Vadim Pavlov 1, Donald Riedeberger 2, Ulrich Rist 2, Ursula Siebert 1.

Transcription

1 DFG-SPP-1207 Strömungseeinflussung in Ntur und Technik. DFG SI 1542/1 Anlysis of the reltion etween skin morphology nd locl flow conditions for fst-swimming dolphin. Vdim Pvlov 1, Donld Riedeerger 2, Ulrich Rist 2, Ursul Sieert Institute of Terrestril nd Aqutic Wildlife Reserch, University of Veterinry Medicine Hnnover, Foundtion, Werftstr. 6, Büsum 2. Institute of Aerodynmics nd Gs Dynmics, University of Stuttgrt, Pfffenwldring 21, Stuttgrt E-mil:

2 2 Summry The dolphin skin close to the nisotropic complint wll design could potentilly reduce the friction drg. The gol of this work ws to study the reltion etween locl flow conditions round dolphin model nd prmeters of skin morphology relevnt in flow/skin interfce. Three-dimensionl CAD models presenting uthentic geometry of fst-swimming common dolphin Delphinus delphis nd low-swimming hror porpoise Phocen phocen were constructed. CFD study of the flow prmeters were crried out for the nturl rnge of dolphin swimming velocities. The results of this study llow to conclude tht the stremwise vriility of the dolphin skin structure ppers to e ssocited with the stremlined ody geometry nd corresponding grdients of the velocity nd pressure rther thn with specific locl Re numers. The hypotheses on different optiml conditions for potentil drg-reducing properties of dolphin skin re proposed. Introduction The sic ide of iomimetics or ionics is to develop new technologies sed on highly effective nd specilized solutions found in nture. Fst moving nimls re usully optimized for efficiency y evolution. Since mrine top predtors move within high density nd therefore high drg nd high uoyncy medium, their need for efficient drg reduction mechnisms ppers quite evident. Modern engineering designs of mrine nd ir trnsport vehicles mke use of stremlined shpes to reduce the form or pressure drg while severl solutions imed t reducing friction drg cme from the study of se nimls. Dolphins re one of the most fmous exmples of extreme dpttions to drg reduction. Interest in the understnding of dolphin s hydrodynmics ws initited y Sir J Gry who pulished his nlysis of dolphin s energetics with unexpected outcome, lter clled Gry s prdox [1]. Assuming fully turulent flow Gry cme to the conclusion tht dolphin should possess either enormously powerful muscles (seven times more power per unit mss thn ny other mmmlin) or must e cple of mintining lminr flow y some extrordinry mens. In the lte 1950s the erodynmicist Mx Krmer climed tht dolphin ensured low level of friction drg y mintining lminr flow over most prts of its ody. The dolphin s skin hving n unusully ordered inner structure ws considered to e nturl complint wll effectively suppressing the growth of Tollmien-Schlichting wves in the trnsition region of the flow, Krmer [2], [3]. This suppression delys the trnsition from lminr to turulent flow in the oundry lyer thus decresing the friction drg. Krmer proposed the drg-reducing properties of dolphin s skin s solution of Gry s prdox nd initited numer-

