and 16.6°C formed west of 140°E, at 140°–150°E, and east of 150°E, respectively, in the recirculation gyre south of the Kuroshio Extension. After spring, the newly formed STMW gradually shift southward, decreasing in thickness. Simultaneously, the STMWs of 16.6° and 17.7°C are gradually stirred and then mixed in terms of properties. In late fall, they seem to be integrated to form a single group of STMWs having a temperature centered at 17.2°C. Such STMW circulation in 2008 is much more turbulent than that in 2006, which was investigated in a previous study. The difference between the two years is attributed to the more variable state of the Kuroshio Extension in 2008, associated with stronger eddy activities in the STMW formation region, which enhance the eddy transport of STMW. High-resolution shipboard observations were carried out southeast of Japan at 141°–147°E in the early fall of 2008. To the south of the Kuroshio Extension, STMW exists as a sequence of patches with a horizontal scale of 100–200 km, whose thick portions correspond well to the mesoscale deepening of the permanent pycnocline. The western (eastern) hydrographic sections are occupied mostly by the 17.7°C (16.6°C) STMW, within which the 16.6°C (17.7°C) STMW exists locally, mostly at locations where both the permanent pycnocline depth and the STMW thickness are maximum. This structure implies that the STMW patches are transported away from their respective formation sites, corresponding to a shift in the mesoscale anticyclonic circulations south of the Kuroshio Extension. Furthermore, 20%–30% of the observed STMW pycnostads have two or three potential vorticity minima, mostly near temperatures of 16.6° and 17.7°C. The authors presume that such a structure formed as a result of the interleaving of the 16.6° and 17.7°C STMWs after they are stirred by mesoscale circulations, following which they are vertically mixed to form the 17.2°C STMW observed in late fall. These results indicate the importance of horizontal processes in destroying the vertically uniform structure of STMW after spring, particularly when the Kuroshio Extension is in a variable state.

Alignment of Hurricane-like Vortices on f and β Planes

Abstract A nonlinear, two-layer, vortex-tracking semispectral model (i.e., Fourier transformed in azimuth only) is used to study the evolution of dry, but otherwise hurricane-like, initially tilted vortices in quiescent surroundings on f and β planes. The tilt projects onto vorticity asymmetries that are dynamically vortex Rossby waves. Since the swirling wind in the principal mean vortex used here decays exponentially outside the eyewall, it has an initial potential vorticity (PV) minimum. The resulting reversal of PV gradient meets the necessary condition for inflectional (i.e., barotropic or baroclinic) instability. Thus, the vortex may be inflectionally stable or unstable. On an f plane, the tilt precesses relatively slowly because the critical radius, where the phase speeds of the waves match the mean swirling flow, is far from the center. An alternative Gaussian-like PV monopole that has a monotonic outward decrease of PV is stable to inflectional instability. It has a smaller critical radius and rapid tilt precession. Generally, vortices with fast tilt precession are more stable, as are stronger vortices in higher latitudes. On a β plane, the interaction between the symmetric vortex and the planetary PV gradient induces β gyres that push the vortex poleward and westward. The interaction between the β gyres and the planetary PV gradient may either create a PV minimum or intensify a minimum inherited from the initial condition. Thus, the nonlinear β effect reduces the ability of the vortex to recover from initial tilt, relative to the same vortex on an f plane. This result contrasts with previous studies of barotropic vortices on f planes, where the linear and nonlinear solutions were nearly identical.

Ventilation of the Upper Labrador Sea Water, 2003–2005

[1] In 2003 and in 2005, hydrographic data provided sufficient spatial coverage in the Labrador Sea to infer basin wide changes in the water mass characteristic of the Upper Labrador Sea Water (ULSW). The ULSW was considerably saltier and warmer in 2005 than in 2003. Although convection in the Labrador Sea leads to mixing with salinity-poor surface water and is opposed to the observed salinity trend, the increased vertical homogeneity of the CTD profiles, the increase in the ULSW thickness and the intensification of the potential vorticity minimum for the isopycnals σΘ = 27.700–27.734 kg/m3 in 2005 point to convection in winter 2005 which ventilated at least about 20% of the Labrador Sea region.

