1 CHARACTERIZATION OF TRANSITION TO TURBULENCE IN SOLITARY WAVE BOUNDARY LAYER BY: BAMBANG WINARTA - TOHOKU UNIVERSITY HITOSHI TANAKA - TOHOKU UNIVERSITY HIROTO YAMAJI - TOHOKU UNIVERSITY

2 OUTLINE OF PRESENTATION 1.GENERAL INTRODUCTION 2.PREVIOUS RESEARCHES 3.THE OBJECTIVE OF RESEARCH 4.GENERATION METHOD OVERVIEW 5.RESULTS AND DISSCUSSIONS 6.CONCLUSIONS

3 GENERAL INTRODUCTION Solitary wave with narrow crests without trough often used as an approximation of surface profile of ocean water wave propagating in shoaling water Moreover, a tsunami wave approaching shallow water can also be frequently replaced with solitary wave to a first approximation (Photo 1) Fig. 1 Sketch of solitary wave Photo 1. Tsunami – Japan 2011 (Taken from Helicopter-National self defense, Japan )

44 PREVIOUS RESEARCHES Sumer et al. (2008,2010) U-shaped oscillating tunnel ⇒ In laminar regime and transition to turbulence regime ⇒ Practically difficult to do periodical measurement to achieve reliable ensemble average ⇒ 50 wave number ⇒ The portion of the data with negative velocities was disregarded in the data analysis Fig. 2 Experimental facility by Sumer et al. (2008)

5 Fig. 3 Stability diagram (Tanaka et al. 2011) The critical Reynolds number proposed by Sumer et al. (2010), DNS by Vittori and Blondeaux (2008, 2011) and present experiment ( R e = 5.64 x 10 5 ) were plotted in stability diagram. where: h : the water depth or half of the closed conduit tunnel height;  1 : conventional thickness equal to (2  /  ) 1/2. PREVIOUS RESEARCHES

6 THE OBJECTIVE OF RESEARCH By considering the fundamental importance to the study of fluid motion, boundary layer problem in transition to turbulence flow is still attracting much attention The objective of research: to enhance our understanding in the boundary layer characteristics under a solitary wave by doing investigation comprehensively in order to identify the flow characteristics in transition to turbulence flow regime

7 GENERATION METHOD OVERVIEW SKETCH OF GENERATION SYSTEM The experimental set-up consisted of overflows head tank, downstream gate, flow velocity measurement device and conduit water tunnel. The overflows head tank maintains a constant pressure head and then flows into measurement section along a conduit water tunnel. The downstream gate can be raised up and dropped down regularly using a mechanism of circular disc connected with the motor Fig. 4 Sketch of the experimental generation system

The expression form for the velocity: GENERATION METHOD OVERVIEW ROTATING DISK DESIGN & OPERATION Fig. 5 Circular disc shape based on the solitary wave formula for where: z d (t) : distance from the centre of the disc to the edge at  t Fig. 6 Operational system of rotating disc 1 The downstream gate will start to open at  t =-  /2 2 The downstream gate will fully open at  t = 0  (z g (t) = z g max ) and the peak of periodical velocity arrives 3 The downstream gate will close gradually up to  t =-  /2

9 RESULT AND DISCUSSIONS No  (cm 2 /s) U c (cm/s)  (s -1 ) RMSE (cm/s) ReRe Measurement condition S = single P = periodical x 10 5 S x 10 5 S,P x 10 5 S,P x 10 5 S,P Table. 1 Experimental condition The experimental conditions are summarized in Table 1 where: U c : max of free stream velocity;  : kinematics viscosity; the  values were found out by fitting the exact solution of solitary wave to the measured free stream velocity. Laminar Transition to Turbulent

10 RESULT AND DISCUSSIONS Fig. 7 Instantaneous velocity Transition to Turbulent Hino et al. (1976) defined conditionally turbulent flow when turbulence is generated suddenly in the decelerating phase and in the accelerating phase the flow recovers to laminar = → Case 3 and Case 4. Reduction of flow reversal in the near bottom because of turbulence generation occurred in these cases.

11 Fig. 8 Turbulence intermittency in various value of R e Dissimilar fluctuation in deferent values of R e Increasing of R e can be indicated by the characteristics of flow velocity fluctuation Deviation from numerical laminar is getting bigger by increasing value of R e The degree of deviation from numerical laminar  relaminarization Transition to Turbulent Case 2; R e = 5.64 x 10 5 Case 3; R e = 6.06 x 10 5 Case 4; R e = 7.34 x 10 5 RESULT AND DISCUSSIONS

12 z = cm; vel. exp > the numerical laminar vel. z = cm; vel. exp >>> the numerical laminar vel. z = cm; vel. exp >>>> the numerical laminar vel. z = cm; vel. exp >>> the numerical laminar vel. z = cm; vel. exp > the numerical laminar vel. z = cm; vel. exp = the numerical laminar vel. z = cm; vel. exp < the numerical laminar vel.  similar to flow velocity across a pipe flow. Fig. 9 Turbulence intermittency in variation of depth measurement at t = 1.50s; Case 2-3; (R e = 6.06 x 10 5 )

13 RESULT AND DISCUSSIONS Case 2, Case 3 and Case 4, → gradually deviate from numerical laminar simulation. Fig. 10 Vertical velocity distribution during decelerating phases Case 2 Case 4 Case 3 Transition to Turbulent

14 RESULT AND DISCUSSIONS Fig. 11 Velocity profile in the variation of time Transition to Turbulent t = 0.00s, experimental velocity = numerical laminar,  a small deviation  R e = 7.34 x The exp-velocity  R e >>>> deviate from numerical laminar earlier The interesting fact  discontinue in velocity profile R e = 6.06 x 10 5, at t = 1.50s, z = cm and z = cm  caused by turbulence intermittency The identical behavior  R e = 7.34 x 10 5, at t =1.25s, z = cm & z = cm.  similar to previous experimental studies by Sumer et al for R e = 1.8 x 10 6

15 Fig. 12 Instantaneous velocity at z = cm and z = cm RESULT AND DISCUSSIONS

16 RESULT AND DISCUSSIONS Accelerating phase   = 0 (Case 2 and Case 3), the flow is laminar.  > 0 (Case 4)  relaminarization The turbulence intensity typically takes place in the decelerating phases but a small turbulence intensity can be found in accelerating phases when R e = 7.34 x 10 5 Case 4; R e = 7.34 x 10 5 Fig. 13 Turbulent intensity overlaid with intermittency factor The intermittency factor  (z,t) is probability that flow at (z,t) is turbulent Transition to Turbulent Case 2; R e = 5.64 x 10 5 Case 3; R e = 6.06 x 10 5 Accelerating phases Decelerating phases Accelerating phases Decelerating phases Accelerating phases Decelerating phases

17 RESULT AND DISCUSSIONS Accelerating phase  close agreement with numerical laminar solution. R e = 5.64 x 10 5 ; decelerating phase  slight deviation occurs after end of decelerating phase. R e = 6.06 x 10 5 ; decelerating phase  deviation from numerical laminar solution is getting bigger as compared to Case 2 R e = 7.34 x 10 5 ; deviation from numerical laminar solution  getting higher and come earlier than 2 previous cases. Momentum methods where u : stream wise velocity, U : velocity at z =  or free stream velocity Transition to Turbulent Fig. 14 Bottom shear stress

18 A phase difference between the maximum values of bottom shear stress takes place and the maximum of free stream velocity (  ). The present experiment case  fall in laminar solution although 3 of them has R e > Critical Reynolds number at 5 x 10 5 Fig. 15 Phase difference RESULT AND DISCUSSIONS

19 The experimental wave friction factor ( f w ) can be computed by following equation from measured bottom shear stress, Analytical laminar solution for wave friction factor in term of Reynolds number Fig. 16 Wave friction factor where  0 max : the maximum bottom shear stress RESULT AND DISCUSSIONS

20 Sinusoidal wave Solitary wave In sinusoidal wave case  consistent critical Reynolds number for friction factor, phase difference and boundary layer thickness (Jensen et al., 1989; Tanaka and Thu, 1994) In solitary wave case  critical Reynolds number = 5 x 10 5, but boundary layer thickness up to 1.8 x 10 6 is still closed to laminar solution (in-consistent R ecr ) RESULT AND DISCUSSIONS

21 CONCLUSIONS Transition to turbulent flow characteristics under solitary wave have been analyzed based on the present experiment with R e value 5.64 x 10 5, 6.06 x 10 5 and 7.34 x 10 5 Turbulence intermittency, turbulence intensity, bottom shear stress, wave friction factor and phase difference are our concern in order to observe transition to turbulence flow behavior The phase difference obtained from the present study has a fairly good agreement with previous studies

22 CONCLUSIONS In this present study can be found in-consistency of critical Reynolds number in terms of boundary layer thickness and wave friction factor for solitary wave. This observable fact is distinct difference with sinusoidal wave case which has consistency in critical Reynolds number of boundary layer thickness, phase difference and wave friction factor. And as an additional information: A new generation system which has developed in our study can overcome some difficulties of the experimental facilities applied in the previous experimental studies, particularly in achieving a reliable ensemble averaging with ease and also in conducting the advance experiment such as: sediment transport experiment.

23 Thank for your kindly attention