Roughness Effects of Subaquaeous Ripples and Dunes
Abstract
:1. Reasons and Task
1.1. Reasons
1.2. Tasks
- a comprehensive comparison of the different approaches and
- the development of an improved prediction function.
2. Hydromechanical Relationships
3. Classes of Approaches for Determination of Bed Roughness
3.1. Determination of Skin Roughness
3.2. Determination of Form Roughness
3.2.1. Determination via an Effective Bed Form Roughness Height and Length
3.2.2. Determination via the Borda–Carnot Loss Approach
4. Approaches from the Literature
4.1. Approaches via Empirical Determination of an Effective Form-Roughness Height
4.2. Approaches via Energy Loss at Sudden Widening (Borda–Carnot)
4.3. Empirical Approaches
Author | Year | Formula |
---|---|---|
Vittal et al. * | 1977 [13] | |
Lefebvre et al. | 2016 [14] | |
Schippa et al. | 2019 [15] |
4.4. Intermediate Evaluation
5. Comparison of the Approaches versus Data
5.1. Data
5.2. “Measured” Form Roughness
- In a measured section, there are generally many more ripples than dunes.
- According to various observations, including those of Zanke 1976 [32], the variation of the dune parameters H and L from one dune to the next is often considerable. Echograms from the Rio Parana of Stückrath 1969 [22] show, e.g., differences in H of about 60% and in L of about a factor of 2 for dunes following each other directly.
- The determination of the sediment grain size is more accurate for ripples than for dunes, because typically several ripples are captured during sampling, while for dunes, the sediment determination is much more uncertain.
5.3. Comparison of the Approaches from Tables 1–3 to the Data from Table 4
5.3.1. Case 1: Ripples
Approaches via the Logarithmic Velocity Profile
Approaches via Borda–Carnot Expansion Law
Purely or Widely Empirical Approaches
5.3.2. Case 2: Ripples and Dunes
Approaches via the Logarithmic Velocity Profile
Approaches via the Borda–Carnot Expansion Law
Purely or Widely Empirical Approaches
5.3.3. Quality Characteristics
6. Approaches to Further Improve the Quality of Forecasts
6.1. Regarding the Effects of Relative Water Coverage,
6.2. Enhancements with Respect to the “Measured” Form Roughness
6.2.1. Regarding the Flow Path with Effective Skin Friction
6.2.2. Influence of the Choice of on the “Measured” Friction Factor
6.2.3. Skin Friction Assumed as Active on Full Length of the Ripples and Dunes and B Determined by Iteration
7. Discussion and Conclusions
- semi-analytical with roughness estimation based on the logarithmic velocity profile with the definition of an effective roughness height,
- semi-analytical based on the Borda–Carnot approach for the energy loss due to flow expansion in the lee of the crests of ripple and dunes and
- entirely or largely empirical approaches.
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
B | integration constant of log. velocity profile | - |
d | grain diameter | m |
dimensionless grain diameter = | - | |
-damping coefficient in the case of low relative water coverage | - | |
f | friction factor | - |
grain (or skin) roughness-induced friction factor | - | |
friction factor in the case of low relative water coverage | - | |
friction factor due to ripples and dunes = | - | |
total friction factor | - | |
g | acceleration of gravity | m/s2 |
H | height of bedforms | m |
h | mean water depth = | m |
water depth over the crests of ripples and dunes | m | |
water depth at reattachment point of ripples and dunes | m | |
energy loss head | m | |
I | longitudinal bed slope | - |
energy slope | - | |
equivalent sand roughness height, in case of skin roughness we use | m | |
= | - | |
equivalent sand roughness height due to grain roughness ( is taken here) | m | |
effective roughness height of ripples and dunes | m | |
L | length of bedforms | m |
length of bedforms with significant skin friction | m | |
= | - | |
= , particle Reynolds number | - | |
depth- and time-averaged flow velocity | m/s | |
