Barotropic energetics analysis of tropical cyclone Khai Muk

bl 'kks/k i= esa 11&14 uoEcj 2008 ds nkSjku caxky dh [kkM+h esa cuus vkSj mlds vkxs c<+us okys m".kdfVca/kh; pØokr dSeqd dh xfrdh; fLFkfr;ksa ds fo’kys"k.k ij fopkj&foe’kZ fd;k x;k tks fupys Lrj ij ifjofrZr ok;qnkc&m".kdfVca/k ¼csjksVªkfid½ mtkZ ij dsfUnzr FkkA bl nkSjku ;g ik;k x;k fd if’peh iz’kkar egklkxj ls miks".kh; iwohZ gok;sa e/; caxky dh [kkM+h ds mRrj rd c<+h vkSj Åij m)`r vof/k esa Hkwe/;js[kh; if’peh gok;sa ¼iNok¡½ vkbZ-Vh-lh-tsM+- ds nf{k.k rd c<+h ftlds dkj.k {kSfrt; vi:i.k izokg vR;kf/kd ek=k esa cukA blls pØokrh vi:i.k Hkzfeyrk mRiUu gqbZ vkSj fo{kksHk cuk] tks ckn esa m".kdfVca/kh; pØokr dSeqd esa fodflr gks x;kA fupys {kksHkeaM+y esa ewyHkwr {ks=h; izokg ok;qnkcm".kdfVca/k :i ls vfLFkj Fkk ftls fujis{k Hkzfeyrk ds ;kE;ksrjh forj.k ds y{k.k ds ifjorZu }kjk crk;k x;k gS ftlls coaMj ds cuus esa xfrdh; ÅtkZ feyhA bl nkSjku fujis{k Hkzfeyrk ds ek/; {ks=h; izokg vkSj ;kE;ksrjh izo.krk ds chp ldkjkRed lglaca/k Fkk ftlls ok;qnkcm".kdfVca/k }kjk coaMj ek/; izokg dh vUrjfØ;kvksa ds }kjk coaM+j dh xfrdh; ÅtkZ esa o`f) gqbZA ÅtZLoh fo’ys"k.k ls irk pyk gS fd coaM+j okyh xfrdh; ÅtkZ ds ldkjkRed ifjorZu ds mPp nj ds {ks= ifjorhZ ok;qnkc m".kdfVca/k ds ldkjkRed {ks=ksa ls esy [kkrs gSa vkSj ifjorhZ m".kdfVca/k ds ifjek.k Hkzfey mRifRr okys {ks= ds vkl&ikl coaM+j okyh xfrdh; ÅtkZ ds ifjorZu ds LFkkuh; le; ds lkFk esy [kkrs gaSA ewyHkwr {ks=h; izokg ds ;kE;ksrjh vi:i.k }kjk ifjofrZr ok;qnkc m".kdfVca/k ÅtkZ m".kdfVca/kh; pØokr dSeqd ds cuus vkSj mlds vkxs c<+us okys ,d egRoiw.kZ ÅtkZ L=ksr FkkA Analysis of dynamical conditions in respect of formation and growth of tropical cyclone Khai Muk over the Bay of Bengal during 11-14 November 2008 is discussed with focus on barotropic energy conversion at lower level. It is observed that the extension of subtropical easterlies from the Western Pacific in to central Bay of Bengal to the north and equatorial westerlies to the south of ITCZ during the above period constituted a large scale horizontal shear flow. This led to generation of cyclonic shear vorticity and initiation of disturbance which later developed in to tropical cyclone Khai Muk. The basic zonal flow in the lower troposphere was barotropically unstable as depicted by change of sign of meridional distribution of absolute vorticity which provided the kinetic energy for the growth of eddy. There existed positive correlation between mean zonal flow and the meridional gradient of absolute vorticity which favoured increase of eddy kinetic energy through barotropic eddy-mean flow interactions. Energetic analysis indicated that areas of high rate of positive change of eddy kinetic energy coincided with positive areas of barotropic conversion and the magnitude of barotropic conversion matched with local rate of change of eddy kinetic energy around the area of vortex generation. Barotropic energy conversion by meridional shear of basic zonal flow was an important energy source for the formation and initial growth of tropical cyclone Khai Muk.

Why does rapid contraction of the radius of maximum wind precede rapid intensification in tropical cyclones?

The radius of maximum wind (RMW) has been found to contract rapidly well preceding rapid intensification in tropical cyclones (TCs) in recent literature but the understanding of the involved dynamics is incomplete. In this study, this phenomenon is revisited based on ensemble axisymmetric numerical simulations. Consistent with previous studies, because the absolute angular momentum (AAM) is not conserved following the RMW, the phenomenon can not be understood based on the AAM-based dynamics. Both budgets of tangential wind and the rate of change in the RMW are shown to provide dynamical insights into the simulated relationship between the rapid intensification and rapid RMW contraction. During the rapid RMW contraction stage, due to the weak TC intensity and large RMW, the moderate negative radial gradient of radial vorticity flux and small curvature of the radial distribution of tangential wind near the RMW favor rapid RMW contraction but weak diabatic heating far inside the RMW leads to weak low-level inflow and small radial absolute vorticity flux near the RMW and thus a relatively small intensification rate. As RMW contraction continues and TC intensity increases, diabatic heating inside the RMW and radial inflow near the RMW increase, leading to a substantial increase in radial absolute vorticity flux near the RMW and thus the rapid TC intensification. However, the RMW contraction rate decreases rapidly due to the rapid increase in the curvature of the radial distribution of tangential wind near the RMW as the TC intensifies rapidly and RMW decreases.

