Abstract
The thermal wind balance in tropical cyclone (TC) eyewalls has been controversial for decades. This study reveals the relationship between the acceleration and curvature on the TC secondary circulation streamline, providing a way to judge thermal wind balance or imbalance in TCs from a simple but clear perspective. According to the relationship between the curvature and acceleration on the streamline, the vertical and radial components of the acceleration cannot be zero simultaneously on the streamline curve, implying that the thermal wind imbalance corresponds to the curvature of the streamline. On the regular scales of TCs, we discuss the conditions of the thermal wind balance approximation and find that the conditions become more stringent with increasing altitudes. In the TC secondary circulation, as an indication of thermal wind imbalance, gradient wind imbalance can be found in the low-level eyewall since there is usually a large curvature when the inflow in the low-level eyewall turns into updrafts sharply. Additionally, gradient wind imbalance also appears at the top level of TC eyewalls because the stringent conditions are too easily broken there.
References
Braun, S. A., 2002: A cloud-resolving simulation of Hurricane Bob (1991): Storm structure and eyewall buoyancy. Mon. Wea. Rev., 130, 1573–1592, doi: https://doi.org/10.1175/1520-0493(2002)130<1573:ACRSOH>2.0.CO;2.
Bryan, G. H., and R. Rotunno, 2009: Evaluation of an analytical model for the maximum intensity of tropical cyclones. J. Atmos. Sci., 66, 3042–3060, doi: https://doi.org/10.1175/2009JAS3038.1.
Charney, J. G., and A. Eliassen, 1964: On the growth of the hurricane depression. J. Atmos. Sci., 21, 68–75, doi: https://doi.org/10.1175/1520-0469(1964)021<0068:OTGOTH>2.0.CO;2.
Cohen, Y., N. Harnik, E. Heifetz, et al., 2017: On the violation of gradient wind balance at the top of tropical cyclones. Geophys. Res. Lett., 44, 8017–8026, doi: https://doi.org/10.1002/2017GL074552.
Eliassen, A., 1951: Slow thermally or frictionally controlled meridional circulation in a circular vortex. Astrophys. Norv., 5, 19–60.
Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585–605, doi: https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.
Hawkins, H. F., and D. T. Rubsam, 1968: Hurricane Hilda, 1964. Mon. Wea. Rev., 96, 617–636, doi: https://doi.org/10.1175/1520-0493(1968)096<0617:HH>2.0.CO;2.
Huang, Y. W., Y. H. Duan, J. C. L. Chan, et al., 2019: A method for diagnosing the secondary circulation with saturated moist entropy structure in a mature tropical cyclone. Adv. Atmos. Sci., 36, 804–810, doi: https://doi.org/10.1007/s00376-019-9054-5.
Jorgensen, D. P., 1984: Mesoscale and convective-scale characteristics of mature hurricanes. Part II. Inner core structure of Hurricane Allen (1980). J. Atmos. Sci., 41, 1287–1311, doi: https://doi.org/10.1175/1520-0469(1984)041<1287:MACSCO>2.0.CO;2.
Kepert, J., 2001: The dynamics of boundary layer jets within the tropical cyclone core. Part I: Linear theory. J. Atmos. Sci., 58, 2469–2484, doi: https://doi.org/10.1175/1520-0469(2001)058<2469:TDOBLJ>2.0.CO;2.
Kreyszig, E., 1991: Differential Geometry. Dover Publications, New York, 366 pp.
La Seur, N. E., and H. F. Hawkins, 1963: An analysis of Hurricane Cleo (1958) based on data from research reconnaissance aircraft. Mon. Wea. Rev., 91, 694–709, doi: https://doi.org/10.1175/1520-0493(1963)091<0694:AAOHCB>2.3.CO;2.
Liu, Y. B., 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, doi: https://doi.org/10.1175/1520-0493(1999)127<2597:AMNSOH>2.0.CO;2.
Montgomery, M. T., J. A. Zhang, and R. K. Smith, 2014: An analysis of the observed low-level structure of rapidly intensifying and mature Hurricane Earl (2010). Quart. J. Roy. Meteor. Soc., 140, 2132–2146, doi: https://doi.org/10.1002/QJ.2283.
Schwendike, J., and J. D. Kepert, 2008: The boundary layer winds in Hurricanes Danielle (1998) and Isabel (2003). Mon. Wea. Rev., 136, 3168–3192, doi: https://doi.org/10.1175/2007MWR2296.1.
Shapiro, L. J., and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39, 378–394, doi: 10.1175/1520–0469(1982)039<0378:TROBHT>2.0.CO;2.
Smith, R. K., 1980: Tropical cyclone eye dynamics. J. Atmos. Sci., 37, 1227–1232, doi: https://doi.org/10.1175/1520-0469(1980)037<1227:TCED>2.0.CO;2.
Smith, R. K., 2003: A simple model of the hurricane boundary layer. Quart. J. Roy. Meteor. Soc., 129, 1007–1027, doi: https://doi.org/10.1256/qj.01.197.
Smith, R. K., and S. Vogl, 2008: A simple model of the hurricane boundary layer revisited. Quart. J. Roy. Meteor. Soc., 134, 337–351, doi: https://doi.org/10.1002/qj.216.
Smith, R. K., M. T. Montgomery, and N. van Sang, 2009: Tropical cyclone spin-up revisited. Quart. J. Roy. Meteor. Soc., 135, 1321–1335, doi: https://doi.org/10.1002/qj.428.
Stern, D. P., and D. S. Nolan, 2009: Reexamining the vertical structure of tangential winds in tropical cyclones: Observations and theory. J. Atmos. Sci., 66, 3579–3600, doi: https://doi.org/10.1175/2009JAS2916.1.
Wang, H., C.-C. Wu, and Y. Q. Wang, 2016: Secondary eyewall formation in an idealized tropical cyclone simulation: Balanced and unbalanced dynamics. J. Atmos. Sci., 73, 3911–3930, doi: https://doi.org/10.1175/JAS-D-15-0146.1.
Wang, X. B., Y. M. Ma, and N. E. Davidson, 2013: Secondary eyewall formation and eyewall replacement cycles in a simulated hurricane: Effect of the net radial force in the hurricane boundary layer. J. Atmos. Sci., 70, 1317–1341, doi: https://doi.org/10.1175/JAS-D-12-017.1.
Willoughby, H. E., 1979: Forced secondary circulations in hurricanes. J. Geophys. Res. Atmos., 84, 3173–3183, doi: https://doi.org/10.1029/JC084iC06p03173.
Willoughby, H. E., 1990: Gradient balance in tropical cyclones. J. Atmos. Sci., 47, 265–274, doi: https://doi.org/10.1175/1520-0469(1990)047<0265:GBITC>2.0.CO;2.
Wirth, V., and T. J. Dunkerton, 2009: The dynamics of eye formation and maintenance in axisymmetric diabatic vortices. J. Atmos. Sci., 66, 3601–3620, doi: https://doi.org/10.1175/2009JAS3031.1.
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The authors would like to thank Dr. Tim Dunkerton of the NorthWest Research Associates for his helpful suggestions on this manuscript.
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Supported by the National Natural Science Foundation of China (42175016).
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Huang, Y., Duan, Y. & Lyu, X. Thermal Wind Imbalance along the Curved Streamline of the Secondary Circulation in Tropical Cyclones. J Meteorol Res 37, 107–111 (2023). https://doi.org/10.1007/s13351-023-2092-z
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DOI: https://doi.org/10.1007/s13351-023-2092-z