Impact of Tibetan Orography and Heating on the Summer Flow over Asia

The influence on the summer flow over Asia of both the orographic and thermal forcing of the Tibetan Plateau is investigated using a sequence of idealised experiments with a global primitive equation model. The zonally averaged flow is prescribed and both realistic and idealised orography and heating are used. There is some similarity between the responses to the two forcings when applied separately. The upper tropospheric Tibetan anticyclone is predominantly forced by the heating but also weakly by the orography. Below this, both forcings tend to give air descending in an equatorward anticyclonic circulation down the isentropes to the west and rising in a similar poleward circulation to the east. However the heating-only response has a strong ascending southwesterly flow that is guided around the south and south-east of the orography when it is included. On the northern side, the westerly flow over the orography gives ascent on the upslope and descent on the downslope. It is found that heating over the Plateau leads to a potential vorticity (PV) minimum and that if it is sufficiently strong the flow is unstable, producing a quasi-biweekly oscillation. During this oscillation the Tibetan anticyclone changes between a single centre over the southwestern side of the Plateau and a split/double structure with centres over China and the Middle East. These characteristics are similar to observed variability in the region. Associated with this quasi-biweekly oscillation are significant variations in the strength of the ascent over the Plateau and the Rossby wave pattern over the North Pacific. The origin of the variability is instability associated with the zonally extended potential vorticity PV minimum on a θ-surface, as proposed by Hsu and Plumb (2000). This minimum is due to the tendency to reduce the PV above the heating over the Plateau and to advection by the consequent anticyclone of high PV around from the east and low PV to the west. The deep convection to the south and southeast of the Plateau tends to suppress the quasi-biweekly oscillation because the low PV produced above it acts to reduce the meridional PV gradient reversal. The occurrence of the oscillation depends on the relative magnitude of the heating in the two regions.

Enhanced ventilation in the Okhotsk Sea through tidal mixing at the Kuril Straits

The role played by tide-induced diapycnal mixing at the Kuril Straits in the formation of the Okhotsk Sea water is examined using an ocean general circulation model. The result shows that tidal mixing causes a freshening of intermediate water down to ∼ 27.6 σ θ . This implies an enhancement of ventilation by tidal mixing, since a freshening flux can come only from above in the Okhotsk Sea. In fact, when compared with the case without tidal mixing, the production rate of Dense Shelf Water (DSW) increases from 0.01 to 0.13 Sv ( 10 6 m 3 s - 1 ) with maximum DSW density increased from 26.6 to 26.8 σ θ . This enhanced production of DSW allows us to successfully reproduce a layer of local potential vorticity minimum in the Okhotsk Sea, which characterizes the Okhotsk Sea Mode Water. The analysis reveals that tidal mixing at the Kuril Straits has two roles in enhancing ventilation. First, it preconditions the water properties of the DSW because tidal mixing at the Kuril Straits induces an upward salt flux from the saltier lower layer. The subsequent transport of the saline water from the Straits to regions of sea-ice generation increases the density of subducting water, resulting in more realistic densities and production rates of DSW. Second, tidal mixing directly modifies water properties throughout the water column. The ventilation due to this mechanical mixing further enhances the intermediate layer ventilation, and is dominant in the Kuril Straits and in the layer denser than the DSW. Although the effect of double diffusion on ventilation in the Okhotsk Sea is also examined, it is much less effective than the tidal mixing. Since the Okhotsk Sea is a key location for the ventilation of the North Pacific intermediate layer, the important implication here is that tidal mixing at the Kuril Straits enhances the meridional overturning in the entire North Pacific Ocean.

A Neutral Wave Observed in the Antarctic Polar Vortex

An intensive radiosonde observation with time intervals of 3 h was performed in June 2002 at Syowa Station (39.6°E, 69°S) in the Antarctic. A wavelike disturbance with a wave period of 12-15 h, having a nearly barotropic structure was observed above a height of 22 km in the time period of 27-28 June 2002. A result of the hodograph analysis suggests that the short-period disturbance is not due to an inertiagravity wave. A similar short-period disturbance is observed in the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis data. Results of detailed analysis using the ECMWF data show that the short-period disturbance has a horizontal wavelength of about 2000 km, and propagates along a potential vorticity minimum region with a horizontal phase velocity of about 40 m s−1. This phase velocity is equal to the background horizontal wind velocity at the potential vorticity minimum. A necessary condition for the barotropic instability is locally satisfied at the potential vorticity minimum. However, it is rather appropriate that the short-period disturbance is interpreted as a neutral wave than as an unstable wave in the barotropically unstable background flow. This result implies any unknown mechanism of the suppression of barotropic instability in the locally unstable background flow associated with a disturbed polar vortex.