3 3 ous investigtions of the structure nd function oth of dolphin skins nd complint wlls. The structure of the dolphin skin presents morphologicl dpttions which ppered s result of 50 millions yer of evolution of cetcens. A thick lyer of skin covers the ody of dolphins nd stremlines his skeleton nd muscles. The skin surfce is smooth, hirless nd elstic. Skin glnds re sent with little exceptions only nd the numer of lyers of the epidermis is reduced compred to other mmmls, Sokolov [4]. The structure of the dolphin skin nd the luer lyer is highly orgnized nd complex (Prry [6], Sokolov [5], Aleyev [7], Hun et l. [8], Pershin [9], Toedt et l. [10], Hmilton et l. [11]). Unlike the chotic rrngement for terrestril mmmls, the derml ridges in cetcens skins re rrnged in highly ordered mnner. This feture of dolphins skin inspired suggestions of its possile reltion with the flow direction (Sokolov [4], Plmer & Weddell [12], Purves [13], Surkin [14]). In ddition, vrile lood pressure in cpillry vessels in the ppillry nd su-ppillry lyers cn modify the rnge of mechnicl properties of the dolphin skin, Pershin [9]. The mechnicl properties of dolphin skins relted to species, position on the ody, degree of trining, nd physicl condition ws investigted y Benko et l. [15] or Toedt et l. [10], for instnce. They found tht the modulus of elsticity E ws lower in the middle of the common dolphin compred to more nterior nd posterior sections of the ody [16]. For freshly cptured ottle-nosed dolphin, E ws higher thn for the sme niml fter trining, when the dolphin ws clm. The higher vlue of the modulus of elsticity ws interpreted to etter correspond to the condition of high-speed swimming [15]. The elstic properties of the integument re prticulrly dependent on the deeper lyer of thick luer. The luer lyer is highly resilient, with E-modulus similr to iologicl ruers (e.g. Pst et l. [17]). Experimentl studies of living dolphins did, however, not confirm Gry s supposition out fully lminr flow of swimming dolphin. Direct mesurements of turulence y mens of trnsducers ttched to the dolphin s ody s well s visuliztion studies of the flow of swimming dolphins indicted turulent oundry lyers over the most prt of the ody (Romnenko [18], Rohr et l. [19]). Nevertheless, the level of turulence mesured in the oundry lyer of swimming dolphins ws significntly lower compred with the flow over rigid or solid model of the dolphin (Romnenko [18]). The stte-of-the-rt view of dolphin hydrodynmics ssumes numer of simultneous dpttions, e.g. to unstedy velocity nd pressure grdients from ccelerting wter over the ody, skin tension nd micro virtions, shedding of the

4 4 superficil lyer of epidermis s well s skin dmping, which provides dditionl oundry lyer stiliztion for the swimming dolphin (Gry [1], Hider & Lindsley [20], Ridgwy & Crder [21], Benko & Crpenter [22], Romnenko [18], Ngmine et l. [23]). Considerle progress hs lso een chieved in the theoreticl modeling nd understnding of complint wlls nd the current level of knowledge ssumes sustntil dely of lminr-turulent trnsition s well s drg reduction in turulent oundry lyer y ppropritely designed complint wlls (Gd-el-Hk [24], Choi et l. [25], Crpenter et l. [26]). According to these two-lyer nisotropic complint wll which comes close to the ctul dolphin s skin structure possesses the est drg-reducing properties (Sokolov [26], [4], Plmer & Weddell [12], Grosskreutz [28], Stromerg [29], Crpenter & Morris [30], Yeo [31]). At the sme time, the mechnism of dolphin skin/flow interction is still uncler. There re severl ojective resons: First, there is still considerle lck of quntittive dt of potentilly drg-reducing fetures of dolphin skin morphologies. Second, these were rrely considered in connection to the locl flow properties. The gol of this work is to study the reltion etween locl flow conditions round dolphin model nd prmeters of skin morphology relevnt in flow/skin interfce. Methods Scheme of smpling. The scheme of smpling ws elorted oth for study of skin morphology nd prmeters of the flow simulted round the dolphin model. As the gol of the study ws to compre the flow/skin interfce in regions which re chrcterized y different Reynolds numers, two prts of the ody were selected for tht purpose. The first is the dorsl fin tht presents typicl wing-like shpe nd is uilt of symmetricl cross-sections. The second is limited y the tip of the melon on the hed on one side nd the position etween dorsl fin nd genitl slit on the other side. Both regions present smooth stremlined odies with similr geometry t different size. For the comprtive purpose in oth regions the smpling ws done in 20 points locted on equl intervls long line on the ody surfce. The dimensionless scheme of smpling llowed comprison of the flow/skin interfce for the different prts of the dolphin ody. Skin morphology nd morphometry The skin smples of 4x4x4 mm 3 in size were fixed in 10% formlin, dehydrted nd emedded y the Technovit 7100 medi. Both verticl cross-sections nd sections prllel to the skin surfce were mde with the thickness of 7 mkm. Sections were dried nd stined y hemtoxylin-eosin for the generl picture nd ldehyde-fuchsin to revel the elstic fiers in dermis lyer of the skin.