A vorticity-and-stability diagram as a means to study potential vorticity nonconservation

The study of atmospheric circulation from a potential vorticity (PV) perspective has advanced our mechanistic understanding of the development and propagation of weather systems. The formation of PV anomalies by nonconservative processes can provide additional insight into the diabatic-to-adiabatic coupling in the atmosphere. PV nonconservation can be driven by changes in static stability, vorticity or a combination of both. For example, in the presence of localized latent heating, the static stability increases below the level of maximum heating and decreases above this level. However, the vorticity changes in response to the changes in static stability (and vice versa), making it difficult to disentangle stability from vorticity-driven PV changes. Further diabatic processes, such as friction or turbulent momentum mixing, result in momentum-driven, and hence vorticity-driven, PV changes in the absence of moist diabatic processes. In this study, a vorticity-and-stability diagram is introduced as a means to study and identify periods of stability- and vorticity-driven changes in PV. Potential insights and limitations from such a hyperbolic diagram are investigated based on three case studies. The first case is an idealized warm conveyor belt (WCB) in a baroclinic channel simulation. The simulation allows only condensation and evaporation. In this idealized case, PV along the WCB is first conserved, while stability decreases and vorticity increases as the air parcels move poleward near the surface in the cyclone warm sector. The subsequent PV modification and increase during the strong WCB ascent is, at low levels, dominated by an increase in static stability. However, the following PV decrease at upper levels is due to a decrease in absolute vorticity with only small changes in static stability. The vorticity decrease occurs first at a rate of 0.5 f per hour and later decreases to approximately 0.25 f per hour, while static stability is fairly well conserved throughout the period of PV reduction. One possible explanation for this observation is the combined influence of diabatic and adiabatic processes on vorticity and static stability. At upper levels, large-scale divergence ahead of the trough leads to a negative vorticity tendency and a positive static stability tendency. In a dry atmosphere, the two changes would occur in tandem to conserve PV. In the case of additional diabatic heating in the mid troposphere, the positive static stability tendency caused by the dry dynamics appears to be offset by the diabatic tendency to reduce the static stability above the level of maximum heating. This combination of diabatically and adiabatically driven static stability changes leads to its conservation, while the adiabatically forced negative vorticity tendency continues. Hence, PV is not conserved and reduces along the upper branch of the WCB. Second, in a fullfledged real case study with the Integrated Forecasting System (IFS), the PV changes along the WCB appear to be dominated by vorticity changes throughout the flow of the air. However, accumulated PV tendencies are dominated by latent heat release from the large-scale cloud and convection schemes, which mainly produce temperature tendencies. The absolute vorticity decrease during the period of PV reduction lasts for several hours, and is first in the order of 0.5 f per hour and later decreases to 0.1f per hour when latent heat release becomes small, while static stability reduces moderately. PV and absolute vorticity turn negative after several hours. In a third case study of an air parcel impinging on the warm front of an extratropical cyclone, changes in the horizontal PV components dominate the total PV change along the flow and thereby violate a key approximation of the two-dimensional vorticity-and-stability diagram. In such a situation where the PV change cannot be approximated by its vertical component, a higher-dimensional vorticity-and-stability diagram is required. Nevertheless, the vorticity-and-stability diagram can provide supplementary insights into the nature of diabatic PV changes.

Solsticial Hadley Cell ascending edge theory from supercriticality

How far the Hadley circulation’s ascending branch extends into the summer hemisphere is a fundamental but incompletely understood characteristic of Earth’s climate. Here, we present a predictive, analytical theory for this ascending edge latitude based on the extent of supercritical forcing. Supercriticality sets the minimum extent of a large-scale circulation based on the angular momentum and absolute vorticity distributions of the hypothetical state were the circulation absent. We explicitly simulate this latitude-by-latitude radiative-convective equilibrium (RCE) state. Its depth-averaged temperature profile is suitably captured by a simple analytical approximation that increases linearly with sinφ, where φ is latitude, from the winter to the summer pole. This, in turn, yields a one-third power-law scaling of the supercritical forcing extent with the thermal Rossby number. In moist and dry idealized GCM simulations under solsticial forcing performed with a wide range of planetary rotation rates, the ascending edge latitudes largely behave according to this scaling.

