An approach to determine coefficients of logarithmic velocity vertical profile in the bottom boundary layer -- Journal of Oceanology and Limnology,2021,39(6):2144-2152

	Cite this paper:
	Xiaowei WEI, Yiming ZHANG, Changming DONG, Meibing JIN, Changshui XIA. An approach to determine coefficients of logarithmic velocity vertical profile in the bottom boundary layer[J]. Journal of Oceanology and Limnology, 2021, 39(6): 2144-2152

An approach to determine coefficients of logarithmic velocity vertical profile in the bottom boundary layer

Xiaowei WEI^1,3, Yiming ZHANG¹, Changming DONG^1,2, Meibing JIN^1,2, Changshui XIA³

1 School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2 Southern Laboratory of Ocean Science and Engineering, Zhuhai 519000, China;
3 First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266101, China

Abstract:

Velocity vertical profiles in the bottom boundary layer are important to understand the oceanic circulation. The logarithmic vertical profile, u=Alnz+B, is the universal profile for the horizontal velocity in the boundary layer, in which two coefficients (A and B) need to be determined. The two coefficients are the functions of the friction velocity (u_*) and the roughness length (z₀), and they are calculated using u_* and z₀. However, the measurement of u_* and z₀ is a challenge. In the present study, an approach is developed to estimate the two coefficients (A and B) by using a series of flume laboratory experiments with flat boundary and regularly distributed cylinders as the rough boundaries. An acoustic doppler velocimeter (ADV) is used to measure the velocity vertical profiles of the steady flow. Using the measured velocity data, the regressed logarithmic profiles are obtained. Based on the series of the A and B values, the mathematical formula for A and B are statistically established as the function of the cylinder height, inflow velocity, and the water depth, which avoids the measurement of the friction velocity and the roughness length.

Key words: velocity vertical logarithmic distribution|bottom boundary layer|the friction velocity

