Final Report Summary - EITC (Emergence and intensification of tropical cyclones)
The goal of this project is to provide a theory of the systematic organisation of turbulent motions that can intensify a weak tropical cyclone and maintain it at large intensity against dissipation. The turbulent motions are intermittently generated by convection with a wide variety of scales and form organised patches of swirling motion. As these patches are deformed (sheared) by the mean vortex, they transfer their momentum to the vortex and intensify it in this process that is termed as axisymmetrisation. While axisymmetrisation has been shown in previous studies to intensify the mean vortex, the continuous and random stirring of the vortex by the patches has not been treated.
In this project we formulate a statistical framework for the interaction of the randomly generated vorticity patches and the mean vortex and provide a theory that can make quantitative predictions for the characteristics of the vortex. The first objective of this project is to address whether axisymmetrisation can lead to the transformation of a small depression into a tropical cyclone of sufficient intensity. Obtaining the scales and characteristics of the emergent vortices, as well as understanding the eddy-mean vortex dynamics leading to such intensification is the focal point of this objective. The second objective is to address whether the organisation of the turbulent motions can maintain a strong tropical cyclone against processes that tend to disrupt it. Again, focus is on the eddy-mean vortex dynamics and on the scales and the structure of the vortex. The third objective is to study the effect of stratification and externally imposed perturbations on the aforementioned processes.
The process of axisymmetrisation in which the patches are deformed by the vortex and transfer their momentum is analogous to the mechanism by which small scale storms (eddies) intensify and maintain the jet stream in the midlatitudes. As a result, insight into the axisymmetrisation dynamics can be gained by first studying the emergence of a zonal jet out of a background of stochastically forced eddies, because of the simplification that planar geometry brings. So we first studied the problem of jet formation in a two dimensional flow with no height variation. We developed new analytical tools and were able to show that two competing mechanisms control the instability giving rise to a zonal jet: deformation (shearing) of the eddies that is jet forming and eddy propagation that opposes the formation of a mean flow. We also showed that jets emerge only when the eddies have sufficiently small scales and their stochastic excitation has an amplitude exceeding a threshold and developed the theory that can make quantitative predictions for these thresholds.
The insights from the problem of jet formation and the tools developed were used to study a two dimensional model of the interaction between stochastically forced vorticity patches and a mean vortex. Under a statistical framework, an autonomous non-linear system governing the evolution of the mean vortex and the eddy (vorticity patches) statistics was obtained. The initial instability of this nonlinear system giving rise to a circular vortex was investigated and the characteristics of the emergent cyclone were obtained. In direct analogy to the problem of jet formation, the same mechanisms were found to control the instability: shearing of the eddies that is destabilising and propagation of the eddies that is stabilising. In addition, patches with small (large) scales were found to be destabilising (stabilising). A threshold for the amplitude of the excitation was found, above which an infinitesimal vortex is intensified. This means that a sufficient amount of turbulence should coexist with a tropical depression, for the depression to grow.
The equilibration of the patches-mean vortex system was then studied and the characteristics of the strong, equilibrated vortex were obtained. The organisation of the turbulent fluxes by the mean vortex is able to maintain it at finite amplitude against dissipation. We found that the key feature of the equilibrium structure is that the angular velocity profile is configured so that the vortex is close to the stability boundary. That is, if its intensity is further increases it will be deformed by small perturbations and break.
The effect of stratification and externally imposed perturbations was then addressed. While stratification and divergent motions were found to quantitatively alter some of the characteristics of intensification and maintenance, the qualitative features remain the same. A large environmental perturbation that imposes significant stress on the cyclones is the variation of the Coriolis force with latitude (the gradient of planetary vorticity beta), as previous studies have showed that in the presence of beta, the cyclones change their track and are also significantly deformed. We investigated the effect of beta on the emergence and equilibration process. We found that the vortices propagate in the presence of beta in the retrograde direction with at most the Rossby wave phase speed. The vortex equilibrates at a structure that is close to the stability boundary that is now influenced by beta. However, when the vortex excitation by the patches is above a threshold the vortex breaks to form a zonal jet.
We have therefore achieved a comprehensive derstanding of the organisation of turbulent fluxes in the intensification and maintenance of a coherent vortex, a key process in both the intensification of a tropical cyclone and in the formation of secondary eye walls. We have also obtained a theory that can make quantitative predictions about the level of random stirring above which a weak depression develops into a robust cyclone and about the structure of the resulting vortex as a function of large scale parameters (stratification, beta). A better understanding of tropical cyclone dynamics is of great interest for organisations making important environmental policy decisions due to the catastrophic consequences of these phenomena.
