EXPERIMENTAL STUDY ON BOTTOM BOUNDARY LAYER BENEATH SOLITARY WAVE

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1 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved. EXPERIMENTAL STUDY ON BOTTOM BOUNDARY LAYER BENEATH SOLITARY WAVE Bambang Winarta 1, Nadiatul Adilah Ahmad Abdul Ghani 1, Hitoshi Tanaka, Hiroto Yamaji and Mohammad Fadhli Ahmad 3 1 Faulty of Civil Engineering & Earth Resoures, Universiti Malaysia Pahang, Gambang, Pahang, Malaysia Department of Civil Engineering, Tohoku University, Sendai, Japan 3 Shool of Oean Engineering, Universiti Malaysia Trengganu, Kuala Terengganu, Terengganu, Malaysia fadhli@umt.edu.my ABSTRACT A tsunami as long wave and an osillatory wave moves into shoaling water have behavior similar to solitary wave and therefore omprehension on its bottom boundary layer harateristis ome to be essential key on near-shore sediment transport modeling. In the present study, the hydraulis phenomena of solitary wave are studied in deep through experiments utilizing a losed onduit generation system. This result was examined by analytial and numerial laminar solution. Moreover, wave frition fator is disussed based on the present laboratory experiment and previous studies of (Sumer et al., 1); (Vittory and Blondeaux, 11, 1). As onlusions, in-onsistent ritial Reynolds number was found for solitary wave ase. This observable fat is distint differene with sinusoidal wave ase whih has onsisteny in ritial Reynolds number. As a main onlusion that a new generation system proposed in the present study will be able and appliable to shore up an experiment on sediment transport indued by solitary wave. Keywords: solitary wave, boundary layer, losed onduit generation system. INTRODUCTION Comprehension on sea bottom boundary layer harateristis is primay in near-shore sediment transport modeling. A tsunamis or seismi sea wave has behavior resembling to solitary waves. Besides that, as an osillatory wave moves into shoaling water, its amplitude beomes progressively higher, the rests beome shorter and the trough beomes longer and flatter and it is similar to solitary wave. Beause of these reasons, laboratory experiment and numerial experiment studies onerning solitary wave boundary layer will be neessary to hold up in its appliation for pratial purposes suh as sediment transport. Solitary wave boundary layer harateristis on laminar flow have been studied in both laboratory experiments and also in theoretial study. Wave flume with free surfae was ommonly used on previous studies. One of them is (Liu et al., 7); their experimental system is assisted by Partile Image Veloimetri (PIV) to measure veloity in the thin boundary layer. It is onluded that the experiments fall in laminar regime and still annot investigate in transitional and turbulent regimes. Indeed, wave flume experiment failities have diffiulty to attain high Shield s number. Another problem is hard to reprodue near-bed harateristis at pratial sale. Due to these inonvenienes, a proper generation set up to shore up an experiment on sediment transport indued by solitary wave is highly required. To figure out some diffiulties found in the previous sediment transport experiment, losed onduit and osillating water tunnel are used. The purpose is to reprodue near-bed hydrodynami and sediment transport phenomena at a realisti sale. Reently, (Sumer et al., 1), arried out laboratory experiment using an osillating water tunnel on investigation turbulent solitary wave boundary layer. However, it will be pratially diffiult to generate boundary layer flow exatly orresponds to solitary wave motion beause of restorative fore in a tunnel, whih may indue osillating motion with flow reversal. Beside that U-shape osillating water tunnel has diffiulty to do periodial measurement. As we know that one wave yle is not suffiient to make an adequate amount of sediment movement and onsequently, it will be less of auray. In the present study, the hydraulis phenomena of solitary wave are studied in deep through experiments utilizing a losed onduit generation system. Furthermore by ombining with previous experiments of (Sumer et al., 1) and numerial approah by (Vittori and Blondeaux, 11, 1) diagram for wave frition fator is obtained. EXPERIMENTAL CONDITION The detail explanation of a new laboratory generation system suh as: general sketh, generation system mehanism was given in the previous publiation (Tanaka et al., 11). A series of experiments with different value of Reynolds number has been arried out using a losed onduit generation system. Laser Dopller Veloimeter (LDV) installed in generation set-up measured instantaneous veloity at 17- points in the vertial diretion at 1 ms intervals, the sample of instantaneous horizontal veloity at three different elevation an be seen in Figure-1. The mean veloity was obtained by averaging over 5 wave yles, while the values were found out by fitting equation (1) to the measured free stream veloity. al Reynolds number () written in Table-1 were estimated by following equation. U Re (1) 5358

2 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved. U = = the maximum veloity under wave rest, = kinemati visosity, value was determined by fitting the exat solution of solitary wave to the measured free stream veloity. The various onditions in present experiment are summarized in Table-1. Parameter T(s) in the seond olumn of this table is period of rotating dis. Table-1. al onditions. U (s -1 ) T (s) (m /s) (m/s) Case x 1 5 Case x 1 5 Case x 1 5 Re Figure-1. Instantaneous horizontal veloity (Case 1, = 5.64 x 1 5 ) in 3 different measured elevations. 5359