depth- and time-averaged flow velocity at the crests of ripples and dunes | m/s | |
depth- and time-averaged flow velocity at the reattachment points of ripples and dunes | m/s |
shear velocity = | m/s | |
angle of free turbulence | ||
angle of inclination of the windward slope of ripple and dunes | ||
angle of repose = angle of internal friction of sediment | ||
kinematic viscosity of fluid | m2/s | |
von Karman constant | - | |
density of fluid | kg/m3 | |
density of sediment | kg/m3 | |
, relative density | - | |
, shear stress at the bed | N/m2 | |
peak values of shear stress in the case of turbulence | N/m2 | |
= shear stress at the bed in the case of low water coverage | N/m2 | |
, dimensionless shear stress | N/m2 | |
critical dimensionless Shields stress for the initiation of sediment motion | - | |
Index ‘RD’ stands for the case of ripples and dunes |
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Author(s) | Year | Lab./Nature | Water Depth h (m) | Number of Data |
---|---|---|---|---|
Shinohara and Tsubaki | 1959 [4] | Hii-River | 36 | |
Stein | 1965 [20] | Lab | 17 | |
Simons and Richardson | 1966 [21] | Lab | 163 | |
Vanoni and Hwang | 1967 [6] | Lab | 22 | |
Stückrath | 1969 [22] | Rio Parana | 1 | |
Zanke | 1977 [*] | Lab | 4 | |
Grazer | 1982 [23] | Lab | 6 | |
Engel and Lau | 1980 [24] | Lab | 37 | |
Höfer | 1984 [8] | Lab | 55 | |
Hong, Karim and Kennedy | 1984 [25] | Lab | 19 | |
Klaassen | 1992 [26] | Lab | 14 | |
Julien | 1992 [27] | Missouri | 23 | |
Julien | 1992 [27] | Rio Parana | 13 | |
Julien | 1992 [27] | Jamuna | 33 | |
Julien | 1992 [27] | Zaire River | 21 | |
Julien | 1992 [27] | Maas | 26 | |
Julien | 1992 [27] | Meuse | 60 | |
Kühlborn | 1993 [28] | Lab | 39 | |
Gaweesh and v. Rijn | 1994 [29] | River Nile | 6 | |
Gaweesh and v. Rijn | 1994 [29] | River Rhein | 4 | |
Gaweesh and v. Rijn | 1994 [29] | Lab | 9 | |
Wallisch | 1996 [30] | Lab | 1 | |
Wieprecht | 2001 [31] | Lab | 29 |
d | h | H | L | H/L | H/h | h/d | Fr | I | ||
---|---|---|---|---|---|---|---|---|---|---|
mm | m | m | m | - | - | - | - | - | - | |
min. | 0.02 | 0.047 | 0.006 | 0.09 | 0.0012 | 0.023 | 19.6 | 0.07 | 0.26 | |
max. | 90 | 26 | 7.5 | 735 | 0.22 | 0.83 | 97500 | 1.2 | 0.0032 | 146 |
d | h | H | L | H/L | H/h | h/d | Fr | I | ||
---|---|---|---|---|---|---|---|---|---|---|
mm | m | m | m | - | - | - | - | - | - | |
min. | 0.02 | 0.047 | 0.006 | 0.09 | 0.033 | 0.023 | 133 | 0.04 | 6.6 · 10 | 0.26 |
max. | 0.7 | 0.5 | 0.51 | 0.6 | 0.155 | 0.455 | 6200 | 0.77 | 0.0043 | 9 |
Author | Year | Ripples | Rank | All Data | Rank |
---|---|---|---|---|---|
Motzfeld | 1937 [3] | 0.35 | 9 | 8 | |
Shinohara and Tsubaki | 1959 [4] | 0.36 | 8 | 10 | |
Ackers | 1964 [5] | 0.38 | 6 | 7 | |
Vanoni and Hwang | 1967 [6] | 0.55 | 3 | 6 | |
Swart | 1967 [6] | 0.39 | 5 | 9 | |
van Rijn | 1982 [7] | 0.29 | 10 | 10 | |
Höfer | 1984 [8] | 0.36 | 8 | 8 | |
Soulsby | 1997 [9] | 0.38 | 6 | 8 | |
Bartholdy et al. | 2010 [10] | 0.22 | 11 | 11 | |
Engelund and Hansen | 1967 [11] | 0.51 | 4 | 0.41 | 4 |
Engelund | 1977 [12] | 0.65 | 2 | 0.51 | 2 |
Vittal et al. | 1977 [13] | 0.39 | 5 | 0.49 | 3 |
Lefebvre et al. | 2016 [14] | 0.37 | 7 | 0.18 | 9 |
Schippa et al. | 2019 [15] | 0.14 | 12 | 0.38 | 5 |
this paper | 2022 | 0.72 | 1 | 0.60 | 1 |
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Zanke, U.; Roland, A.; Wurpts, A. Roughness Effects of Subaquaeous Ripples and Dunes. Water 2022, 14, 2024. https://doi.org/10.3390/w14132024
Zanke U, Roland A, Wurpts A. Roughness Effects of Subaquaeous Ripples and Dunes. Water. 2022; 14(13):2024. https://doi.org/10.3390/w14132024
Chicago/Turabian StyleZanke, Ulrich, Aron Roland, and Andreas Wurpts. 2022. "Roughness Effects of Subaquaeous Ripples and Dunes" Water 14, no. 13: 2024. https://doi.org/10.3390/w14132024
APA StyleZanke, U., Roland, A., & Wurpts, A. (2022). Roughness Effects of Subaquaeous Ripples and Dunes. Water, 14(13), 2024. https://doi.org/10.3390/w14132024