5 5 All mesurements of the skin fetures on the histologicl sections were done with mesurement system including n Olympus CK X41 microscope nd morphometry softwre. The imges of skin sections were cptured y the video cmer, clirted, nd sved in JPG file formt. On the verticl cross sections of the skin the following prmeters were mesured: 1. Height of the epidermis (HEP), mm 2. Height of the derml ppillry lyer (HDP), mm 3. Height of the suppillry lyer of dermis (HSL), mm 4. Thickness of the derml ridges (TDR), mm 5. Thickness of the epiderml ridges (TER), mm The ngle etween the derml ridges direction nd the long xis of the ody ws mesured on sections prllel to the skin surfce. The verge vlues of ll morphologicl prmeters were clculted sed on three repeted mesurements. CAD modeling A full-scle, three-dimensionl CAD model of common dolphin Delphinus Delphis ws constructed with SolidWorks softwre. For the common dolphin the mesurements nd photos of the ody of newly strnded niml were used. All mesurements were tken ccording to the stndrd protocol of postmortem exmintion (Kuiken nd Hrtmnn 1993). Lser scnning dt of the rigid model of the sme species held t the Germn Ocenogrphic Museum in Strlsund were used for correction of the dolphin s ody geometry. The resulting model presents n uthentic geometry of n dult femle common dolphin of 1.94 m length. Additionlly, three-dimensionl geometry of y-cught hrour porpoise ws otined y n Atos V7 opticl scnning system y IGS Development GmH. Scnned dt were processed with the GOM softwre nd exported in CAD formt s set of cross-sections. The resulting model uilt with the SolidWorks softwre presents n uthentic geometry of su-dult mle hror porpoise of 1.1 m length. For oth species models of fins were constructed seprtely using photos of fin outlines s well s cross-sectionl mesurements of fins nd joined to the models of the odies. A strightened ody position, which corresponds to the gliding phse of the dolphin s swimming cycle, ws chosen for the CFD study. CFD study The flow round the dolphin nd porpoise model ws studied with the Flo- Works softwre. The flow prmeters long with oth smpling lines on the common dolphin were mesured for the rnge of nturl swimming velocities.

6 6 The clcultions were done under the following conditions: Sttic pressure P, temperture 20 C, turulence intensity 0.1%, nd turulent length scle of 3.44E-04 m. The velocity in X direction (long long xis of the model) vried from 2 to 8 m/sec t fixed 0 m/sec for the velocity oth in Y nd Z direction. FloWorks uses the finite volume method to solve the Reynolds-verged Nvier Stokes equtions, implementing the k ε turulence model. The numericl simultion of lminr-turulent trnsition on the sme model of common dolphin using the empiricl -Re trnsition model ws crried out y Donld Riedeerger [32] t IAG, Stuttgrt University. The finite-volume code STAR-CCM+ ws used with RANS formultion nd SST-k-ω closure together with similr oundry conditions s prescried efore. Simulted swimming speed vried in the rnge from 0.25 to 5 m/sec, with the turulent intensity rnging from 0.25% to 5%. Model of the flow/skin interfce The simplified model of the flow/skin interfce includes the ngle formed y the velocity vector on the outer edge of the oundry lyer nd the plne of the derml ridges. The ngle formed y the derml ridges with the Y-xis ws used for the clcultion of 2D vector of derml ridges. Then 3D vector of the derml ridges ws otined y the projection of the 2D vector on the surfce of the 3D model (Pvlov 2003). Figure 1. Definitions of ngles of the dolphin skin structures, used for the clcultion of the ngle. The ngle formed y the derml ppille with the Z-xis s well s the vector norml to the fin surfce ws used for the clcultion of 3D vector of the derml ppille. Vectors nd were used for the clcultion of the locl sptil

