Scaling Laws for Barotropic Vortex Energy Dispersion

• Main Authors: Hua-Fu Wu, 吳華富
• Other Authors: 郭鴻基
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/18307592518316175769

碩士 === 國立臺灣大學 === 大氣科學研究所 === 97 === In this research, we extend the work in Smith(1993, 1997) to generalize the scaling laws for vortex energy dispersion and drift speed to include the influences of variable vortex profile and meridional shear in the zonal environmental wind. The vortex profiles used in barotropic model are DC vortex (DeMaria and Chan, 1984) and modified Rankine vortex. The physical problem of beta-drift and vortex energy dispersion we consider here has 7 parameters; drift speed , vortex energy dispersion , maximum tangential wind speed in the vortex , the radius of maximum wind , planetary vorticity gradient , the integration time and the shear in the zonal environmental wind 。The use of dimensional analysis reduces these 7 parameters to 5, and a non-dimensional exponent related to the decrease of wind speed with radius in the outer part of the vortex: non-dimensional drift speed , non-dimensional vortex energy dispersion , Rossby number , non-dimensional time , non-dimensional horizontal shear and non-dimensional exponent and . In this research, we attempt to obtain the following scaling laws. 1. Scaling laws for vortex energy dispersion and drift speed. 2. The influences of vortex structure on the scaling law. 3. The influences of horizontal shear on the scaling laws. There are three groups of experiments in this research. The non-dimensional drift speed and non-dimensional vortex energy dispersion are given by 、 and . In experiment 1, we examine the case with no horizontal shear ( ) and investigate the scaling laws for a range of Rossby number, vortex profile factor and non-dimensional time . In experiment 2, we replace in experiment 1 with . In experiment 3, we fix the vortex profile ( ) and investigate the scaling laws for a range of Rossby number, horizontal shear and non-dimensional time . From the scaling laws we have the following conclusions: 1. When non-dimensional time are fixed with no shear, non-dimensional energy dispersion is large with small Rossby number. 2. When non-dimensional time, beta, vortex profile and circulation are fixed with no shear, energy dispersion is large with large radius of maximum wind speed. 3. When integration time, beta, vortex profile and circulation are fixed with no shear, energy dispersion is large with large vortex maximum tangential wind speed. 4. When non-dimensional time, beta, maximum tangential wind speed and radius of maximum wind speed are fixed with no shear, energy dispersion is large with small vortex profile factor. 5. When non-dimensional time, beta, maximum tangential wind speed and radius of maximum wind speed are fixed with no shear, Rankine vortex has less energy dispersion and larger drift speed than DC vortex with . 6. When we fix non-dimensional time, beta, maximum tangential wind speed, radius of maximum wind speed and , energy dispersion is large with large horizontal shear. 7. When non-dimensional time with are fixed no shear, non-dimensional energy dispersion is proportional to the square of drift speed.