3 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved z =.31 m z =.5 m Numerial laminar u z =.7 m Numerial laminar u Numerial laminar u Figure-. Quantitative value of u (u = u experiment u lam.). Parameter u is used to know the quantitative differene value between veloity obtained from the present laboratory experiment and numerial laminar omputation and defined as subtration of numerial laminar omputation from the measured stream wise veloity (u = u experiment u lam.). The alulation results of u is performed in Figure-. It an be learly observed that veloity during aelerating phases is reover to laminar, u value is in between -3 m/s to 3 m/s and during deelerating phases u value is getting higher, it is in -1 m/s to 18 m/s for Case 1, = 5.64 x 1 5. This is learly indiating redution proess of flow reversal in the near bottom due to turbulene generation. RESULTS AND DISCUSSIONS Shear stress estimation Bed shear stress quantity ontrols the sediment transport proess. In oeans the total bed shear stress is summation of bed shear stress aused by tidal urrents as unidiretional flows and also osillatory wave. It is general known that grain of sediment will start motion when ritial bed shear stress is exeeded. Therefore orret alulation of bottom shear stress is prior step needed in sediment transport alulation and analysis. Loal bottom shear stress an be estimated from linear fitting measured veloity in the near bottom or in the visous layer ( v). It an be expressed as: u u* z () u* 11.6 v (3) u* u = the vertial veloity in the boundary layer, u* = the shear veloity, z = the vertial oordinate. And bottom shear stress ( ) is expressed by following equation, u* u* (4) = the fluids density. The other formulation to alulate bottom shear stress ( ) is using Manning equation. This expression is frequently used to asses this quantity. gn U U (5) 1 3 R h g = aeleration gravity, n = Manning roughness oeffiient, R h = (Rh = A/P, where A is wetted area and P is wetted perimeter), U = depth averaged veloity. 536

4 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved. in whih; ' 1 (8) Figure-3. Estimation of shear veloity. Shear veloity is alulated by doing linear fitting to measured veloity and ross-heking the suitable visous layer thikness simultaneously. Figure-3 illustrate the visous layer thikness in variation of time, it is getting lower during aelerating phase up to wave rest and then gradually higher during deelerating phase. Bottom shear stress is square of shear veloity as shown in equation (4). In the present study this quantity is also estimated by Manning equation. Manning roughness oeffiient (n) used in bottom shear stress alulation is.1 (for glass), this (n) value reflet losed onduit material of generation system applied in the present experiment. (Keulegan, 1948) have derived the expressions inside boundary layer for veloity and bottom shear stress in the spatial variation, onsidering linearized boundary layer equation in the laminar flow regime. And then, it is onverted by (Tanaka et al., 1998) for both expressions in temporal variation and written as follows: Figure-3 illustrated the bottom shear in a variation of Reynolds number with different methods of alulation. During aelerating phase bottom shear stress has lose agreement with analytial laminar solution, it means during this phase veloity distribution in visous layer is in laminar distribution. At = 5.64 x 1 5, during aelerating phase up to end of deelerating phase, bottom shear stress has a good agreement with analytial laminar solution, it has meaning veloity distribution is almost laminar. However, slight deviation from analytial laminar solution ours after end of deeleration period, it is indiating that veloity distribution near wall has already moved to higher flow regime. Other harateristis indiate flow regime hanging is appearing spike in instantaneous horizontal veloity. Detail analysis of horizontal and vertial veloity distribution an be seen in the previous publiation (Tanaka et al., 11). When = 6.6 x 1 5 deviation from analytial laminar solution ome earlier than previous ase and bottom shear stress during flow reversal is almost zero. Quite different behavior when = 7.34 x 1 5, deviation from analytial laminar solution is getting higher and ome earlier than previous ases. From Figure-3 we also an observe the magnitude of bottom shear stress using Manning equation is giving 3 times different with other methods. The Manning equation estimates the bottom shear stress as a funtion of square of veloity per depth as shown in equation (5). In ase of unsteady flow ondition, this relation is not always orret and as onsequene bottom shear stress is also not aurate. (m /s ) Analytial laminar solution Manning Equation t (s) (a) Case 1, = 5.64 x 1 5 u U ' z se h t se h t e d (6) R e 4U se h tan U 4 R e t h t d (7) 5361