7 7 orienttion of the plne of the derml ridges in the dt points (figure 1). The velocity vector c t the sme points on the fin surfce ws used for the clcultion of the ngle etween the plne of the derml ridges nd line corresponding to the locl flow direction: sin ( y z ( y z z y z ) 2 y ) x ( x c z ( x z z x z ) 2 x ) y ( x y c ( x y y x ) y 2 x ) z ( x 2 c c y 2 c z 2 c ) where ridges vector, ppille vector, nd c velocity vector. Results Hydrodynmics The stremlined ody of the common dolphin hs complex shpe tht resemles ody of revolution in the region from lowhole to the leding edge of the dorsl fin only. The hed of the dolphin, especilly the externl morphology of the melon nd the ek ffects the flow nd forms specific grdients of the velocity nd pressure in tht region. This prt of the dolphin s ody looks importnt in sense of flow control nd formtion of specific flow ptterns round the dolphin ody. The rer prt of the dolphin s ody, pproximtely 1/3 of the ody length is flttened strting from the genitl re to the til flukes. To void the influence of nturl turultors like eye or lowhole, the position of the smpling line ws defined to lie on the plne oriented t 45 degrees to the plne of symmetry of the dolphin ody. This prt of the ody ws found to show more homogeneous (i.e. less grdients in circumference direction), representtive flow on the min ody compred to other res in the CFD simultion thus verifying the pproch. For the dorsl fin the shpe of the smpling line is close to conventionl irfoil shpe. The cross-section of the dorsl fin mde t the mid of the wing spn is close to the NACA A nd GOE 459 symmetricl irfoils. The min difference occurs t the thickened triling edge of the fin. The similrity in shpe etween fin nd ody section leds to resemlnce of grdients of the flow prmeters in oth regions (figure 2). The ovious difference in pressure grdient on the lst third of the dolphin s ody tht ssocited with the strokes of the til fin.

8 Pressure (P) Pressure (P) 8 fin cross-section Length, m 8 m/sec 6 m/sec 4 m/sec 2 m/sec dolphin ody Length, (m) 8 m/sec 6 m/sec 4 m/sec 2 m/sec Figure 2. Pressure distriution long the cross-section of the dorsl fin (upper grphics) nd ody of the common dolphin (lower grphics) clculted for the rnge of dolphin swimming velocities. The results of the flow simultions otined with Floworks show shift of the trnsition zone in frontwrd direction s well s reduction of the lminr regions with incresing speed of swimming from 2 to 8 m/sec. For the miniml speed of swimming the lminr region on the upper prt of the ody reches the dorsl fin position tht corresponds pproximtely to the hlf of the ody length. For the

9 9 mximl speed of 8 m/sec this region is reduced to the position of the pectorl fins tht is less thn one third of the ody length. While preliminry simultions in STAR-CCM+ with low turulence environment verified the ove results, detiled study of the trnsition on the common dolphin model crried out y Riedeerger hs shown tht for the cruising speed of swimming round 3 m/sec in moderte 1% turulence-intensity environment the flow round the dolphin is minly turulent with limited lminr regions t the front of the hed (figures 3, 4). The influence from the fin ppendices on the min ody pressure distriution ws found to e of negligile impct. Estimtions of possile surfce drg reduction due to downstrem shift of trnsition were s high s 25 %. Figure 3. Distriution of pressure coefficient Cp for free-strem velocities of u = 1.0 m/s, side (upper) nd top (lower) projection, turulence intensity Tu = 1%

10 10 Figure 4. Turulent kinetic energy k for free-strem velocities of u = 0.25 (upper), 1.0 (mid) nd 2.5 m/s (lower), turulence intensity Tu = 1%. Skin morphology Skin prmeters of the common dolphin were compred in two loctions, on the dorsl fin nd on the ody of the niml. Difference in men vlues of thickness of dermis nd epidermis ridges, height of the suppillry lyer, s well s ngle ws found significnt t p<0.05. The significnce of difference in men vlues of the height of derml ppillry lyer s well s totl height of epidermis ws found lower, t p>0.05. A sketch of the different skin three-dimensionl structures for oth smpling lines is presented in Figure 5. The height of the composite upper lyer of skin

