QU et al 2022a - Revision history

Rimni at 09:56, 15 September 2022

2022-09-15T09:56:51Z

Rimni at 09:33, 15 September 2022

2022-09-15T09:33:24Z

Rimni at 09:27, 15 September 2022

2022-09-15T09:27:20Z

Rimni at 09:25, 15 September 2022

2022-09-15T09:25:50Z

Rimni at 08:49, 15 September 2022

2022-09-15T08:49:32Z

Rimni at 08:48, 15 September 2022

2022-09-15T08:48:58Z

Rimni: /* 2.2 Governing equations */

2022-09-15T08:47:03Z

‎2.2 Governing equations

Rimni: /* (2) Effect of wave amplitude (cross the wave surface) */

2022-09-14T14:34:26Z

‎(2) Effect of wave amplitude (cross the wave surface)

Rimni: /* 3.2 Load characteristics analysis */

2022-09-14T14:31:33Z

‎3.2 Load characteristics analysis

Rimni: /* 3.2 Load characteristics analysis */

2022-09-14T14:27:22Z

‎3.2 Load characteristics analysis

@@ Line 522: / Line 522: @@
 ==References==
-<span id='_nebDA44E60A_2C14_425A_BBE8_EB5D1EB74680'></span> [1] Guo, C., Chen X.. A review of internal solitary wave dynamics in the northern South China Sea. Progress in oceanography, 121: 7-23, 2014.
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-<span id='_neb42C02115_BD21_4385_83EF_CF686EEDF990'></span> [2] Osborne, A. R., Burch, T. L.. Internal solitons in the Andaman Sea. Science, 208(4443): 451-460, 1980.
+<span id='_nebDA44E60A_2C14_425A_BBE8_EB5D1EB74680'></span>
-<span id='_nebA1B3473E_F351_4D32_B948_3DA0003B2C7B'></span> [3] Huang, X., Chen, Z., Zhao, W., et al. An extreme internal solitary wave event observed in the northern South China Sea. Scientific Reports, 6(1): 30041, 2016.
+<span id='_neb42C02115_BD21_4385_83EF_CF686EEDF990'></span>
-<span id='_neb94BC959E_B0A2_463B_9112_4356E703C4FD'></span> [4] Orr, M. H.. Nonlinear internal waves in the South China Sea: Observation of the conversion of depression internal waves to elevation internal waves. Journal of Geophysical Research, 108(C3), 3064, 2003.
+<span id='_nebA1B3473E_F351_4D32_B948_3DA0003B2C7B'></span>
-<span id='_nebB0B99C6E_F214_49DB_8071_899C36AE0AD7'></span> [5] Alford, M. H., Lien, R., Simmons, H., et al. Speed and evolution of nonlinear internal waves transiting the south China sea. Journal of Physical Oceanography, 40(6): 1338-1355, 2010.
+<span id='_neb94BC959E_B0A2_463B_9112_4356E703C4FD'></span>
-<span id='_neb43E60C32_8DAE_4BD2_A848_D63F02128FA4'></span> [6] Cui, J., Dong, S., Wang, Z.. Study on applicability of internal solitary wave theories by theoretical and numerical method. Applied ocean research, 111: 102629, 2021.
+<span id='_nebB0B99C6E_F214_49DB_8071_899C36AE0AD7'></span>
-[7] Miles, J. W.. On internal solitary waves. Tellus 31, 456–462, 1979.
+<span id='_neb43E60C32_8DAE_4BD2_A848_D63F02128FA4'></span>
-<span id='_nebEA94831D_DAD0_43BF_ADD5_AE940F12B5B4'></span> [8] Chen, C. Y., Hsu, R. C., Chen, H. H., et al. Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes. Ocean Engineering, 34(1): 157-170, 2007.
+[7] Miles J.W. On internal solitary waves. Tellus 31(5):456–462, 1979.
-<span id='_nebD4AB8BD3_91CC_430F_8077_75AD44876CD4'></span> [9] Zhao, B., Wang, Z., Duan, W., et al. Experimental and numerical studies on internal solitary waves with a free surface Journal of Fluid Mechanics, 899:A17-1 to A17-27, 2020.
+<span id='_nebEA94831D_DAD0_43BF_ADD5_AE940F12B5B4'></span>
-<span id='_nebF5C32B04_2029_4CB8_9EBF_623F40B8A232'></span>[10] Lin, Z., Zan, X.. Numerical study on load characteristics by internal solitary wave on cylinder sections at different depth and its parameterization. Ocean Engineering, 219: 108343, 2021.
+<span id='_nebD4AB8BD3_91CC_430F_8077_75AD44876CD4'></span>
-<span id='_neb70BE7145_9EDC_4C2E_9BA7_36B1DEEAC8FB'></span>[11] Zou, P. X., Bricke,r J. D., Uijttewaal, W. S. J.. The impacts of internal solitary waves on a submerged floating tunnel. Ocean Engineering, 238: 109762, 2021.
+<span id='_nebF5C32B04_2029_4CB8_9EBF_623F40B8A232'></span>
-<span id='_neb7E1675DA_6A67_46D0_BD31_11035A3811E1'></span>[12] Ding, W., Ai, C., Jin, S., et al. 3D numerical investigation of forces and flow field around the semi-submersible platform in an internal solitary wave. Water, 12(1): 208, 2020.
+<span id='_neb70BE7145_9EDC_4C2E_9BA7_36B1DEEAC8FB'></span>
-<span id='_nebC1AB4008_0311_447F_B3B9_585AFCDB0050'></span>[13] Chen, J., You, Y. X., Liu, X. D., et al. Numerical simulation of interaction of internal solitary waves with a moving submarine. Chinese Journal of Hydrodynamics, 03(25):344-351, 2010.
+<span id='_neb7E1675DA_6A67_46D0_BD31_11035A3811E1'></span>
-<span id='_neb7CE8CB30_1770_4BDA_8C4F_A16DCD76F9E1'></span>[14] Ostrovsky, L. A., Stepanyants, Y. A.. DO INTERNAL SOLITONS EXIST IN THE OCEAN ?. Reviews of Geophysics , 27(3):293-310,1989.
+<span id='_nebC1AB4008_0311_447F_B3B9_585AFCDB0050'></span>
-<span id='_neb27BB17FF_BE73_4FB5_AC41_DE323084BB34'></span>[15] Small, R. J., Hornby, R. P.. A comparison of weakly and fully non-linear models of the shoaling of a solitary internal wave. Ocean modelling (Oxford), 8(4): 395-416, 2005.
+<span id='_neb7CE8CB30_1770_4BDA_8C4F_A16DCD76F9E1'></span>
-<span id='_neb04947D4F_CF08_4173_92C3_CFE114E0746D'></span>[16] Groves, N. C., Huang, T. T., Chang, M. S.. Geometric characteristics of DARPA (Defense Advanced Research Projects Agency) SUBOFF models (DTRC model numbers 5470 and 5471). David Taylor Research Center, Bethesda, Maryland, 1989.
+<span id='_neb27BB17FF_BE73_4FB5_AC41_DE323084BB34'></span>