5 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved. (m /s ) Analytial laminar solution Manning Equation wave frition fators fall in analytial laminar solution (equation (1)). It is aused by transition to turbulene phenomenon happened in deelerating period, while during aelerating phase flows reover to laminar where the maximum bottom shear stress ourred. As a onlusion, wave frition fator under solitary wave also show in-onsisteny of ritial Reynolds number, it is similar to boundary layer thikness t (s) (b) Case, = 6.6 x 1 5 (m /s ) Analytial laminar solution Manning Equation t (s) () Case 3, = 7.34 x 1 5 Figure-4. Bottom shear stress. Wave frition fator Wave frition fator (f w) is dimensionless parameter used to estimate bed shear stress indued by wave. This parameter is related to the Shields parameter for unidiretional urrent. The wave frition fator an be omputed by following equation from measured bottom shear stress, max f w (9) U max = the maximum bottom shear stress. Analytial laminar solution for wave frition fator under solitary wave an be obtained from the equation (7) and then expressed in term of Reynolds number as following equation, 1.71 f w (1) R e Figure-5. Wave frition fator. Sinusoidal wave versus solitary wave Figures-6 and 7 are summary three riteria: wave frition fator, phase differene and boundary layer thikness in two different of wave ases: sinusoidal wave and solitary wave. Sinusoidal wave ase has onsisteny in ritial Reynolds number in terms of boundary layer thikness, phase differene and wave frition fator as display in Figure-6 (Jensen et al., 1989; Tanaka and Thu, 1994). A dissimilar observable fat an be found in solitary wave ase whih has inonsisteny of ritial Reynolds number. A ritial Reynolds number proposed by (Sumer et al., 1) is at 5 x 1 5 and this value is similar to DNS simulation result by (Vittori and Blondeaux, 11). The same finding also was found from the present laboratory experiments of Case 1 with Reynolds number () = 5.64 x 1 5, this ase onfirmed a good agreement with previous findings in a stability diagram. After omprehensive investigation of the present experiments data, an inonsisteny of ritial Reynolds number is also found in wave frition fator and boundary layer thikness as shown in Figure-7. The wave frition fator from the previous experiment study and diret numerial simulation (DNS) are plotted in similar Figure with present laboratory experiment as shown in Figure-5 and among them show a good agreement with equation (1), although attain at =.7 x 1 6, it has to be 5 times of = 5 x 1 5 as ritial Reynolds number. The ases of present experiments with = 5.64 x 1 5, = 6.6 x 1 5 and = 7.34 x 1 5 are above of ritial Reynolds number but the 536

6 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved. 1 7 r = 5 x 1 5 f w Present experiment DNS (Vittori & Blondeaux, 8) s (Sumer et al., 1) h/ 1 (a) Stability diagram 1 s 1.71 (Sumer et al., 1) fw 1-1 Present Rexperiment e Vittori and Blondeaux 11, 1 for * =.83 x fw Re Vittori and Blondeaux 11, 1 for * = 4.75 x 1-4 Vittori and Blondeaux 11, 1 for * = 7.99 x (b) Wave frition fator.5. Laminar solution (Liu et al., 7) s (Sumer et al., 1) Present experiment -.5 Figure-6. Charateristis of sinusoidal wave. CONCLUSIONS A series of experiments with different value of Reynolds number has been arried out using a losed onduit generation system. Estimation and evaluation of some parameters have been done: shear stress and wave frition fator. A new knowledge an be found from this present study is in-onsisteny of ritial Reynolds number in terms of boundary layer thikness and wave frition fator for solitary wave. This observable fat is distint differene with sinusoidal wave ase whih has onsisteny in ritial Reynolds number of boundary layer thikness, phase differene and wave frition fator. /a m () Phase differene.3.9 a m..1 Present experiment s (Sumer et al., 1) (d) Boundary layer thikness Figure-7. Charateristis of solitary wave. REFERENCES Blondeaux, P. and Vittori, G. 1. RANS modeling of the turbulent boundary layer under solitary wave. Coastal Eng., 6, pp. 1-1 Fredsøe, J Turbulent boundary layer in waveurrent motion. Journal of Hydraulis Engineering, ASCE, 11(HY8), pp Jensen, B., Sumer, B.M. and Fredsøe, J Turbulent osillatory boundary layer at high Reynolds number. J. Fluid Meh., 6, pp Keulegan, G. H Gradual damping of solitary waves. U.S. Department of Commere, National Bureau of Standards. RP1895, 4, pp Liu, P. L. -F., Park, Y. S. and Cowen, E. A. 7. Boundary layer flow and bed shear stress under a solitary wave. J. Fluid Meh., 574, pp

7 VOL. 11, NO. 8, APRIL 16 ISSN Asian Researh Publishing Network (ARPN). All rights reserved. Sleath, J.F.A Turbulent osillatory flow over rough beds. J. Fluid Meh., 18, pp Sumer, B. M., Jensen, P. M., Sørensen, L. B., Fredsøe, J., Liu, P. L.-F and Cartesen, S. 1. Coherent strutures in wave boundary layers. Part. Solitary motion. J. Fluid Meh., 646, pp Suntoyo and Tanaka, H. 9. Numerial modeling of boundary layer flows for a solitary wave. J. Hydro- Environ. Res., 3(3), pp Tanaka, H., Bambang Winarta, Suntoyo and Yamaji, H. 11. Validation of a new generation system for bottom boundary layer beneath solitary wave, Coastal Eng., 59, pp Tanaka, H., Sumer, B. M. and Lodahl, C Theoretial and experimental investigation on laminar boundary layers under noidal wave motion. Coastal Eng. J. 4(1), pp Tanaka, H. and Thu, A Full-range equation of frition oeffiient and phase differene in a wave-urrent boundary layer. Coastal Eng.,, pp Vittori, G. and Blondeaux, P. 11. Charateristis of the boundary layer at the bottom of a solitary wave. Coastal Eng. 58, pp