DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.

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1 DSTRBUTON STATEMENT A: Appoved fo publi elease; disibuio is uliied. Popagaio of Low-Fequey Tasie Aousi Sigals hough a Fluuaig Oea: Develope of a 3D Saeig Theoy ad Copaiso wih NPAL Expeieal Daa Alexade G. Vooovih NOAA/ESRL PSD3 35 Boadway Boulde CO phoe: fax: eail: alexade.vooovih@oaa.gov Vladii E. Osashev Uivesiy of Coloado/CRES 35 Boadway Boulde CO phoe: fax: eail: vladii.osashev@oaa.gov Ga Nube: N00040P0048 hp:// LONG-TERM GOALS Develope of a ew 3D heoy of low-fequey log-age soud popagaio hough a fluuaig oea iludig boh CW ad asie aousi sigals. Copaiso of heoeial ad ueial esuls wih NPAL expeieal daa. OBJECTVES To develop a 3D odal heoy of boadbad soud popagaio hough a fluuaig oea iludig aalysis of he oheee fuio fo asie aousi sigals ad epoal oheee. To develop opue odes fo alulaio of he hoioal ad veial oheee fuios of asie aousi sigals ad epoal oheee. To opae heoeial ad ueial esuls wih ad 004 NPAL expeieal daa ad hose whih will be obaied i he 00-0 NPAL expeie i he Philippie Sea. APPROACH Sudies of saisial haaeisis of low-fequey soud waves popagaig hough a fluuaig oea ae ipoa fo ay paial appliaios. Wih he suppo of ou pevious ad ue ONR gas we have bee developig a 3D odal heoy of soud popagaio i a fluuaig oea [- 94-7]. his heoy we have alulaed ad aalyed he ea soud field he ea iesiy he

2 Repo Doueaio Page Fo Appoved OMB No Publi epoig bude fo he olleio of ifoaio is esiaed o aveage hou pe espose iludig he ie fo eviewig isuios seahig exisig daa soues gaheig ad aiaiig he daa eeded ad opleig ad eviewig he olleio of ifoaio. Sed oes egadig his bude esiae o ay ohe aspe of his olleio of ifoaio iludig suggesios fo eduig his bude o Washigo Headquaes Sevies Dieoae fo foaio Opeaios ad Repos 5 Jeffeso Davis Highway Suie 04 Aligo VA Respodes should be awae ha owihsadig ay ohe povisio of law o peso shall be subje o a pealy fo failig o oply wih a olleio of ifoaio if i does o display a uely valid OMB ool ube.. REPORT DATE 00. REPORT TYPE 3. DATES COVERED o TTLE AND SUBTTLE Popagaio of Low-Fequey Tasie Aousi Sigals hough a Fluuaig Oea: Develope of a 3D Saeig Theoy ad Copaiso wih NPAL Expeieal Daa 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5. PROGRAM ELEMENT NUMBER 6. AUTHORS 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNT NUMBER 7. PERFORMNG ORGANZATON NAMES AND ADDRESSES Naioal Oeai ad Aosphei Adiisaio NOAA/ESRL PSD335 BoadwayBouldeCO PERFORMNG ORGANZATON REPORT NUMBER 9. SPONSORNG/MONTORNG AGENCY NAMES AND ADDRESSES 0. SPONSOR/MONTOR S ACRONYMS. DSTRBUTON/AVALABLTY STATEMENT Appoved fo publi elease; disibuio uliied 3. SUPPLEMENTARY NOTES 4. ABSTRACT. SPONSOR/MONTOR S REPORT NUMBERS 5. SUBJECT TERMS 6. SECURTY CLASSFCATON OF: 7. LMTATON OF ABSTRACT a. REPORT ulassified b. ABSTRACT ulassified. THS PAGE ulassified Sae as Repo SAR 8. NUMBER OF PAGES 7 9a. NAME OF RESPONSBLE PERSON Sadad Fo 98 Rev Pesibed by ANS Sd Z39-8