11 11 which presents the iologicl nlog on to n nisotropic complint wll in engineering is similr t oth loctions. The difference in three-dimensionl structure is relted to the density nd dimensions of the derml ridges s well s their orienttion with respect to the flow direction. Figure 5. Sketch of three-dimensionl structure of dolphin skin. A on dorsl fin. B long ody. At similr velocity grdient the distriution of the skin prmeters is not uniform long the fin nd the ody of the dolphin. The skin prmeters HEP, HDP, nd HSL which mke up the complint wll of the dolphin correlte with the velocity grdient nd smoothly decrese in cudl direction in oth regions (figure 6). This reltion stnds out stronger for HEP nd HDP nd is weker for the HSL prmeter. Aprt of tht, the thickness oth of derml nd epiderml ridges is negtively correlted with the chord-wise velocity distriution. This correltion is stronger on the dorsl fin compred with the ody region Body line Velocity sin φ HEP HDP HSL TDR TER

12 Fin line Velocity sin φ HEP HDP HSL TDR TER Figure 6. Vriility of the flow nd the skin structure prmeters long two smpling lines. Dt re normlized from 0 to 1. Dt otined for the dorsl fin of the common dolphin cn e compred with the previous results of the study for the dorsl fin of hror porpoise Phocen Phocen. As the cross-sections of the fins re close to conventionl irfoils, the hypothesis of possile reltion etween skin morphology prmeters nd derivtives of the functions of cross-sectionl geometry ws exmined. For tht purpose curve fits of cross-sections of the dorsl fins were done with CurveExpert 1.4 y Dniel Hyms. The chord-wise thickness distriution Z(X) ws interpolted y 4th degree polynomil fit with the following coefficients for the common dolphin: = -1.20E-03, = 3.49E-03, c= -3.23E-04, d=1.12e-05, nd e= -1.77E-07. For the cross-section of the hror porpoise the pproprite coefficients were: = -9.50E- 01, = 3.21E+00, c= -4.37E-01, d= 2.36E-02, nd e= -4.79E-04. For the common dolphin it ws found tht sin ϕ hs negtive correltion with the 1 st derivtive of Z(X) function significnt t p<0.05. This correltion reveled to e lower for the hror porpoise. The difference in this correltion etween two species is relted with less ordered rrngement of the derml ridges on the dorsl fin of the hror porpoise. The first two prmeters of skin lyer composition, HEP nd HDP, hve positive correltion with the 1 st derivtive of Z(X) significnt t p<0.05 in oth species, while for the HSL this correltion ws found to e low. Tle 1. Correltions etween skin morphology prmeters nd derivtives of the functions of cross-sectionl geometry of the dorsl fin of common dolphin. Mrked correltions re significnt t p <.05000, N=20 (Csewise deletion of missing dt).

13 13 1st drv 2nd drv Pressure sin HEP HDP HSL 1st drv nd drv Pressure sin HEP HDP SPL Tle 2. Correltions etween skin morphology prmeters nd derivtives of the functions of cross-sectionl geometry of the dorsl fin of hror porpoise. Mrked correltions re significnt t p <.05000, N=20 (Csewise deletion of missing dt). 1st drv 2nd drv Pressure sin HEP HDP HSL 1st drv nd drv Pressure sin HEP HDP SPL Discussion The chllenge in iomimetics studies of nturl phenomen is the complexity of the iologicl ojects. As rule, ny iologicl structure is multifunctionl y its nture nd serves different functions. The min tsk in modeling of useful effects of iologicl system is to revel the vriles tht define the most prt of the system ehvior. In highly specilized systems showing n extremity in dpttion to () specific function(s), the numer of significnt vriles cn e limited, tht helps in modeling the iologicl phenomenon. The dolphin skin differs from the skin of terrestril mmmls y n unusully ordered inner structure nd considerly simplified composition with reduced glnds, hirs, nd lyers of the epidermis. These peculirities of the dolphin skin were considered s dpttion to the life in the wter which re potentilly le to decrese the friction drg. The choice of prmeters relevnt for the flow/skin interfce is fcilitted if one considers the dolphin skin s nturl nlogue of nisotropic complint wlls.