Vortices in the Co-orbital Region of an Embedded Protoplanet

We present global 2-D inviscid disk simulations with an embedded planet, emphasizing the non-linear dynamics in its co-orbital region. We find that the potential vorticity of the flow in this region is not conserved due to the presence of two spiral shocks produced by the planet. As the system evolves, the potential vorticity profile develops extrema (inflection points) which eventually render the flow unstable. Vortices are produced in association with the potential vorticity minima. Born in the separatrix region, these vortices experience close-encounters with the planet, consequently exerting strong torques on the planet. The existence of these vortices have important implications on understanding the migration rates of low mass planets.

Hydrographic structure and transport of the Oyashio south of Hokkaido and the formation of North Pacific Intermediate Water

Hydrographic structure and transport of the Oyashio south of Hokkaido were described with conductivity‐temperature‐depth and lowered acoustic Doppler current profiler (LADCP) survey performed in June 1998. The southwestward Oyashio transport just off the Hokkaido coast was 10.1 Sv in the density of 26.6–27.5σθ, in which 2.5 Sv was from the Okhotsk Sea and 7.6 Sv was from the Western Subarctic Gyre (WSAG). The Oyashio northeastward countercurrent was 4.9 Sv. The cross‐gyre Oyashio transport in the area from the east coast of Hokkaido to the Subarctic Front was estimated to be 5.2 Sv; 2.4 Sv in 26.6–27.0σθ was mainly composed of low potential vorticity Okhotsk Sea water and 2.8 Sv in 27.0–27.5σθ mostly from WSAG, suggesting that the Okhotsk Sea water (WSAG water) would contribute to the formation of the upper (lower) part of the North Pacific Intermediate Water (NPIW). The Oyashio water was lower in oxygen than in the subtropical areas south of the Subarctic Front in the density of 26.9–27.6σθ, possibly because of the absence of the Antarctic Intermediate Water (AAIW) influence with the relatively high oxygen water that might be transported along the western boundary of the North Pacific Ocean and along the Kuroshio Extension, increasing the oxygen in the areas south of the Subarctic Front. Just south of the Subarctic Front, a cold‐ and fresh‐core anticyclonic eddy was observed with a salinity minimum in the core, suggesting one possible formation process of NPIW. The density of the potential vorticity minimum in the southwestward Oyashio near Hokkaido was at around 26.65σθ, which was lower than 26.8–26.9σθ observed in the early 1990s. This is possibly because the potential vorticity vertical profiles in the Okhotsk Sea and WSAG significantly changed corresponding to the water mass regime shift occurred in the Subarctic Pacific in the mid‐1990s [Kawasaki, 1999].

Mode waters and subduction rates in a high-resolution South Atlantic simulation

Water mass production and destruction in the subtropical South Atlantic gyre is studied. A high resolution numerical model is used to examine regional mode water formation and estimate the associated instantaneous and mean subduction rates. Primitive equation dynamics expressed in depth following (sigma) coordinates are employed. The main hydrographic and kinematic features of the South Atlantic are faithfully reproduced by the model. In particular, the principle current systems appear and the model exhibits a sequence of ventilated potential vorticity minima on density surfaces coinciding with those of observed South Atlantic mode waters. The formation sequence within the model of these mode waters is described. Net formation rates are estimated using a pseudo-Lagrangian method and by diagnosing the time history of subsurface water mass volumes. Maximum formation rates occur in the density bands of the mode waters. It is argued that the roots of the model mode waters are found along open ocean late winter outcrops, rather than in the waters entering the gyre from the Brazil Current/Malvinas Current Confluence region. Eddies generate interannual variability in mode water formation and precondition the waters in the outcrop regions for convection. On the other hand, the eddy kinetic energy of the Confluence region is too intense to permit a direct connection between deep convection cells in the western boundary current and those in the open South Atlantic that directly form mode water.

Subtropical mode water in the Northeast Pacific Basin

A new type of mode water in the upper thermocline of the eastern subtropical North Pacific is identified and examined using data from World Ocean Circulation Experiment high‐resolution repeat expendable bathythermograph (XBT) section PX37 and archives of historical XBT data. This water mass (labeled Eastern Subtropical Mode Water) is characterized by a subsurface potential vorticity minimum and is located east of Hawaii (Northeast Pacific Basin) in a density range of 24–25.4 σθ. It is a distinct water mass from the classical subtropical mode water (STMW) of the western Pacific. Eastern STMW is formed as a relatively deep late‐winter mixed layer, associated with the subtropical/subpolar water mass boundary near 25°–30°N, 135°–140°W, and is capped and subducted into the permanent thermocline. Along a section between San Francisco and Honolulu, Eastern STMW production is seen in every year for which there is adequate data. In this section the volume of Eastern STMW formed each winter and the temperature of the potential vorticity minimum are similar during the periods 1970–1979 and 1991–1997.

