Transitional Behavior of a Flow Regime in Shoaling Tsunami Boundary Layers
Abstract
:1. Introduction
2. Flow Regime in a Wave Boundary Layer
3. Calculation Method of Tsunami Transformation
3.1. Tsunami Shoaling Process
3.2. Calculation of Friction Factor and Friction Velocity
3.3. Calculation of Boundary Layer Thickness
4. Results and Discussion
4.1. Transitional Flow Regime in Terms of Boundary Layer Thickness
4.2. Transitional Flow Regime in Terms of the Re vs. am/ks Relationship
4.3. Laminar-to-Turbulent Transition
4.4. Smooth-to-Rough Transition
4.5. Transitional Flow Regime in Terms of Friction Coefficient
4.6. Comparison with Steady Friction Laws
4.7. Transitional Flow Regime and Transitional Friction Factor under a Tsunami
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Quantity | Input Value | |
---|---|---|
Water depth of tsunami source | h0 = 4000 m | |
Tsunami height in the source | H0 = 1 m | |
Case 1 | Wave period | T = 15 min |
Sand diameter | d = 0.3 mm | |
Case 2 | Wave period | T = 30 min |
Sand diameter | d = 0.3 mm | |
Case 3 | Wave period | T = 15 min |
Sand diameter | d = 0.1 mm | |
Case 4 | Wave period | T = 30 min |
Sand diameter | d = 0.1 mm |
x (km) | h (m) | H (m) | Um (m/s) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Case 1 | Case 2 | Case 3 | Case 4 | Case 1, Case 3 | Case 2, Case 4 | |||||
0 | 4000 | 1.00 | 0.025 | 5.91 × 103 | 1.18 × 104 | 1.77 × 104 | 3.54 × 104 | 8.77 × 104 | 1.75 × 105 | 9.90 × 107 |
25 | 3500 | 1.03 | 0.027 | 6.53 × 103 | 1.31 × 104 | 1.96 × 104 | 3.92 × 104 | 1.07 × 105 | 2.14 × 105 | 9.57 × 107 |
50 | 3000 | 1.08 | 0.031 | 7.33 × 103 | 1.47 × 104 | 2.20 × 104 | 4.40 × 104 | 1.35 × 105 | 2.70 × 105 | 9.21 × 107 |
75 | 2500 | 1.13 | 0.035 | 8.41 × 103 | 1.68 × 104 | 2.52 × 104 | 5.04 × 104 | 1.78 × 105 | 3.55 × 105 | 8.80 × 107 |
100 | 2000 | 1.19 | 0.042 | 9.94 × 103 | 1.99 × 104 | 2.98 × 104 | 5.96 × 104 | 2.48 × 105 | 4.96 × 105 | 8.32 × 107 |
115 | 1700 | 1.24 | 0.047 | 1.12 × 104 | 2.24 × 104 | 3.37 × 104 | 6.73 × 104 | 3.17 × 105 | 6.33 × 105 | 7.99 × 107 |
125 | 1500 | 1.28 | 0.052 | 1.23 × 104 | 2.47 × 104 | 3.70 × 104 | 7.40 × 104 | 3.82 × 105 | 7.64 × 105 | 7.75 × 107 |
132.5 | 1350 | 1.31 | 0.056 | 1.33 × 104 | 2.67 × 104 | 4.00 × 104 | 8.01 × 104 | 4.47 × 105 | 8.95 × 105 | 7.55 × 107 |
140 | 1200 | 1.35 | 0.061 | 1.46 × 104 | 2.92 × 104 | 4.37 × 104 | 8.75 × 104 | 5.34 × 105 | 1.07 × 106 | 7.33 × 107 |
150 | 1000 | 1.41 | 0.07 | 1.67 × 104 | 3.34 × 104 | 5.01 × 104 | 1.00 × 105 | 7.02 × 105 | 1.40 × 106 | 7.00 × 107 |
