Abstract
The Earth’s atmosphere is generally a stochastic dynamical system in which physical processes take place within a wide range of temporal and spatial scales. Dynamical systems associated with small-scale perturbations often have a characteristically low predictability due to our lacked understanding of various physical processes and their feedback mechanisms. In contrast, the atmospheric motion at the meso- to synoptic-scales tends to possess a slow manifold with more predictable behaviours. It is this slow manifold component, often referred to as the balanced flow to be distinguished from the fast smaller-scale motion, that is more of our interest because it plays a critical role in evolution of common weather systems such as midlatitude baroclinic disturbances, mesoscale convective systems (MCSs), or tropical cyclones (TCs). Any weather system that differs too far from a balanced state will undergo a brief period of rapid adjustment, i.e., the so-called adjustment processes. From the balanced perspective, the evolution of mesoscale and larger-scale systems can be viewed as a series of continuous balanced adjustments, often referred to as the quasi-balanced dynamics. Herein, the quasi-balanced dynamic is simply that the mean flows are in a near-balanced state, but the (weak) superimposed perturbation flows are not, which are often related to the development of secondary circulation beyond the framework of balanced appropriations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
One can see this directly by doing a simple coordinate transformation from z to p-coordinates as follows. Define the coordinate transformation as: x p = x z ; y p = y z ; p = p (x z , y z , z); t p = t z , and then the Jacobian determinant will be J = │p∂p/∂z│. Under this coordinate transformation, the relative vorticity defined as ζ i ≡ ε ijk ∂u j /∂x k , where ε ijk is Levi-Civia symbol, will transform to \( {\zeta}_i^p=\left|J\right|\partial {x}_j^p/\partial {x}_i{\zeta}_i^z \). Apparently, |J| ≠ 1, and thus the horizontal component of the relative vorticity in z-coordinates is no longer preserved as it is transformed to p-coordinates. Therefore, the correct definition of PV in curvilinear coordinate needs to take into account properly the pseudo tensor properties of the coordinate transformation.
References
Chen, Y.-S. and M.K. Yau, 2001: Spiral bands in a simulated Hurricane. Part I: Vortex Rossby Wave verification. J. Atmos. Sci., 58, 2128-2145.
Davis, C.A., 1992: Piecewise potential vorticity inversion. J. Atmos. Sci., 49, 1397-1411.
Davis, C.A. and K. Emanuel, 1991: Potential vorticity diagnostics of cyclogenesis. Mon. Wea. Rev., 119, 424-439.
Frank, W. M. and E.A. Ritchie, 2001: Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 129, 2249-2269.
Gall, R.L., J. Tuttle and P. Hildebrand, 1997: Small-scale spiral bands observed in Hurricanes Andrew, Hugo and Erin. Mon. Wea. Rev., 126, 1749-1766.
Huo, Z.-H., D.-L. Zhang and J.R. Gyakum, 1998: An application of potential vorticity inversion to improving the numerical prediction of the March 1993 Superstorm. Mon. Wea. Rev., 126, 424-436.
Huo, Z.-H., D.-L. Zhang and J.R. Gyakum, 1999a: The interaction of potential vorticity anomalies in extratropical cyclogenesis. Part I: Static piecewise inversion. Mon. Wea. Rev., 127, 2546-2561.
Huo, Z.-H., D.-L. Zhang and J.R. Gyakum, 1999b: The interaction of potential vorticity anomalies in extratropical cyclogenesis. Part II: Sensitivity to initial perturbations. Mon. Wea. Rev., 127, 2563-2575.
Hoskins, B.J., M.E. McIntyre and A.W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877-946.
Jones, S.C., 1995: The evolution of Vortices in Vertical Shear. I: Initially barotropic Vortices. Q.J.R. Meterorol. Soc., 121, 821-851.
Kieu, C.Q. and D.-L. Zhang., 2010: A piecewise potential vorticity inversion algorithm and its application to hurricane inner-core anomalies. J. Atmos. Sci., 67, 1745-1758.
Kieu, C.Q. and D.-L. Zhang, 2012: Is the isentropic surface always impermeable to the potential vorticity substance? Adv. Atmos. Sci., 29, doi: 10.1007/s00376-011-0227-0.
Krishnamurti, T.N., 1968: A diagnostic balance model for studies of weather systems of low and high latitudes, Rossby number less than 1. Mon. Wea. Rev., 96, 197-207.