Labrador Sea Water in the Eastern North Atlantic. Part I: A Synoptic Circulation Inferred from a Minimum in Potential Vorticity

Abstract A synoptic distribution of Labrador Sea Water (LSW) in the eastern North Atlantic is determined from a regularly sampled, but sparse (3° resolution), survey covering 39° to 54°N, 11° to 34°W during spring 1991. The core of LSW can be defined by a minimum in potential vorticity (PV). Using property values at this minimum the authors infer the circulation of LSW. In addition, using a known source function for salinities at the core of LSW, estimates are able to be made of LSW vintages. The authors then compared the synoptic circulation to historical data. Youngest, 1986 vintage, LSW crosses the Mid-Atlantic Ridge to the eastern basin between 48° and 51°N at 34°W. This water then flows north to the Iceland Basin and eastward to the Rockall Trough, where it was found to be of 1978 vintage. Tongues of low salinity, low temperature, and high oxygen extend southward on the eastern side of the Mid-Atlantic Ridge, indicating that LSW also flows southward in the eastern basin. At the southern edge of the s...

Synthesizing the Gulf Stream Thermal Structure from XBT Data

Abstract Thirty-six XBT temperature profiles have been used in a parametric model introduced by Hendry to model the Gulf Stream's thermal structure at 65°W between 200 and 1200 dbar, with an rms residual error of 0.56°C. Velocity has been computed geostrophically relative to 1200 dbar, and has been included in calculating potential vorticity analytically from the model. The resulting potential vorticity section for 65°W has been compared with the analogous result from Hendry's parametric model at 59°W, as well as observed potential vorticity sections from 68° to 55°W. There is a significant feature in the potential vorticity structure at 65°W not found at 59°W-namely, a relative minimum in potential vorticity along isopycnals, centered at the Gulf Stream's axis and 350 dbar. The modeled potential vorticity sections are consistent with the observation including the downstream disappearance of this feature. The dynamical implications of these results are briefly discussed.

The vertical thermohaline structure in the Argentine basin

The vertical thermohaline structure in the central Argentine basin is investigated on the basis of high‐resolution hydrographic data. Emphasis is placed on fronts, their horizontal gradients, vertical stability and associated fine structure. Horizontal thermohaline gradients vary strongly with depth, regions of strong gradients alternating with those of weak gradients. The strongest gradients occur often at depths below the upper mixed layer. The salinity gradient maximum occurs above the temperature gradient maximum. Enhanced gradients are found where warm, salty water moves over cooler, fresher water such as between the subtropical water (STW) and antarctic intermediate water (AAIW) and between the North Atlantic deep water (NADW) and the antarctic bottom water (AABW). Temperature, salinity, and density fronts do not always coexist. Density‐compensating temperature and salinity fronts occur in the surface layer of the subantarctic and at abyssal depth below 3500 m. Vertical profiles of the Väisälä frequency indicate much reduced hydrostatic stabilities in the Brazil current and subantarctic frontal zones. Potential vorticity minima indicate the formation of subantarctic mode water just north of the subantarctic front and its subsequent northward and upward spread across isopycnals. The thermohaline fine structure is vertically intermittent. The amplitude variances between the enhanced and quiet regions vary by almost 2 orders of magnitude. Enhanced fine structure amplitudes are found near the STW‐AAIW and NADW‐AABW interfaces, where large horizontal thermohaline gradients occur and the hydrostatic stability is low. The temperature and salinity fine structures are largely density compensating. The coherence between the temperature and salinity fine structure is strongly depth dependent and is highest in regions where warm, salty water moves over cooler, fresher water.

Evolution of potential vorticity in tropical cyclones

AbstractWe explore the simultaneous use of potential radius and potential temperature coordinates in the Eliassen balanced vortex model of tropical cyclones. This results in a simple flux form for the equation governing the inverse potential vorticity. the fluxes are accomplished by R and θ, which are given in terms of the angular momentum and heat sources. If the sources are specified functions of R and θ, analytic solutions for the time evolution of the potential vorticity distribution can be obtained. the solutions illustrate how latent heat release generates potential vorticity at low levels, destroys it at upper levels, and through vertical advection causes a deepening of the low‐level potential vorticity maximum and a pinching off of the upper‐level potential vorticity minimum. to recover the tangential wind and mass fields from the known potential vorticity, one must solve a second‐order nonlinear partial differential equation. Numerical solutions of this equation result in tangential wind fields which are similar in many ways to observed tropical cyclones.