14 14 The ltter hve ordered inner structure nd hve good potentil in decresing friction drg. In the generl cse, the wll mtrix is reinforced y the ligned elements (fiers or voids) mking the inner structure of the wll ordered [28]. The structure of the nisotropic wll is rrnged so tht rther thn eing displced up nd down y the fluctuting pressure it is displced sidewys s well mking sustntil ngle to the verticl, therey generting negtive Reynolds sher stress on the complint surfce [30]. The first group of selected morphologicl prmeters includes prmeters of skin composition, i.e. the totl height of the skin, s well s the height of two sic lyers of skin. This corresponds to the sic design of two-lyer nisotropic complint wll y Crpenter. The ngle presents the ngle etween flow direction nd derml ridges s n nlogue to the ordered elements in the complint wll mtrix. The second group of prmeters consists of the thickness of the ordered elements nd distnce etween them. The prmeters of this group cn e considered s the next step from the two-dimensionl cse of n nisotropic complint wll to the more complex three-dimensionl one. For etter understnding the correltions etween locl flow prmeters nd skin structure t two different loctions hving similr shpe ut different Reynolds numers, i.e., the ody nd dorsl fin of the dolphin, were compred. Additionlly, the results for the dorsl fin were compred with the previously otined dt for the hror porpoise. The lst comprison imed to revel possile differences in the flow/skin interfce in fst-swimming (common dolphin) nd lowswimming (hror porpoise) species. The dt otined show ovious correltions etween prmeters of the twodimensionl skin composition nd reltive grdients of the velocity nd pressure. This correltion ws found similr for the dolphin ody nd the fin, hving different rnges of Re numer. A similr reltionship ws lso oserved for the prmeters of the three-dimensionl structure of the skin. Aprt from tht, the reltion etween the ngle nd pressure nd velocity grdients ws found to e non-liner. The results of this study llow to conclude tht the strem-wise vriility of the dolphin skin structure ppers to e ssocited with the stremlined ody geometry nd corresponding grdients of the velocity nd pressure rther thn with specific locl Re numers. The difference in results for the dolphin s ody nd cross-section of the dorsl fin cn e relted to the degree of speciliztion of these two regions. The dorsl fin hving wing-like shpe presents n extremum in hydrodynmic function while the fin cross-sections re close to conventionl symmetricl irfoils. Aprt from the ody region, the reltion etween irfoil geometry nd surfce structure is presented clerer there. All morphologicl p-