Steady flow in a frictionless homogenous ocean

A mathematical model is developed to study the free (frictionless) steady horizontal flow which can occur in a homogeneous ocean of constant depth. The flow satisfies the dynamic constraint that the vertical component of absolute vorticity is constant along a streamline. The conclusion is reached that in an enclosed ocean a free steady circulation cannot have any slow broad eastward currents. The eastward currents must occur as narrow streams of high velocity and high relative vorticity. Intensified currents are present along the eastern and western coasts. The theory which is developed for the homogeneous ocean of constant depth can be applied to the two-layer ocean if the horizontal divergence of flow is negligible. If the horizontal divergence is not negligible, then the intensification of poleward currents is more pronounced and that of equatorward currents less pronounced as compared with the homogeneous ocean.

The Role of Multiscale Interaction in Tropical Cyclogenesis and Its Predictability in Near-Global Aquaplanet Cloud-Resolving Simulations

Tropical cyclogenesis (TCG) is a multiscale process that involves interactions between large-scale circulation and small-scale convection. A near-global aquaplanet cloud-resolving model (NGAqua) with 4-km horizontal grid spacing that produces tropical cyclones (TCs) is used to investigate TCG and its predictability. This study analyzes an ensemble of three 20-day NGAqua simulations, with initial white-noise perturbations of low-level humidity. TCs develop spontaneously from the northern edge of the intertropical convergence zone (ITCZ), where large-scale flows and tropical convection provide necessary conditions for barotropic instability. Zonal bands of positive low-level absolute vorticity organize into cyclonic vortices, some of which develop into TCs. A new algorithm is developed to track the cyclonic vortices. A vortex-following framework analysis of the low-level vorticity budget shows that vertical stretching of absolute vorticity due to convective heating contributes positively to the vorticity spinup of the TCs. A case study and composite analyses suggest that sufficient humidity is key for convective development. TCG in these three NGAqua simulations undergoes the same series of interactions. The locations of cyclonic vortices are broadly predetermined by planetary-scale circulation and humidity patterns associated with ITCZ breakdown, which are predictable up to 10 days. Whether and when the cyclonic vortices become TCs depend on the somewhat more random feedback between convection and vorticity.

A more complete Rossby wave source

&lt;p&gt;Tropical convection drives extratropical variability on subseasonal to interannual time-scales by exciting Rossby wave trains in the upper troposphere. Traditionally the relevant Rossby wave source is considered to be the sum of vortex stretching and vorticity advection by the divergent horizontal flow ( - &amp;#8711;&amp;#183;&lt;strong&gt;u&lt;/strong&gt;&lt;sub&gt;&amp;#967;&lt;/sub&gt; (&amp;#950;+f) - &lt;strong&gt;u&lt;/strong&gt;&lt;sub&gt;&amp;#967;&lt;/sub&gt;&amp;#183;&amp;#8711; (&amp;#950;+f)). Since absolute vorticity is very small at the equator, the equatorward flanks of the upper tropospheric jets have been regarded the source region of Rossby wave trains. In these considerations vertical momentum advection is neglected, although, it is an important source for westerly momentum at the equator. The curl of vertical momentum advection is the sum of vertical vorticity advection and vortex tilting ( -&amp;#160; &amp;#969; &amp;#950;&lt;sub&gt;p&lt;/sub&gt; - &amp;#969;&lt;sub&gt;x&lt;/sub&gt; v&lt;sub&gt;p&lt;/sub&gt; + &amp;#969;&lt;sub&gt;y&lt;/sub&gt; u&lt;sub&gt;p&lt;/sub&gt;). These contributions are smaller than the traditional Rossby wave source in midlatidues by about one order of magnitude but they are of similar size in the tropics.&lt;/p&gt;

Extending Square Conservation to Arbitrarily Structured C-grids with Shallow Water Equations

The square conservation theory is widely used on latitude–longitude grids, but it is rarely implemented on quasi-uniform grids, given the difficulty involved in constructing anti-symmetrical spatial discrete operators on these grids. Increasingly more models are developed on quasi-uniform grids, such as arbitrarily structured C-grids. Thuburn–Ringler–Skamarock–Klemp (TRiSK) is a shallow water dynamic core on an arbitrarily structured C-grid. The spatial discrete operator of TRiSK is able to naturally maintain the conservation properties of total mass, total absolute vorticity and instantaneous total energy. The first 2 integral invariants are entirely conserved during integration, but the total energy dissipates when using the dissipative temporal integration schemes, i.e., Runge-Kutta. The method of strictly conserving the total energy simultaneously uses both an anti-symmetrical spatial discrete operator and square conservative temporal integration scheme. In this study, we demonstrate that square conservation is equivalent to energy conservation in both a continuous shallow water system and a discrete shallow water system of TRiSK, attempting to extend the square conservation theory to the TRiSK framework. To overcome the challenge of constructing an anti-symmetrical spatial discrete operator, we unify the unit of evolution variables of shallow water equations by Institute of Atmospheric Physics (IAP) transformation, expressing the temporal trend of the evolution variable by using the original operators of TRiSK. Using the square conservative Runge-Kutta scheme, the total energy is completely conserved, and there is no influence on the properties of conserving total mass and total absolute vorticity. In the standard shallow water numerical test, the square conservative scheme not only helps maintain total conservation of the three integral invariants but also creates less simulation error norms.