Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study
For solitary waves on a horizontal bed, the study deals experimentally with the high ratio of wave height (<i>H</i><sub>0</sub>) to still water depth (<i>h</i><sub>0</sub>) that amplifies the wave nonlinearity. The value of <i>H</i><sub&...
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MDPI AG
2022-11-01
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| Online Access: | https://www.mdpi.com/2073-4441/14/22/3609 |
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| author | Chang Lin Ming-Jer Kao James Yang Juan-Ming Yuan Shih-Chun Hsieh |
| author_facet | Chang Lin Ming-Jer Kao James Yang Juan-Ming Yuan Shih-Chun Hsieh |
| author_sort | Chang Lin |
| collection | DOAJ |
| description | For solitary waves on a horizontal bed, the study deals experimentally with the high ratio of wave height (<i>H</i><sub>0</sub>) to still water depth (<i>h</i><sub>0</sub>) that amplifies the wave nonlinearity. The value of <i>H</i><sub>0</sub><i>/h</i><sub>0</sub> tested in a wave flume ranges from 0.050 to 0.550, indicating the shift from a quasi-linear solitary wave to a highly nonlinear one. A high-speed particle image velocimetry (HSPIV) and a flow visualization technique of particle-trajectory tracking method are utilized to measure velocity fields and identify near-bed flow structures. The unsteady free-stream velocities with equal magnitude take place in a free-stream zone, FSZ). The FSZ underlies the internal flow zone, over which the external free surface of solitary wave exists and is situated beyond the boundary layer. The spatio-temporal variation of free-stream velocity, moving in phase with the free surface elevation, characterizes the pattern of pressure gradient in the FSZ and thus dominates the behavior of boundary layer flow. Accordingly, nonlinear effects on the time series as well as the maximum values of horizontal velocity, particle acceleration, and pressure gradient in the FSZs of solitary waves are presented. Before, at, and after the wave crest’s intersection with a given measurement location, favorable, zero, and adverse pressure gradients occur in the FSZ, respectively. For <i>H</i><sub>0</sub>/<i>h</i><sub>0</sub> = 0.179, 0.363, and 0.550, the values of the dimensionless maximum free-stream velocity are about 3.10, 5.32, and 6.20 times that (= 0.0473) for <i>H<sub>0</sub>/h<sub>0</sub></i> = 0.050; and the corresponding values of the dimensionless maximum adverse pressure gradient are about 5.74, 14.54 and 19.84 times that (= 0.0061) for <i>H</i><sub>0</sub>/<i>h</i><sub>0</sub> = 0.050. This evidence highlights the nonlinear effect on the kinematic and hydrodynamic features of solitary waves. Finally, the effect of nonlinearity on the relationship between the dimensionless time for the maximum adverse pressure gradient in the FSZ and that for the incipient flow reversal in the bottom boundary layer is explored for the first time. It is found that the incipient flow reversal takes place immediately after the maximum adverse pressure gradient, together with a decrease in the dimensionless time for flow reversal if <i>H</i><sub>0</sub>/<i>h</i><sub>0</sub> increases. The fact accentuates the nonlinear effect on the incipient flow reversal right above the bed. |
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| language | English |
| last_indexed | 2024-03-09T17:56:24Z |
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| spelling | doaj.art-9f84d60f0c76451a91b5fe32d832fc052023-11-24T10:20:02ZengMDPI AGWater2073-44412022-11-011422360910.3390/w14223609Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental StudyChang Lin0Ming-Jer Kao1James Yang2Juan-Ming Yuan3Shih-Chun Hsieh4Department of Civil Engineering, National Chung Hsing University, Taichung 40227, TaiwanDepartment of Civil Engineering, National Chung Hsing University, Taichung 40227, TaiwanVattenfall AB, R&D Hydraulic Laboratory, 81426 Älvkarleby, SwedenDepartment of Data Science and Big Data Analytics, Providence University, Taichung 43301, TaiwanAxesea Engineering Technology Co., Ltd., Taichung 407034, TaiwanFor solitary waves on a horizontal bed, the study deals experimentally with the high ratio of wave height (<i>H</i><sub>0</sub>) to still water depth (<i>h</i><sub>0</sub>) that amplifies the wave nonlinearity. The value of <i>H</i><sub>0</sub><i>/h</i><sub>0</sub> tested in a wave flume ranges from 0.050 to 0.550, indicating the shift from a quasi-linear solitary wave to a highly nonlinear one. A high-speed particle image velocimetry (HSPIV) and a flow visualization technique of particle-trajectory tracking method are utilized to measure velocity fields and identify near-bed flow structures. The unsteady free-stream velocities with equal magnitude take place in a free-stream zone, FSZ). The FSZ underlies the internal flow zone, over which the external free surface of solitary wave exists and is situated beyond the boundary layer. The spatio-temporal variation of free-stream velocity, moving in phase with the free surface elevation, characterizes the pattern of pressure gradient in the FSZ and thus dominates the behavior of boundary layer flow. Accordingly, nonlinear effects on the time series as well as the maximum values of horizontal velocity, particle acceleration, and pressure gradient in the FSZs of solitary waves are presented. Before, at, and after the wave crest’s intersection with a given measurement location, favorable, zero, and adverse pressure gradients occur in the FSZ, respectively. For <i>H</i><sub>0</sub>/<i>h</i><sub>0</sub> = 0.179, 0.363, and 0.550, the values of the dimensionless maximum free-stream velocity are about 3.10, 5.32, and 6.20 times that (= 0.0473) for <i>H<sub>0</sub>/h<sub>0</sub></i> = 0.050; and the corresponding values of the dimensionless maximum adverse pressure gradient are about 5.74, 14.54 and 19.84 times that (= 0.0061) for <i>H</i><sub>0</sub>/<i>h</i><sub>0</sub> = 0.050. This evidence highlights the nonlinear effect on the kinematic and hydrodynamic features of solitary waves. Finally, the effect of nonlinearity on the relationship between the dimensionless time for the maximum adverse pressure gradient in the FSZ and that for the incipient flow reversal in the bottom boundary layer is explored for the first time. It is found that the incipient flow reversal takes place immediately after the maximum adverse pressure gradient, together with a decrease in the dimensionless time for flow reversal if <i>H</i><sub>0</sub>/<i>h</i><sub>0</sub> increases. The fact accentuates the nonlinear effect on the incipient flow reversal right above the bed.https://www.mdpi.com/2073-4441/14/22/3609solitary wavenonlinearityfree-stream velocityaccelerationpressure gradientincipient flow reversal |
| spellingShingle | Chang Lin Ming-Jer Kao James Yang Juan-Ming Yuan Shih-Chun Hsieh Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study Water solitary wave nonlinearity free-stream velocity acceleration pressure gradient incipient flow reversal |
| title | Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study |
| title_full | Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study |
| title_fullStr | Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study |
| title_full_unstemmed | Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study |
| title_short | Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study |
| title_sort | effects of nonlinearity on velocity acceleration and pressure gradient in free stream zone of solitary wave over horizontal bed an experimental study |
| topic | solitary wave nonlinearity free-stream velocity acceleration pressure gradient incipient flow reversal |
| url | https://www.mdpi.com/2073-4441/14/22/3609 |
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