15 15 rmeters including the ngle correlte with the 1 st derivtive of the interpolted cross-sectionl geometry. Comprison of this correltion etween common dolphin nd hror porpoise hs shown tht it is stronger for the first species. This distinction could reflect the difference in hydrodynmic performnce, s the common dolphin is recognized to e fst swimmer, while the hror porpoise hs n pproximtely hlf s lrge verge-speed of swimming. To check if the difference in the flow/skin interfce refers to the potentil drg reduction rther thn the txonomic fetures, n dditionl study of species with different swimming performnce is needed. Theoreticl nd experimentl studies of complint wlls hve shown tht drg cn e minimized y delying the trnsition from lminr to the turulent flow nd y stiliztion of the turulent flow in the oundry lyer. Potentilly, dolphin skin close to the nisotropic complint wll design could reduce the friction drg in oth wys. Menwhile, the potentil drg-reducing effect depends considerly on the externl flow conditions, such s initil flow velocity nd turulence level. A generl question of possile friction-drg reduction y the skin of swimming dolphin cn e posed s follows: Which flow conditions is it optimized for? Dolphins use vriety of swimming speeds nd modes, the cruising speed is normlly within the rnge of 1-4 m/sec, while the top speed of the urst cn rech up to 8-10 m/sec. During swimming the ctive phse cn e interspersed with gliding phses which nticipte different flow regimes nd mechnisms of oundry-lyer stiliztion. From the point of view of optimiztion of energy expenditures, two hypotheses on potentil drg-reducing properties of dolphin skin cn e proposed. The first ssumes tht the skin is optimized for the cruising motion with moderte speed of swimming 1-4 m/sec in low depth with reltively high initil turulence. The fct, tht dolphins spend most of their time moving with moderte speed speks in fvor of this supposition. An lterntive hypothesis, sed on the cheeth hunting strtegy [33], nticiptes extreme energy expenditure for short-time period with chnce to ctch prey nd compenste energy losses. Following this ide, the dolphin skin could e optimized for the reduction of friction drg during fst swimming t moderte or high depth with reltively low initil turulence. Outlook The next step in the study of the flow/skin interfce in dolphins is getting the complete distriution of skin morphology nd flow prmeters ll over the ody of the dolphin. The complex geometry of dolphins presents vriety of specific locl flow conditions tht gives n opportunity to verify the reltion etween skin struc-

16 16 ture nd locl flow prmeters otined in the ongoing study. An importnt prerequisite for future study is the vriility of the swimming performnce nd Re numers of different species tht llows crrying out comprtive studies of the potentil drg-reducing properties of dolphin skin. From the point of numericl simultion the next steps would include more detiled understnding of the mrine turulent environment to more ccurtely ccount for the relity in simultion oundry conditions. Furthermore unstedy effects on trnsition loction due to swimming ody motion would enle more insight to the phenomen wheres comprtive study of the possiilities of ville turulence modeling pproches cn shed more insight in the limittions of simultion nd in the end enle more precise nswers to drg-reduction cpilities of modeled complint wlls. Acknowledgements Our thnks go to Dr. Vincent, Dr. Din, Dr. Doremus, nd Dr. Jensen for their help with dolphin morphology, nd to the stff of the Lor für Orthopädie und Biomechnik for their help with lser scnning the dolphin model. We lso thnk Dr. Benke for the opportunity to work on dolphin model in the Germn Ocenogrphic Museum in Strlsund. Literture [1] Gry J Studies in Animl Locomotion VI. The Propulsive Powers of the Dolphin J. Exp. Biol. 13: [2] Krmer M. O Boundry Lyer Stiliztion y Distriuted Dmping, J. Amer. Soc. Nv. Eng. 72: [3] Krmer M. O The Dolphins' Secret, New Sci., 7: [4] Sokolov V.E Integument of mmmls. Moscow: Nuk (in Russin). [5] Sokolov V.E Some Similrities nd Dissimilrities in the Structure of the Skin Among the Memers of the Suorders Odontoceti nd Mystcoceti (Cetce), Nture 185: [6] Prry D. A The Swimming of Whles nd Discussion of Gry's Prdox, J. Exp. Biol. 26: [7] Aleyev Y. G Nekton. Junk, The Hgue, Netherlnds. [8] Hun J. E., E. W. Hendricks F. R. Borkt R. W. Ktok D. A. Crder nd N. K. Chun Dolphin Hydrodynmics: Annul Report FY 82. NOSC* TR935. SSC Sn Diego, CA. [9] Pershin S.V Fundmentls of hydroionics. Leningrd: Sudostroyeniye (in Russin).