3 veial ad hoioal oheee fuios ad ohe seod saisial oes of aow-bad aousi sigals popagaig hough a oea peubed by liea ieal waves Ws. The heoeial esuls wee opaed wih expeieal daa obaied i he Noh Paifi Aousi laboaoy NPAL expeies aied ou i he Noh Paifi i [0] ad i 004 []. Ou ex goals ae o geealie he aow-bad 3D odal heoy ad oespodig opue odes o ilude boadbad asie aousi sigals popagaig i a fluuaig oea ad o sudy epoal oheee of aousi sigals i a o-saioay ediu. Theoeial ad ueial esuls obaied will be opaed wih expeieal daa iludig hose obaied i he pevious NPAL expeies ad ha will be obaied i he Philippie Sea. D. A. Vooovih ad D. V. Osashev ae P ad Co-P i his poje. WORK COMPLETED Duig he epoig peiod he followig wo asks wee opleed: Task. The aow-bad 3D odal heoy of soud popagaio i a fluuaig oea was geealied o ilude boadbad aousi sigals ad epoal oheee. Task. The developed heoy was applied o he aalysis of epoal oheee of aow-bad aousi sigals popagaig i a oea peubed by liea Ws wih he Gae-Muk GM speu. was show ha he oheee ie of he sigal deeases wih he popagaio age 0.5 as fo a fixed fequey ad deeases wih fequey as f fo a fixed age. RESULTS The followig esuls wee obaied i FY00: Task. Closed-fo equaios fo he spaial-epoal oheee fuio of boadbad aousi sigals popagaig i a fluuaig oea wee deived ad aalyed i deail. The aalysis is doe i a ylidial oodiae syse whee is age is he aiuhal agle o a obsevaio poi ad is he oea deph. The spaial-epoal oheee fuio of he soud field ~ p is defied as ~ ~ * p p i i * = e Q Q p p d d. Hee ad ae wo pois of obsevaio a whih he oheee fuio is alulaed is ie is soud fequey he fuio Q haaeies a speu of he soue ad he bakes... deoe aveagig ove a eseble of soud-speed ealiaios. A seod oe of he speal apliudes of he soud field appeaig o he igh-had side of Eq. is expessed i he followig fo

4 3 [ ]. exp * π u u i p p = Hee ae popagaio osas u ae ode pofiles is he aix of oss-ode oheees ad suaio is ove all waebo aousi odes. The oss-ode oheees saisfy a se of diffeeial equaios:. * + + = i i i e s e s e d σ 3 Hee = = is he ie lag bewee wo obsevaios s ad σ ae aies whih ae expessed i es of a spaial-epoal oelaio fuio of soud-speed fluuaios: B δ δ = 4 whee δ is a spaial-epoal ado field of soud-speed fluuaios. The developed heoy is ahe geeal ad allows aalysis of he seod-ode saisial haaeisis of boadbad aousi sigals popagaig i a fluuaig oea. Fo exaple usig Eqs. -4 he aveaged apliude ad shape of a aousi pulse popagaig i a fluuaig oea a be sudied. Task. The heoy developed i Task was applied o sudies of epoal oheee of aow-bad aousi sigals fo he ase of a oea peubed by liea Ws wih he GM speu. The epoal oheee fuio Γ is a paiula ase of he spaial-epoal oheee fuio osideed i Task ad is obaied fo he lae by seig 0 = = ad = =. The age ad fequey depedee of he oheee ie wee ivesigaed ueially ad opaed wih expeieal esuls ad pediios of he pah-iegal heoy. he ueial esuls peseed below he Bu-Väisälä fequey ad he soud speed pofiles wee hose as he Muk aoial pofiles. was assued ha oea deph is 3 k ad he soue deph is 807. The soue deph oespods o he NPAL expeie [0]. Calulaios of he epoal oheee fuio Γ wee doe fo five values of he soud fequey / = = π f ad 00 H. Fo hese fequeies ad he osideed oea saifiaio he ube of waeboe aousi odes is = 6 N ad 55 espeively.

5 The oalied epoal oheee fuio Γ / Γ 0 is ploed i Fig. vesus he soud popagaio age ad ie lag fo he soud fequey f = 50 H. follows fo he figue ha wih ieasig popagaio age he epoal oheee deeases fase wih as i should. Figue depis he oalied epoal oheee fuio fo f = 00 H. This plo is siila o he pevious oe exep ha epoal oheee deays fase ha ha i Fig. ; oe he diffeee i sales alog he ie axis i hese figues. The oheee ie is defied as a value of fo whih he epoal oheee fuio Γ deeases by a fao / e. Fig. 3 is ploed vesus popagaio age fo five fequeies f agig fo o 00 H. Apa fo he lef-os pas of he uves oespodig o f = ad 5 H i follows fo Fig. 3 ha he depedee of o a be appoxiaed as ~ 0.5. This depedee is also pedied wih he pah-iegal heoy [] ad is lose o ha fo expeieal daa see Ref. [3]. Noe ha pediios of he pah-iegal heoy ae valid fo a idividual ay pah while pediios of he 3D odal heoy ae valid fo supeposiio of aousi odes e.g. he oal aousi sigal. Figue 4 depis he oheee ie vesus fequey f fo fou popagaio ages. The depedee of o f a be appoxiaed wih ~ f. This depedee is also pedied wih he pah-iegal heoy [] ad is osise wih he expeieal daa epoed i Ref. [3]. Figue. Noalied epoal oheee fuio of a aow-bad soud sigal vesus popagaio age ad ie lag fo soud fequey f = 50 H. The plo oespods o soud popagaio hough a fluuaig oea peubed by liea Ws wih he GM speu. 4

6 Figue. The sae as i Fig. bu fo soud fequey f = 00 H. Figue 3. Coheee ie of a aow-bad soud sigal vesus popagaio age fo diffee soud fequeies f. 5

7 MPACT/APPLCATONS A 3D odal heoy of boadbad soud popagaio i a fluuaig oea was developed. Based o his heoy he depedee of epoal oheee o age ad fequey was sudied ueially. RELATED PROEJCTS a. The NPAL expeie see Ref. []. b. The NPAL Philippie Sea Expeie. REFERENCES Figue 4. Coheee ie of a aow-bad soud sigal vesus soud fequey f fo diffee popagaio ages.. A. G. Vooovih ad V. E. Osashev Coheee fuio of a soud field i a oeai waveguide wih hoioally isoopi saisis J. Aous. So. A [published efeeed].. G. Vooovih ad V. E. Osashev Low-fequey soud saeig by ieal waves J. Aous. So. A [published efeeed]. 3. A. G. Vooovih ad V. E. Osashev Mea field of a low-fequey soud wave popagaig i a fluuaig oea J. Aous. So. A [published efeeed]. 6

8 4. A. G. Vooovih ad V. E. Osashev Coheee fuio of a low-fequey soud field i a oeai waveguide wih ado ihoogeeiies 9h eaioal Cogess o Aousis Madid Spai -7 Sepebe A. G. Vooovih ad V. E. Osashev Appliaio of he aix Ryov ehod o he alulaio of he oheee fuio of a soud field i a oeai waveguide J. Aous. So. A. 3 5 P. p A. G. Vooovih ad V. E. Osashev Coheee fuio of a soud field i a oeai waveguide wih hoioally isoopi ado ihoogeeiies J. Aous. So. A. 5 P A. G. Vooovih ad V. E. Osashev Veial oheee of low-fequey soud waves popagaig hough a fluuaig oea J. Aous. So. A. 0 5 P A. G. Vooovih ad V. E. Osashev Mea field of a soud wave popagaig i a oeai waveguide wih ado ihoogeeiies J. Aous. So. A. 6 4 P V. E. Osashev A.G. Vooovih ad The NPAL Goup Spaial oheee of aousi sigals easued duig he NPAL expeie J. Aous. So. A. 6 4 P P. F. Woese ad R. C. Spidal Noh Paifi Aousi Laboaoy J. Aous. So. A. 7 3 P P. F. Woese: hp://dopbox.usd.edu/~pwoese/npal04_doues.. S. M. Flae ad R. B. Sougho Pediios of ieal-wave effes o oea aousi oheee avel-ie vaiae a iesiy oes fo vey log-age popagaio J. Aous. So. A T. C. Yag Tepoal oheee of soud asissio i deep wae evisied J. Aous. So. A PUBLCATONS 4. A. G. Vooovih V. E. Osashev J. A. Colosi ad A. K. Mooov "Coss-ode oheees ad deouplig of equaios fo ode iesiies i D ad 3D fluuaig oea" J. Aous. So. A. 6 4 P. p [published]. 5. A. G. Vooovih V. E. Osashev ad J. A. Colosi Tepoal oheee of aousi sigals i a fluuaig oea J. Aous. So. A. [subied]. 6. A. G. Vooovih V. E. Osashev ad J. A. Colosi 3D odal heoy of soud popagaio i a fluuaig oea wih spaial-epoal ihoogeeiies J. Aous. So. A. [i pess]. 7. J. A. Colosi T. K. Chadayadula A. G. Vooovih ad V. E. Osashev "Saisis of ode apliudes i a oea wih ado soud speed peubaios: Tepoal oheee" J. Aous. So. A. [i pess]. 7

FBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf

FBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf .4 Base Exiaio Ipoa lass of vibaio aalysis Peveig exiaios fo passig fo a vibaig base hough is ou io a suue Vibaio isolaio Vibaios i you a Saellie opeaio Dis dives, e. FBD of SDOF Base Exiaio x() y() Syse