{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:57:07Z","timestamp":1760151427282,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,23]],"date-time":"2022-03-23T00:00:00Z","timestamp":1647993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Stilling basin with a negative step is an important structure in hydraulic systems, because it can avoid atomization and decrease scouring problems. Although stilling basins with a negative step have attracted much attention from researchers, few researchers have focused on the wave characteristics. In this research, an experimental study on the wave characteristics of stilling basins with a negative step was carried out. The wave height, average period, wave probability density and power spectrum along the flow direction of different stilling basins with a negative step were described based on the wave theory, and the results indicate discharge and step height have a significant effect on the wave characteristics. The relationships between the different characteristic wave heights, and the empirical formula for the relative characteristic wave height are obtained. Finally, the dimensionless standard deviation at the end of the stilling basin with a negative step is linearly related to the flow-energy ratio and the relative step height under B-jump.<\/jats:p>","DOI":"10.3390\/e24040445","type":"journal-article","created":{"date-parts":[[2022,3,23]],"date-time":"2022-03-23T12:20:25Z","timestamp":1648038025000},"page":"445","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Experimental Study on Wave Characteristics of Stilling Basin with a Negative Step"],"prefix":"10.3390","volume":"24","author":[{"given":"Guibing","family":"Huang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Development and Protection, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingjun","family":"Diao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Development and Protection, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Development and Protection, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuan\u2019ai","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Development and Protection, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wang","family":"Jia","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Development and Protection, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,23]]},"reference":[{"key":"ref_1","unstructured":"Dong, T. (2016). Research on Energy Dissipation Mechanism and Fluctuating Pressure of Special-Shaped Stilling Basin. [Ph.D. Thesis, Tianjin University]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/00221689009499088","article-title":"Wave type flow at abrupt drops","volume":"28","author":"Kawagoshi","year":"1990","journal-title":"J. Hydraul. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1080\/00221688709499279","article-title":"Hydraulic Jumps At Positive And Negative Steps","volume":"25","author":"Ohtsu","year":"1987","journal-title":"J. Hydraul. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1080\/09715010.2020.1812008","article-title":"Hydraulic jump control using stilling basin with adverse slope and positive step","volume":"28","author":"Pourabdollah","year":"2020","journal-title":"ISH J. Hydraul. Eng."},{"key":"ref_5","unstructured":"Li, S. (2012). Research on Hydrodynamic Loads of Stilling Basin with Drop Sill. [Ph.D. Thesis, Tianjin University]."},{"key":"ref_6","unstructured":"Li, H. (2012). Research on Hydrodynamic Loads of Underflow Stilling Basin. [Ph.D. Thesis, Tianjin University]."},{"key":"ref_7","first-page":"1","article-title":"Failure Mechanism of Bottom Plate in Stilling Basin and Countermeasure for Protection","volume":"9","author":"Liu","year":"2001","journal-title":"J. Hydraul. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hassanpour, N., Hosseinzadeh Dalir, A., Bayon, A., and Abdollahpour, M. (2020). Pressure Fluctuations in the Spatial Hydraulic Jump in Stilling Basins with Different Expansion Ratio. Water, 13.","DOI":"10.3390\/w13010060"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1080\/00221680009498317","article-title":"On the effects of a negative step in pressure fluctuations at the bottom of a hydraulic jump","volume":"38","author":"Armenio","year":"2000","journal-title":"J. Hydraul. Res."},{"key":"ref_10","first-page":"1188","article-title":"Study on Stilling Basin with Step-down Floor for Energy Dissipation of Hydraulic Jump in High Dams","volume":"36","author":"Sun","year":"2005","journal-title":"J. Hydraul. Eng."},{"key":"ref_11","first-page":"1","article-title":"A Laboratory Study on Hydraulic Characteristics of Waves Downstream from a Hydraulic Jump","volume":"12","author":"Wu","year":"1991","journal-title":"J. Zhengzhou Inst. Technol."},{"key":"ref_12","first-page":"63","article-title":"Experimental study on wave characteristics of water surface on bucket energy dissipators","volume":"34","author":"Dong","year":"1994","journal-title":"J. Tsinghua Univ."},{"key":"ref_13","first-page":"40","article-title":"Study on the Energy Dissipation Mechanism of Mult-horizontal Submerged Jets","volume":"25","author":"Li","year":"2006","journal-title":"J. Hydroelectr. Eng."},{"key":"ref_14","first-page":"65","article-title":"Study on flow regime transition of falling-sill bottom-flow energy dissipation and its control","volume":"47","author":"Zheng","year":"2016","journal-title":"Water Resour. Hydropower Eng."},{"key":"ref_15","unstructured":"Yu, Y. (1999). Random Wave and Its Applications to Engineering, Dalian University of Technology Press."},{"key":"ref_16","first-page":"C09024","article-title":"Short-term statistics of waves observed in deep water","volume":"115","author":"Holthuijsen","year":"2010","journal-title":"J. Geophys. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1061\/(ASCE)WW.1943-5460.0000164","article-title":"Distributions of Wave Heights in Time Domain in Stationary Sea States","volume":"139","author":"Boccotti","year":"2013","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"041105","DOI":"10.1115\/1.3160657","article-title":"Nonlinear Crest, Trough, and Wave Height Distributions in Sea States with Double-Peaked Spectra","volume":"131","author":"Felice","year":"2009","journal-title":"J. Offshore Mech. Arct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"C01015","DOI":"10.1029\/2008JC005077","article-title":"An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield","volume":"114","author":"Shemer","year":"2009","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_20","first-page":"C08005","article-title":"Statistics of nonlinear waves generated in an offshore wave basin","volume":"114","author":"Cherneva","year":"2009","journal-title":"J. Geophys. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"04015026","DOI":"10.1061\/(ASCE)WW.1943-5460.0000327","article-title":"Coastal Wave-Height Statistics during Hurricane Ike","volume":"142","author":"Nayak","year":"2016","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_22","first-page":"245","article-title":"On the Statistical Distribution of the Heights of Sea Waves","volume":"11","year":"1952","journal-title":"J. Mar. Res."},{"key":"ref_23","first-page":"149","article-title":"Distribution of Crest-to-Trough Wave Heights","volume":"107","author":"Tayfun","year":"1981","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1029\/JC085iC03p01519","article-title":"Longuet-Higgins on the distribution of the heights of sea waves: Some effects of nonlinearity and finite band width","volume":"85","author":"Michael","year":"1980","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/0029-8018(85)90014-9","article-title":"On the distribution of crest to trough wave heights","volume":"12","author":"Naess","year":"1985","journal-title":"Ocean Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0141-1187(89)90024-2","article-title":"The statistical distribution of wave heights in a random seaway","volume":"11","author":"Vinje","year":"1989","journal-title":"Appl. Ocean Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1061\/(ASCE)0733-950X(1990)116:6(686)","article-title":"Distribution of Large Wave Heights","volume":"116","author":"Tayfun","year":"1990","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1017\/S002211200400802X","article-title":"Improved joint probability distribution for ocean wave heights and periods","volume":"503","author":"Stansell","year":"2004","journal-title":"J. Fluid Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"06014018","DOI":"10.1061\/(ASCE)EM.1943-7889.0000881","article-title":"Numerical Investigation on Roll-Wave Properties: Wave\u2013Wave Interactions, Generality, and Spectrum","volume":"141","author":"Huang","year":"2015","journal-title":"J. Eng. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"04017029","DOI":"10.1061\/(ASCE)WW.1943-5460.0000415","article-title":"Attenuation of Nonlinear Waves by Rigid Vegetation: Comparison of Different Wave Theories","volume":"143","author":"Zhu","year":"2017","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.ecss.2015.08.009","article-title":"Effects of wave steepness and relative water depth on wave attenuation by emergent vegetation","volume":"164","author":"Wu","year":"2015","journal-title":"Estuar. Coast. Shelf Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1061\/(ASCE)WW.1943-5460.0000215","article-title":"Laboratory Observations and Numerical Simulations of Wave Height Attenuation in Heterogeneous Vegetation","volume":"140","author":"Blackmar","year":"2014","journal-title":"J. Waterw. Port Coast. Ocean Eng."},{"key":"ref_33","unstructured":"Guo, H. (2019). Study on the Influence of Wave Transformation and Overtopping Characteristics of Breakwater on Coral Coast. [Master\u2019s Thesis, Changsha University of Science and Technolgy]."},{"key":"ref_34","unstructured":"Liu, L. (2020). Based on the Inertial Navigation Ocean Characteristic Element Measurement Research. [Master\u2019s Thesis, Tianjin University of Technology]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.flowmeasinst.2018.02.009","article-title":"On the estimation of free-surface turbulence using ultrasonic sensors","volume":"60","author":"Zhang","year":"2018","journal-title":"Flow Meas. Instrum."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"012064","DOI":"10.1088\/1757-899X\/381\/1\/012064","article-title":"Application of Roundness Test on Tires Based on Five-Point Cubic Smoothing Algorithm","volume":"381","author":"Li","year":"2018","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_37","first-page":"2759092","article-title":"Denoising and Trend Terms Elimination Algorithm of Accelerometer Signals","volume":"2016","author":"Zhang","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/00221689109498436","article-title":"Transition from supercritical to subcritical flow at an abrupt drop","volume":"29","author":"Ohtsu","year":"1991","journal-title":"J. Hydraul. Res."},{"key":"ref_39","unstructured":"Sun, G. (2003). The Probe into The Weakening Wave Mechanism and Hydraulic Design of Diffluent Piers with Low Rides. [Master\u2019s Thesis, Guangxi University]."},{"key":"ref_40","first-page":"102","article-title":"Release Pressure Fluctuation and Its Conceptual Design","volume":"12","author":"Sun","year":"1997","journal-title":"J. Hydrodyn."},{"key":"ref_41","first-page":"133","article-title":"Wave Action at Spillways","volume":"89","year":"1963","journal-title":"Am. Soc. Civ. Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/4\/445\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:41:36Z","timestamp":1760136096000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/4\/445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,23]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["e24040445"],"URL":"https:\/\/doi.org\/10.3390\/e24040445","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,3,23]]}}}