17 [10] Toedt M.E., Reuss L.E., Dillmn R.M., Pst D.A Collgen nd elstin rrngement in the luer of common dolphin (Delphinus delphis). Am Zool 37: 56A. [11] Hmilton J. L., W. A. McLelln nd D. A. Pst Functionl Morphology of Hror Porpoise (Phocoen phocoen) Tilstock Bluer, Amer. Zool. 38: 203A. [12] Plmer E., Weddell G The reltion etween structure, innervtion nd function of the skin of the ottlenose dolphin (Tursiops trunctus). Proc Zool Soc Lond 143: [13] Purves P. E The Structure of the Flukes in Reltion to Lminr Flow in Cetcens Z. Sдugertierkd. 34: 1-8 [14] Surkin R.M Structure nd function of the skin muscles of dolphins. Bionik 5: (in Russin). [15] Benko V.V., Koslov L.F., Pershin S.V., Sokolov V.Ye., nd Tomilin A.G Self-djustment of Skin Dmpening in Cetcens in Active Swimming, Bionik 16: 3 10 (in Russin). [16] Benko V.V Investigting the Skin Elsticity of Live Dolphins, Bionik 13: (in Russin). [17] Pst D.A., McLelln W.A., Gosline J.G., nd Piermrini P.M Morphology nd Mechnics of Dolphin Bluer, Amer. Zool. 35: 44A. [18] Romnenko E.V Fish nd Dolphin Swimming (Sofi: Pensoft) [19] Rohr, J., Ltz M. I., Fllon S., Nuen J.C, nd Hendricks E.W Experimentl Approches Towrds Interpreting Dolphin-stimulted Bioluminescence J. Exp. Biol. 201: [20] Hider M. nd Lindsley D. B Microvirtions in Mn nd Dolphin Science 146: [21] Ridgwy S. H. nd Crder D. A Fetures of Dolphin Skin with Potentil Hydrodynmic Importnce, IEEE Eng. Med. Biol. 12: [22] Benko V.V., nd Crpenter P.W Dolphin hydrodynmics Flow Pst Highly Complint Boundries nd in Collpsile Tues ed P.W. Crpenter nd T. J. Pedley (Dordrecht: Kluwer) pp , chpter 13. [23] Ngmine H., Ymht K., Hgiwr Y. nd Mtsur R Turulence modifiction y complint skin nd strt-cornes desqumtion of swimming dolphin J. Tur. 18: [24] Gd-el-Hk M Complint cotings: decde of progress Appl. Mech. Rev. 49: [25] Choi K.S., Yng X., Clyton B.R., Glover E.J., Atlr M., Semenov B.N., nd Kulik V. M Turulent drg reduction using complint surfces Proc. R. Soc. A 453: [26] Sokolov V.E Structure of the integument of some cetcens Byulleten Moskovskogo oshestv Ispittelej prirodi Otdel iologii 60: (in Russin). [27] Crpenter P.W., Dvies C. nd Lucey A.D Hydrodynmics nd complint wlls: does the dolphin hve secret? Curr. Sci. 79:

18 18 [28] Grosskreutz R Wechselwirkungen zwischen turulenten Grenzschichten und weichen Wnden, MPI fьr Strцmungsforschung und der AVA Göttingen Mitt. 53. [29] Stromerg M.W Derml epiderml reltions in the skin of ottlenose dolphin (Tursiops trunctus) Ant. Histol. Emryol. 18: [30] Crpenter P.W. nd Morris P.J The effect of nisotropic wll complince on oundry-lyer stility nd trnsition J. Fluid Mech. 288: [31] Yeo K.S The hydrodynmic stility of oundry-lyer flow over clss of nisotropic complint wlls J. Fluid Mech. 220: [32] Riedeerger D., U. Rist Numericl simultion of lminr-turulent trnsition on dolphin using the γ-re θ model. In High performnce computing in science nd engineering 11 : trnsctions of the High Performnce Computing Center, Stuttgrt (HLRS), Ngel, Wolfgng E.; Kröner, Dietmr B.; Resch, Michel M. (Eds.) (Berlin,London: Springer, 2011). [33] Aguilr Soto, N., M. P. Johnson, P. T. Mdsen, F. Diz, I. Dominguez, A. Brito nd P. Tyck Cheeths of the deep se: Deep forging sprints in short-finned pilot whles off Tenerife (Cnry Islnds). Journl of Animl Ecology 77: