UNCLASSIFIED 



SECURiry Cl.ASSIPICATlON OF THIS PAGt 



REPORT DOCUMENTATION PAGE 



la REPORT SECURITY CLASSIFICATION 



UNCLASSIFIED 



lb RESTRICTIVE MARKINGS 



2a SECURITY CLASSIFICATION AUTHORITY 



2b DECLASSIFICATION /DOWNGRADING SCHEDULE 



3 DISTRIBUTION /AVAILABILITY OF REPORT 



Approved for public release; 

 distribution is unlimited. 



4 PERFORMING ORGANIZATION REPORT NUMBER(S) 



DTNSRDC-86/054 



5 MONITORING ORGANIZATION REPORT NUMaER(S) 



6a NAME OF PERFORMING ORGANIZATION 



David Taylor Naval Ship 

 R&D Center 



6b OFFICE SYMBOL 

 (If applicable) 

 Code 1542 



7a NAME OF MONITORING ORGANIZATION 



6c ADDRESS (Ofy, Sfafe, and ZIPCode) 

 Bethesda, MD 20084-5000 



7b ADDRESS (Ofy. State, and ZIP Code) 



Ha MAME OF FUNDING / SPONSORING 

 ORGANIZATION 



8b OFFICE SYMBOL 

 (If applicable) 



9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 



Br ADDRESS (Oty, State, and Z/P Code) 



10 SOURCE OF FUNDING NUMBERS 



PROGRAM 

 ELEMENT NO 



62543N 



PROJECT 

 NO 



RS43421 



1 IiriE (Include Security Clarification) 

 Far-Field Features of the Kelvin Wake 



TASK 

 NO 



RS43421 



WORK UNIT 

 ACCESSION NO 



DN178067 



P>--SSO'\AL ALjTfHOR{S) 



Barnell, A. and Noblesse, F. 



) lYPf OF REPORT 



Final 



3b TIME COVERED 

 FROM TO 



14 DATE OF REPORT {Year, Month. Day) 



1986, September 



15 PAGE COUNT 



33 



SUPPI EMENTARY NOTATION 



COSATI COOES 



18 SUBJECT TERMS {Continue on reverie if necessary and identify by block number) 



Ship Waves Divergent Waves 

 Kelvin Wake 



ASSFRAfr (Continue on reverse if necessary and identify by block number) 



The classical Kelvin wake trailing a ship advancing at constant speed in calm water 

 is studied. In particular, asymptotic expressions for determining the far-field wake, at 

 large distances behind the ship, are investigated numerically. This analysis, in which 

 surface tension and nonlinearities are ignored, indicates that the divergent waves of a 

 surface ship generally are infinitely steep at the track of the ship, even though their 

 amplitude vanishes there; this result is theoretically possible because the -^^-f ^ °f 

 the divergent waves vanishes at the track of the ship. I^^--"<^^^^ ^"^ ^^^^^^^^-^',^^5 

 waves cannot exist in reality, the linear no-surface-tension analysis presented ^^ J^,s 

 study suggests that no divergent waves can exist within a certain region in the vicinity 

 of the track of the ship, and that the Kelvin wake contains three distinct regions: 

 (i) an inner region where only transverse waves can exist, (ii) an outer region where both 

 transverse and divergent waves are present, and (iii) an intermediate region at the bound 



ary between the inner and outer regions where short steep divergent waves, as well as 



-' (.Continued/ 



.'() [J SIPiBufiON/ AVAILABILlTy OF ABSTRACT 

 (3 iriM ASSlFlEO/UNLlMITED D SAME AS RPT 



Ddtic users 



a -iA'/lE OF RESPONSIBLE INDIVIDUAL 



Alexander Barnell 



21 ABSTRACT SECURITY CLASSIFICATION 



UNCLASSIFIED 



2Zb TELEPHONE (/nc/ude Area Code) 



(301) 227-1865 



OFFICE SYMBOL 



Code 1542 



DD FORM 1473, 84 MAR 



83 APR ec)ition may be used until eKhausled 

 All other editions are obsolete 



SECURITY CLASSIFICATION Of THJS PAGE_ 



~ "" "UNCLASSIFIED 