Scientist in charge: Petros Ioannou, Build IV, office 32, pjioannou@phys. uoa. gr
Project website: http://web. cc. uoa. gr/~pji/eitc
In this project we formulate a statistical framework for the interaction of the randomly generated vorticity patches and the mean vortex and provide a theory that can make quantitative predictions for the characteristics of the vortex. The first objective of this project is to address whether axisymmetrisation can lead to the transformation of a small depression into a tropical cyclone of sufficient intensity. Obtaining the scales and characteristics of the emergent vortices, as well as understanding the eddy-mean vortex dynamics leading to such intensification is the focal point of this objective. The second objective is to address whether the organisation of the turbulent motions can maintain a strong tropical cyclone against processes that tend to disrupt it. Again, focus is on the eddy-mean vortex dynamics and on the scales and the structure of the vortex. The third objective is to study the effect of stratification and externally imposed perturbations on the aforementioned processes.
The process of axisymmetrisation in which the patches are deformed by the vortex and transfer their momentum is analogous to the mechanism by which small scale storms (eddies) intensify and maintain the jet stream in the midlatitudes. As a result, insight into the axisymmetrisation dynamics can be gained by first studying the emergence of a zonal jet out of a background of stochastically forced eddies, because of the simplification that planar geometry brings. So we first studied the problem of jet formation in a two dimensional flow with no height variation. We developed new analytical tools and were able to show that two competing mechanisms control the instability giving rise to a zonal jet: deformation (shearing) of the eddies that is jet forming and eddy propagation that opposes the formation of a mean flow. We also showed that jets emerge only when the eddies have sufficiently small scales and their stochastic excitation has an amplitude exceeding a threshold and developed the theory that can make quantitative predictions for these thresholds.
The insights from the problem of jet formation and the tools developed were used to study a two dimensional model of the interaction between stochastically forced vorticity patches and a mean vortex. Under a statistical framework, an autonomous non-linear system governing the evolution of the mean vortex and the eddy (vorticity patches) statistics was obtained. The initial instability of this nonlinear system giving rise to a circular vortex was investigated and the characteristics of the emergent cyclone were obtained. In direct analogy to the problem of jet formation, the same mechanisms were found to control the instability: shearing of the eddies that is destabilising and propagation of the eddies that is stabilising. In addition, patches with small (large) scales were found to be destabilising (stabilising). A threshold for the amplitude of the excitation was found, above which an infinitesimal vortex is intensified. This means that a sufficient amount of turbulence should coexist with a tropical depression, for the depression to grow.
The equilibration of the patches-mean vortex system was then studied and the characteristics of the strong, equilibrated vortex were obtained. The organisation of the turbulent fluxes by the mean vortex is able to maintain it at finite amplitude against dissipation. We found that the key feature of the equilibrium structure is that the angular velocity profile is configured so that the vortex is close to the stability boundary. That is, if its intensity is further increases it will be deformed by small perturbations and break.
The effect of stratification and externally imposed perturbations was then addressed. While stratification and divergent motions were found to quantitatively alter some of the characteristics of intensification and maintenance, the qualitative features remain the same. A large environmental perturbation that imposes significant stress on the cyclones is the variation of the Coriolis force with latitude (the gradient of planetary vorticity beta), as previous studies have showed that in the presence of beta, the cyclones change their track and are also significantly deformed. We investigated the effect of beta on the emergence and equilibration process. We found that the vortices propagate in the presence of beta in the retrograde direction with at most the Rossby wave phase speed. The vortex equilibrates at a structure that is close to the stability boundary that is now influenced by beta. However, when the vortex excitation by the patches is above a threshold the vortex breaks to form a zonal jet.
We have therefore achieved a comprehensive derstanding of the organisation of turbulent fluxes in the intensification and maintenance of a coherent vortex, a key process in both the intensification of a tropical cyclone and in the formation of secondary eye walls. We have also obtained a theory that can make quantitative predictions about the level of random stirring above which a weak depression develops into a robust cyclone and about the structure of the resulting vortex as a function of large scale parameters (stratification, beta). A better understanding of tropical cyclone dynamics is of great interest for organisations making important environmental policy decisions due to the catastrophic consequences of these phenomena.
Scientist in charge: Petros Ioannou, Build IV, office 32, pjioannou@phys. uoa. gr
Project website: http://web. cc. uoa. gr/~pji/eitc