Received: 2020-09-29 Revised: 2020-11-11

Tools

PDF (2342 KB) Free

Print this page

Add to favorites

Email this article to others

Authors

Articles by Xiaowei WEI

Articles by Yiming ZHANG

Articles by Changming DONG

Articles by Meibing JIN

Articles by Changshui XIA

References:
Alvarez L G. 2010. Bottom boundary layer properties in the Upper Gulf of California derived from velocity profiles. Ciencias Marinas, 36(3):285-299, https://doi.org/10.7773/cm.v36i3.1760.
Bai R N, Cao L K, Li D X. 2016. Applicability of Vectrino Profiler in measurement of open channel flows. Journal of Hydroelectric Engineering, 35(11):35-44. (in Chinese with English abstract)
Chen X W, Chiew Y M. 2004. Velocity distribution of turbulent open-channel flow with bed suction. Journal of Hydraulic Engineering, 130(2):140-148, https://doi.org/10.1061/(ASCE)0733-9429(2004)130:2(140).
Feng D J, Wu L H, Shimozono T, Okayasu A. 2014. Detailed measurements of boundary layer flow under swash with high-resolution PIV. Journal of Japan Society of Civil Engineers Ser B2 (Coastal Engineering), 70(2):I_741-I_745, https://doi.org/10.2208/kaigan.70.I_741.
Guo J K, Julien P Y, Meroney R N. 2005. Modified log-wake law for zero-pressure-gradient turbulent boundary layers. Journal of Hydraulic Research, 43(4):421-430, https://doi.org/10.1080/00221680509500138.
Hao J L, Song Z Y, Yan Y X, Li H Q. 2007. Study on the tidal velocity profile in the estuarine and coastal areas. Journal of Sediment Research, (4):34-41. (in Chinese with English abstract)
Inoue T, Glud R N, Stahl H, Hume A. 2011. Comparison of three different methods for assessing in situ friction velocity:A case study from Loch Etive, Scotland. Limnology and Oceanography:Methods, 9(6):275-287, https://doi.org/10.4319/lom.2011.9.275.
Keulegan G H. 1938. Laws of turbulent flow in open Channels. Journal of Research of the National Bureau of Standards, 21(6):707-741, https://doi.org/10.6028/jres.021.039.
Kim S C, Friedrichs C T, Maa J P Y, Wright L D. 2000. Estimating bottom stress in tidal boundary layer from acoustic Doppler velocimeter data. Journal of Hydraulic Engineering, 126(6):399-406, https://doi.org/10.1061/(ASCE)0733-9429(2000)126:6(399).
Kirkgöz M S. 1989. Turbulent velocity profiles for smooth and rough open channel flow. Journal of Hydraulic Engineering, 115(11):1543-1561, https://doi.org/10.1061/(ASCE)0733-9429(1989)115:11(1543).
Lacy J R. 2011. The influence of current speed and vegetation density on flow structure in two macrotidal eelgrass canopies. Limnology and Oceanography:Fluids and Environments, 1(1):38-55, https://doi.org/10.1215/21573698-1152489.
Lozovatsky I, Jinadasa S U P, Fernando H J S, Lee J H, Chang S. 2015. The wall-layer dynamics in a weakly stratified tidal bottom boundary layer. Journal of Marine Research, 73(6):207-232, https://doi.org/10.1357/002224015817391276.
Lozovatsky I, Liu Z Y, Fernando H, Armengol J, Roget E. 2012. Shallow water tidal currents in close proximity to the seafloor and boundary-induced turbulence. Ocean Dynamics, 62(2):177-191, https://doi.org/10.1007/s10236-011-0495-3.
Mrokowska M M, Rowiński P M, Kalinowska M B. 2015. Evaluation of friction velocity in unsteady flow experiments. Journal of Hydraulic Research, 53(5):659-669, https://doi.org/10.1080/00221686.2015.1072853.
Musker A J. 1979. Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA Journal, 17(6):655-657, https://doi.org/10.2514/3.61193.
O'Donoghue T, Pokrajac D, Hondebrink L J. 2010. Laboratory and numerical study of dambreak-generated swash on impermeable slopes. Coastal Engineering, 57(5):513-530, https://doi.org/10.1016/j.coastaleng.2009.12.007.
Rosman J H, Hench J L. 2011. A framework for understanding drag parameterizations for coral reefs. Journal of Geophysical Research:Oceans, 116(C8):C08025, https://doi.org/10.1029/2010JC006892.
Schlichting H, Gersten K. 2017. Boundary-Layer Theory. Springer, Berlin, Heidelberg. p.150-155, https://doi.org/10.1007/978-3-662-52919-5.
So R M C, Zhang H S, Gatski T B, Speziale C G. 1994. Logarithmic laws from compressible turbulent boundary layers. AIAA Journal, 32(11):2162-2168, https://arc.aiaa.org/doi/10.2514/3.12273.
Umeyama M, Gerritsen F. 1992. Velocity distribution in uniform sediment-laden flow. Journal of Hydraulic Engineering, 118(2):229-245, https://doi.org/10.1061/(ASCE)0733-9429(1992)118:2(229).
Valipour R, Bouffard D, Boegman L. 2015. Parameterization of bottom mixed layer and logarithmic layer heights in central Lake Erie. Journal of Great Lakes Research, 41(3):707-718, https://doi.org/10.1016/j.jglr.2015.06.010.
Wang K J, Bai J X, Tang Z Q, Jiang N. 2019. Comparative study of turbulent boundary layer wall friction velocity measured by average velocity profile method. Journal of Experimental Mechanics, 34(2):209-216. (in Chinese with English abstract)
Wang X Y, Yang Q Y, Lu W Z, Wang X K. 2012. Experimental study of near-wall turbulent characteristics in an openchannel with gravel bed using an acoustic Doppler velocimeter. Experiments in Fluids, 52(1):85-94, https://doi.org/10.1007/s00348-011-1202-3.
Wang Y P, Gao S, Jia J J. 2000. Flow structure in the marine boundary layer and bedload transport:A review. Marine Geology & Quaternary Geology, 20(3):101-106. (in Chinese with English abstract)