TOPOGRAPHIC EFFECT ON A BAROTROPIC CYCLONE ENCOUNTERING A MOUNTAIN: LABORATORY EXPERIMENT AND NUMERICAL SIMULATION Hung-Cheng Chen*, Chien-Cheng Chang and Chin-Chou Chu Institute of Applied Mechanics, National Taiwan University, Taipei, TAIWAN, ROC 1. INTRODUCTION The importance of topographic features on the evolution of tropical cyclones has been revealed in the literatures (e.g., Kuo et al. (2001); Lin et al. (1999)). In the present study, we do not dig into the complicated dynamics of tropical cyclones and their associated impacts from the topographic obstacles. Instead, we investigate the topographic effect of a barotropic vortex simply from the viewpoint of potential vorticity conservation under the framework of shallow water model. Several dimensionless parameters are defined to classify the flow dynamics qualitatively. From the experimental side, a stirred-induced vortex was generated in the vicinity of a scaled 3-D elliptic hill or in the vicinity of a north-south ridge in a rotating tank. From the numerical side, calculations based upon a modified shallow water model were performed to validate the experimental results. Close agreements were found between these two approaches, including the streamlines patterns and the vortex trajectory. 2. THEORETICAL BACKGROUND 2.1 Beta Similarity Laws For a Strong Cyclone Near Topography Under the shallow water framework, we consider a strong cyclone motion ( ) 1 ( O Ro ≈ ) in the vicinity of an isolated topography by assuming small variations of η and B h , we can give an appropriate scaling on the cyclone motion so that the magnitudes of the non-dimensional variables are of order unity. Take the maximum tangential speed of the cyclone m V as the reference velocity, m m m R V = ζ as the reference vorticity and 1 − m ζ as the reference time (the vortex turnaround time). In addition, we choose the maximum vortex depression v η and the maximum topographic height M h as the reference free-surface deviation and reference bottom topographic height, respectively, and thus we have two non-dimensional PV conservation forms where Eqns (1a) and (1b) represents the non-dimensional PV conservation relationship, respectively. In these two equations, we have four important similarity parameters: (a) the planetary beta parameter , (b) the topographic beta parameter and (c) the vortex beta parameter. 6C.1 ( ) ( ) ( ) 0 1 * * * * * * * * * 0 = − + + − + p v b M b p s h s h y Dt D η ζ γµ µ β ( ) ( ) ( ) 0 1 * * * * * * * * * * 0 = − + + + − + m v y b M b m s s h s h y Dt D η ζ γµ µ β m m m y p m m D V R s f V R         =         = 2 0 2 0 * 0 β β D V a R s f m m M 0 = µ D V R s f m m v 2 0 = γ (1a) (1b) (2) (3) (4) * Corresponding author address: Hung-Cheng Cheng, National Taiwan University, Inst. of App. Mech., Taipei, 106 TAIWAN, ROC; e-mail: d5543004@gauss.iam.ntu.edu.tw