1DV structure of turbulent wave boundary layers

Nielsen, Peter (2016) 1DV structure of turbulent wave boundary layers. Coastal Engineering, 112 1-8. doi:10.1016/j.coastaleng.2016.02.001


Author Nielsen, Peter
Title 1DV structure of turbulent wave boundary layers
Journal name Coastal Engineering   Check publisher's open access policy
ISSN 0378-3839
1872-7379
Publication date 2016-06-01
Year available 2016
Sub-type Article (original research)
DOI 10.1016/j.coastaleng.2016.02.001
Open Access Status Not Open Access
Volume 112
Start page 1
End page 8
Total pages 8
Place of publication Amsterdam, Netherlands
Publisher Elsevier BV
Collection year 2017
Language eng
Formatted abstract
The 1DV structure of turbulent oscillatory boundary layers throughout the full relative roughness range 0 < r/A < 1 and Reynolds numbers (A2ω/v) up to 6 × 106 is investigated through experimental data, A is the free stream semi excursion, r the bed roughness, ω the angular frequency and v the kinematic viscosity. It is shown that smooth and rough flows alike can be scaled using the universal vertical scale z1=√2v/ω+0.0081rA, which becomes the Stokes' length √2v/ω for smooth beds (r = 0) and0.09√rA for roughness dominated flows. Extraction of z1 and hence r from experimental data provides a method for determining the effective hydraulic roughness of live sand-beds under waves in analogy with the log-fit method for determining the r from the zero intercept, z0 = r/30 in steady flows. In fairly rough flows, e.g. over vortex ripples, the velocity structure is analogous to laminar flow and hence the eddy viscosity is constant with the value vt = 0.004ωrA, corresponding to z1=0.09√rA=√2vt/ω. In the opposite limit of vanishing roughness and high Reynolds numbers, z1/A < 10-3, the velocity structure, which corresponds to von Karman's vt = kufz, agrees reasonably with data. However, this asymptotic velocity structure deviates considerably from measurements through the naturally occurring r/A-range for sand beds. In the intermediate range 10-3 < r/A < 0.06 the velocity structure does not seem to correspond to any real-valued, time invariant eddy viscosity. Comparison of the Kelvin function solution, which corresponds to vt = κufz, with smooth and almost-smooth, high Reynolds number measurements, shows that, the optimal zero intercepts are not the steady flow values 0.11v/uf respectively r/30, but generally significantly larger. For low-roughness, high-Reynolds number oscillatory flows (z1/A < 0.002), the magnitude of the velocity defect function universally follows |D| ~ exp [-(z/z1)1/3]. This 1/3-power is interesting in that it has previously been shown to correspond maximum energy dissipation. In turbulent '2nd order Stokes flows' the vertical boundary layer scale of the second harmonic is smaller than that of the primary, but by a factor smaller than 21/2, which applies in laminar flow. Density stratification in heavily sediment-laden sheet-flow makes the boundary layer thinner via the power p in |D| ~ exp [-zp] taking greater values than in fixed bed experiments with similar z1/A.
Keyword Eddy viscosity
Energy dissipation
Hydraulic roughness
Stratification in boundary layers
Velocity defect function
Wave boundary layers
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Civil Engineering Publications
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