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The Role of Vortex Structure in Tropical Cyclone Motion Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1987 The role of vortex structure in tropical cyclone motion. Fiorino, Michael. http://hdl.handle.net/10945/22465 :A 9o943-R00fe NAVAL POSTIiRADUATE SCHOOL Monterey, California DISSERTATION THE ROLE OF VORTEX STRUCTURE IN TROPICAL CYCLONE MOTION by Michael Fiorino December 1987 Dissertation Supervisor: R.L. Elsberry Approved for public release; distribution is unlimited T238908 IJJRITY CLASSIFICATION OF THIS PAGE REPORT DOCUMENTATION PAGE 8REP0RT SECURITY CLASSIFICATION lb RESTRICTIVE MARKINGS JNCLASSIFIED aSECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION /AVAILABILITY OF REPORT Approved for public release; / : DECLASSIFICATION DOWNGRADING SCHEDULE distribution is unlimited. ERFORMING ORGANIZATION REPORT NUM8ER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S) INAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION (If applicable) uval Postgraduate School 63 Naval Postgraduate School l^DORESS {City, State, and ZIP Code) 7b. ADDRESS {City, State, and ZIP Code) /.mterey, California 93943-5000 Monterey, California 93943-5000 iNAME OF FUNDING /SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (If applicable) :.\DORESS (City, State, and ZIP Code) 10. SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK WORK UNIT ELEMENT NO. NO. NO ACCESSION NO. TITLE (Include Security Classification) e Role of Vortex Structure in Tropical Cyclone Motion »ERSONAL AUTHOR(S) Fiorino, Michael TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Year, Month, Day) IS. PAGE COUNT .D. Dissertation FROM TO 1987 December 371 UPPLEMENTARY NOTATION COSATl CODES 18. SUBJECT TERMS {Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROUP Tropical cyclone motion, Barotropic model. Tropical cyclones. Circulation analysis, Beta drift ABSTRACT {Continue on reverse if necessary and Identify by block number) The role of vortex structure in tropical cyclone motion is studied using .moving-grid, nondivergent barotropic model on a beta plane in a no-flow vironment. Initial condition sensitivity tests reveal that the northwest- rd "beta" drift of the vortex is controlled by the symmetric circulation the r = 300 - 800 km "critical" annulus. Enhanced cyclonic or anticyclon- flow in this critical annulus leads to long-term cyclonic or anticyclonic rning motions. The dynamics of the motion process is examined in terms of e symmetric and asymmetric circulations. When the vortex is moving in a asi-steady manner, the asymmetric flow appears as a pair of large-scale, unter-rotating gyres with a broad "ventilation" flow through the vortex nter. A second much smaller pair of gyres is also found near the center. is the interaction between these two sets of gyres and the symmetric flow at governs the motion process as revealed by a streamfunction tendency lOlSTRIBUTION/ AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION )(UNCLASSIFIED/UNLIMITED D SAME AS RPT. Q DTIC USERS UNCLASSIFIED NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Code) -:2c. OFFICE SYMBOL R.L. Elsberry (408)-646-2373 63 Es 83 APR edition may be used until exhausted. :F0RM 1473, 84 MAR SECURITY CLASSIFICATION OF THIS PAGE All other editions are obsolete ft U.S. Governmtnt Printlns Office: 1986—«06-24. 1 SECURITY CLASSIFICATION OF TmIS PAGC rVian Dmtm Bntt94) 19. cont. analysis and dynamical sensitivity tests in which the model equation is modified during the integration. Beta drift can be described as a balancing process between linear Rossby disper- sion which generates the asymmetric gyres and nonlinear advec- tion that moves the vortex to limit gyre development. Vortex structure is the key to this balance as it determines both the linear generation of the asymmetric forcing and the nonlinear interaction between the symmetric and asymmetric circulations. S N 0102- LP- 014- 6601 ^ SeCURITY CLASSIFICATION OF THIS P kGt.(WhM% Dmtm Snffd) Approved for public release; distribution is unlimited The Role of Vortex Structure in Tropical Cyclone Motion by Michael Fiorino B.S., Pennsylvania State University, 1975 M.S., Pennsylvania State University, 1978 Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY IN METEOROLOGY from the NAVAL POSTGRADUATE SCHOOL December 1987 -Xt ,- r ABSTRACT The role of vortex structure in tropical cyclone motion is studied using a moving-grid, nondivergent barotropic model on a ^ plane in a no-flow environment. Initial condition sensitivity tests reveal that the northwestward "beta" drift of the vortex is controlled by the symmetric circulation in the r = 300 - 800 km "critical" annulus. Enhanced cyclonic or anticyclonic flow in this critical annulus leads to long-term cyclonic or anticyclonic