Liu, Y., D.-L. Zhang and M.K. Yau, 1999: A multiscale numerical study of Hurricane Andrew (1992). Part II: Kinematics and inner-core structures. Mon. Wea. Rev., 127, 2597-2616.
Möller, J.D. and L.J. Shapiro, 2002: Balanced contributions to the intensification of Hurricane Opal as diagnosed from a GFDL model forecast. Mon. Wea. Rev., 130, 1866-1881.
Möller, J.D. and S.C. Jones, 1998: Potential vorticity inversion for tropical cyclones using the Asymmetric Balance Theory. J. Atmos. Sci., 55, 259.
Montgomery, M.T. and J.L. Franklin, 1998: An assessment of the balance approximation in hurricanes. J. Atmos. Sci., 55, 2193-2200.
Morgan, M.C., 1999: Using Piecewise Potential Vorticity Inversion to Diagnose Frontogenesis. Part I: A partitioning of the Q vector applied to diagnosing surface frontogenesis and vertical motion. Mon. Wea. Rev., 127, 2796-2821.
Shapiro, L.J., 1996: The motion of Hurricane Gloria: A potential vorticity diagnosis. Mon. Wea. Rev., 124, 2497-2508.
Shapiro, L.J. and M.T. Montgomery, 1993: A three-dimensional balance theory for rapidly rotating vortices. J. Atmos. Sci., 50, 3322-3335.
Shapiro, L.J. and J.L. Franklin, 1995: Potential vorticity in Hurricane Gloria. Mon. Wea. Rev., 123, 1465-1475.
Shapiro, L.J. and J.L. Franklin, 1999: Potential vorticity asymmetries and tropical cyclone motion. Mon. Wea. Rev., 127, 124-131.
Wang, X.-B. and D.-L. Zhang, 2003: Potential vorticity diagnosis of a simulated hurricane. Part I: Formulation and quasi-balanced flow. J. Atmos. Sci., 60, 1593-1607.
Wang, Y. and G.J. Holland, 1996: Tropical cyclone motion and evolution in vertical shear. J. Atmos. Sci., 53, 3313-3332.
Wu, C.-C. and K.A. Emanuel, 1995a: Potential vorticity diagnostics of hurricane movement. Part I: A case study of Hurricane Bob (1991). Mon. Wea. Rev., 123, 69-92.
Wu, C.-C. and K.A. Emanuel, 1995b: Potential vorticity diagnostics of hurricane movement. Part II: Tropical storm Ana (1991) and Hurricane Andrew (1992). Mon. Wea. Rev., 123, 93-109.
Yau, M.K., Y.-B. Liu, D.-L. Zhang and Y.-S. Chen, 2004: A multiscale numerical study of Hurricane Andrew (1992). Part VI: Small-scale inner-core structures and wind streaks. Mon. Wea. Rev., 132, 1410-1433.
Zhang, D.-L., Y. Liu and M.K. Yau, 2000: A multiscale numerical study of Hurricane Andrew (1992). Part III: Dynamically induced vertical motion. Mon. Wea. Rev., 128, 3772-3788.
Zhang, D.-L., Y. Liu and M.K. Yau, 2001: A multiscale numerical study of Hurricane Andrew (1992). Part IV: Unbalanced flows. Mon. Wea. Rev., 129, 92-107.
Zhang, D.-L., Y. Liu and M.K. Yau, 2002: A multiscale numerical study of Hurricane Andrew (1992). Part V: Inner-core thermodynamics. Mon. Wea. Rev., 130, 2745-2763.
Zhang, D.-L. and C.K. Kieu, 2005: Shear-forced vertical circulations in tropical cyclones. Geophys. Res. Lett., 32, L13822, doi:10.1029/2005GL023146.
Zhu, T., D.-L. Zhang and F. Weng, 2004: Numerical simulation of Hurricane Bonnie (1998). Part I: Eyewall evolution and intensity changes. Mon. Wea. Rev., 132, 225-241.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Capital Publishing Company
About this chapter
Cite this chapter
Kieu, C.Q., Zhang, DL. (2016). Balanced Dynamics in Tropical Cyclones. In: Mohanty, U.C., Gopalakrishnan, S.G. (eds) Advanced Numerical Modeling and Data Assimilation Techniques for Tropical Cyclone Prediction. Springer, Dordrecht. https://doi.org/10.5822/978-94-024-0896-6_24
Download citation
DOI: https://doi.org/10.5822/978-94-024-0896-6_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-024-0895-9
Online ISBN: 978-94-024-0896-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)