155 | 900 | 1.45 | 0.076 | 1.81 × 104 | 3.62 × 104 | 5.43 × 104 | 1.09 × 105 | 8.22 × 105 | 1.64 × 106 | 6.82 × 107 |
160 | 800 | 1.50 | 0.083 | 1.98 × 104 | 3.95 × 104 | 5.93 × 104 | 1.19 × 105 | 9.81 × 105 | 1.96 × 106 | 6.62 × 107 |
165 | 700 | 1.55 | 0.091 | 2.18 × 104 | 4.37 × 104 | 6.55 × 104 | 1.31 × 105 | 1.20 × 106 | 2.40 × 106 | 6.40 × 107 |
170 | 600 | 1.61 | 0.103 | 2.45 × 104 | 4.90 × 104 | 7.35 × 104 | 1.47 × 105 | 1.51 × 106 | 3.02 × 106 | 6.16 × 107 |
175 | 500 | 1.68 | 0.118 | 2.81 × 104 | 5.62 × 104 | 8.43 × 104 | 1.69 × 105 | 1.99 × 106 | 3.97 × 106 | 5.89 × 107 |
180 | 400 | 1.78 | 0.139 | 3.32 × 104 | 6.64 × 104 | 9.97 × 104 | 1.99 × 105 | 2.77 × 106 | 5.55 × 106 | 5.57 × 107 |
185 | 300 | 1.91 | 0.173 | 4.12 × 104 | 8.25 × 104 | 1.24 × 105 | 2.47 × 105 | 4.27 × 106 | 8.54 × 106 | 5.18 × 107 |
190 | 200 | 2.12 | 0.234 | 5.59 × 104 | 1.12 × 105 | 1.68 × 105 | 3.35 × 105 | 7.85 × 106 | 1.57 × 107 | 4.68 × 107 |
195 | 100 | 2.52 | 0.394 | 9.40 × 104 | 1.88 × 105 | 2.82 × 105 | 5.64 × 105 | 2.22 × 107 | 4.44 × 107 | 3.94 × 107 |
196 | 80 | 2.66 | 0.465 | 1.11 × 105 | 2.22 × 105 | 3.33 × 105 | 6.67 × 105 | 3.10 × 107 | 6.20 × 107 | 3.72 × 107 |
197.5 | 50 | 2.99 | 0.662 | 1.58 × 105 | 3.16 × 105 | 4.74 × 105 | 9.48 × 105 | 6.28 × 107 | 1.26 × 108 | 3.31 × 107 |
198.5 | 30 | 3.40 | 0.971 | 2.32 × 105 | 4.64 × 105 | 6.95 × 105 | 1.39 × 106 | 1.35 × 108 | 2.70 × 108 | 2.91 × 107 |
199 | 20 | 3.76 | 1.316 | 3.14 × 105 | 6.28 × 105 | 9.43 × 105 | 1.89 × 106 | 2.48 × 108 | 4.96 × 108 | 2.63 × 107 |
199.25 | 15 | 4.04 | 1.633 | 3.90 × 105 | 7.80 × 105 | 1.17 × 106 | 2.34 × 106 | 3.82 × 108 | 7.64 × 108 | 2.45 × 107 |
199.5 | 10 | 4.47 | 2.214 | 5.28 × 105 | 1.06 × 106 | 1.59 × 106 | 3.17 × 106 | 7.02 × 108 | 1.40 × 109 | 2.21 × 107 |
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Tanaka, H.; Tinh, N.X.; Sana, A. Transitional Behavior of a Flow Regime in Shoaling Tsunami Boundary Layers. J. Mar. Sci. Eng. 2020, 8, 700. https://doi.org/10.3390/jmse8090700
Tanaka H, Tinh NX, Sana A. Transitional Behavior of a Flow Regime in Shoaling Tsunami Boundary Layers. Journal of Marine Science and Engineering. 2020; 8(9):700. https://doi.org/10.3390/jmse8090700
Chicago/Turabian StyleTanaka, Hitoshi, Nguyen Xuan Tinh, and Ahmad Sana. 2020. "Transitional Behavior of a Flow Regime in Shoaling Tsunami Boundary Layers" Journal of Marine Science and Engineering 8, no. 9: 700. https://doi.org/10.3390/jmse8090700