turning motions. The dynamics of the motion process is examined in terms of the symmetric and asymmetric circulations. When the vortex is moving in a quasi-steady manner, the asymmetric flow appears as a pair of large-scale, counter- rotating gyres with a broad "ventilation" flow through the vortex center. A second much smaller pair of gyres is also found near the center. It is the interaction between these two sets of gyres and the symmetric flow that governs the motion process as revealed by a streamfunction tendency analysis and dynamical sensitivity tests in which the model equation is modified during the integration. Beta drift can be described as a balancing process between linear Rossby dispersion which generates the asymmetric gyres and nonlinear advection that moves the vortex to limit gyre development. Vortex structure is the key to this balance as it determines both the linear generation of the asymmetric forcing and the nonlinear interaction between the symmetric and asymmetric circulations. TABLE OF CONTENTS I. INTRODUCTION 19 A. CURRENT UNDERSTANDING 20 B. RESEARCH GOALS 25 II. THE MODEL AND NUMERICAL PROCEDURES 28 A. ANALYTICAL FORMULATION 28 B. NUMERICAL FORMULATION 30 1. Boundary Conditions 31 2. Moving Grid 31 3. Vortex Center Definition 3 2 4. Summary 33 C. NUMERICAL PRECISION 33 1. Radius of Maximum Wind Test 34 2. Horizontal Resolution Effects 36 3. Domain Size Effects 44 D. SUMMARY 46 III. DEPENDENCE OF VORTEX MOTION ON THE INITIAL SYMMETRIC FLOW 48 A. VORTEX STRUCTURE 48 B. VORTEX SPECIFICATION 51 1. Combining Two Profiles 52 2. Forcing a Zero in a Profile 54 C. EXPERIMENT DESIGN 56 D. TRACK RESULTS WITH THE BASIC PROFILES 57 E. THE INNER-OUTER STRENGTH CHANGE PROFILES 61 F. SYMMETRIC PERTURBATIONS 66 G. FAR OUTER FLOW 69 H. SPEED OF MOTION AS A FUNCTION OF STRENGTH 72 I. SUMMARY AND DISCUSSION 72 IV. EVOLUTION OF THE SYMMETRIC AND ASYMMETRIC CIRCULATIONS -77 A. SYMMETRIC/ASYMMETRIC SEPARATION PROCEDURE -78 B. SYMMETRIC WIND PROFILE — 82 C. THE ASYMMETRIC CIRCULATION —— -86 1. Growth of the Asymmetric Gyres 94 2. The Asymmetric Flow — 100 D. DESCRIPTION OF THE DYNAMICS OF BETA DRIFT 106 1. Overview 107 2. Discussion 111 E. STREAMFUNCTION TENDENCY ANALYSIS 116 1. Total Tendency Analysis 124 2. Symmetric and Asymmetric Tendencies 146 a. Weakening of the Maximum Wind 146 b^ Formation of the Asymmetric Gyres 152 c. Nonlinear Effects 156 d. Rotation of the Large-scale Asymmetric Gyres 172 e. Westward Component of Beta Drift 17 3 F. VENTILATION FLOW VECTOR 17*3 G. SUMMARY OF THE DYNAMICS OF BETA DRIFT 177 V. DYNAMICAL SENSITIVITY 181 A. VENTILATION FLOW DYNAMICS 182 1. The Hypothesized Ventilation Speed Function — • — 183 2. Experiment Design 184 3. Linear Solutions -•— 185 4. Results with Varying a/b Ratios 189 5. The Calculated Ventilation Speed Function 197 6. Summary 203 B. NONLINEAR-ONLY INTEGRATIONS AFTER LINEAR FORCING 204 1. Experiment Design 204 2. Track Results -205 3. The Asymmetric Streamfunction • 211 4. Very Long Integrations 226 5. Tangential Wind Profiles 231 6. Smnmary 231 C. MODIFYING THE SYMMETRIC/ASYMMETRIC NONLINEAR INTERACTIONS 236 1. Symmetric/Asymmetric Form of the Model Equation 237 2. Experiment Design 238 3. Setting ASVA to Zero 239 4. Setting AAVS to Zero 240 5. Modifying AAVS 253 6. Modifying ASVA 261 7. Summary 261 D. SUMMARY AND CONCLUSIONS 268 VI. ULTRA-LONG INTEGRATIONS 271 A. TRACK RESULTS 271 B. TANGENTIAL WIND PROFILES 274 C. DISCUSSION AND SUMMARY 274 VII. CONTRIBUTION TO THE MOTION BY DIFFERENT SCALES IN THE INITIAL VORTEX 280 A. THE FOURIER TRANSFORM PROCEDURE 280 B. EXPERIMENT DESIGN 283 C. PERFORMANCE CHARACTERISTICS OF THE FOURIER FILTER 285 D. TRACK RESULTS 306 E. IMPLICATIONS FOR VORTEX SPECIFICATION IN TRACK FORECAST MODELS AND TROPICAL CYCLONE ANALYSIS 328 F. SUMMARY 335 VIII. SUMMARY AND CONCLUSIONS 3 37 A. RESEARCH APPROACH 337 B. NUMERICAL EFFECTS 338 C. DEPENDENCE ON THE INITIAL SYMMETRIC VORTEX — 338 1. Radius of Maximum Wind 339 2. Inner/Outer Changes 339 3. Symmetric Perturbations 339 4. Far Outer Flow 340 D. EVOLUTION OF THE SYMMETRIC AND ASYMMETRIC FLOW 340 1. The Asymmetric Flow —= 340 2. Circulation Tendency Analysis • 341 E. DYNAMICAL SENSITIVITY —^— 342 1. Balance between Motion and Ventilation Flow Generation —— —-= 342 2. Nonlinear-only Integrations after Initialization with a Linear Solution 343 3. Modification of the Symmetric/Asymmetric Tendencies 344 F. ULTRA-LONG INTEGRATIONS 345 G. CONTRIBUTION TO THE MOTION BY DIFFERENT SCALES IN THE INITIAL VORTEX 346 H. SUMMARY OF STRUCTURE DEPENDENCE 347 I. SUMMARY OF NEW FINDING REGARDING THE DYNAMICS OF BETA DRIFT 347 J. APPLICATIONS TO FUTURE THEORETICAL STUDIES AND FORECAST MODELS 348 APPENDIX A: DERIVING THE TANGENTIAL WIND PROFILE AND VORTEX
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