@@ Line 481: / Line 481: @@
 ====='''(3) Effect of submergence depth (below the wave surface)'''=====
-When the submerged body is completely below the ISW, in order to study the influence of the distance between the submerged body and the wave peak, the wave amplitude is selected as  <math display="inline">{\eta }_0\mbox{=20m}</math> , and the submergence depths are 30m and 45m respectively, namely Case A22 and CaseA23, as shown in Figure 11.
+When the submerged body is completely below the ISW, in order to study the influence of the distance between the submerged body and the wave peak, the wave amplitude is selected as  <math display="inline">{\eta }_0=20\mbox{m}</math>, and the submergence depths are 30m and 45m respectively, namely Case A22 and CaseA23, as shown in [[#img-11|Figure 11]].
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-11'></div>
-[[Image:Draft_Lai_342303871-image88-c.jpeg|414px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 11. Sketch diagram of SUBOFF below the wave</div>
-−
-−
-Figure 12 shows the forces and torques on the submerged body when the submerged body is completely below the ISW surface. Case A23 dived 15 meters deeper than Case A22, and its force was basically the same as that of Case A22. The increase of 15m depth had little effect on the force. Since the submerged body did not pass through the ISW, the buoyancy of the submerged body did not change, and the horizontal and vertical forces were mainly due to the change of flow field structure when it encountered the ISW. Therefore, the change of the forces on the submerged body only came from the contribution of ISW itself.
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-−
-{|
 |-
-| [[Image:Draft_Lai_342303871-image89.jpeg|288px]]
+|style="padding:10px;"|  [[Image:Draft_Lai_342303871-image88-c.jpeg|414px]]
-| [[Image:Draft_Lai_342303871-image90.jpeg|center|288px]]
+|- style="text-align: center; font-size: 75%;"
 |}
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+[[#img-12|Figure 12]] shows the forces and torques on the submerged body when the submerged body is completely below the ISW surface. Case A23 dived 15 meters deeper than Case A22, and its force was basically the same as that of Case A22. The increase of 15m depth had little effect on the force. Since the submerged body did not pass through the ISW, the buoyancy of the submerged body did not change, and the horizontal and vertical forces were mainly due to the change of flow field structure when it encountered the ISW. Therefore, the change of the forces on the submerged body only came from the contribution of ISW itself.
-(c) torque</div>
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-12'></div>
-Figure 12. Forces and torques on SUBOFF below the wave</div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 ==4. Conclusions==

← Older revision		Revision as of 09:27, 15 September 2022
Line 333:		Line 333:


−	At the monitoring point x=~~1500m~~, the comparison of <math display="inline">{\eta }_0\mbox{~~=30m~~}</math> waveforms are shown in [[#img-5\|Figure 5]]. The results of the CFD simulation and the waveforms calculated by KdV theory are shown in a high coincidence. Therefore, the numerical simulation method adopted in this paper is reliable.	+	At the monitoring point <math display="inline">x=1500</math>m, the comparison of <math display="inline">{\eta }_0=30\mbox{m}</math> waveforms are shown in [[#img-5\|Figure 5]]. The results of the CFD simulation and the waveforms calculated by KdV theory are shown in a high coincidence. Therefore, the numerical simulation method adopted in this paper is reliable.

	<div id='img-5'></div>		<div id='img-5'></div>

@@ Line 296: / Line 296: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|  style="text-align: center;padding:10px;"| [[Image:Draft_Lai_342303871-image63-c.png|288px]]
+|  style="text-align: center;padding:0px;"| [[Image:Draft_Lai_342303871-image63-c.png|288px]]
 |-
 |  style="text-align: center;font-size: 75%;"|(a) Schematic diagram of DARPA SUBOFF

@@ Line 214: / Line 214: @@
 |}
-where  <math display="inline">S_M</math> is the sum of body forces; <math display="inline">p^'</math> is the modified pressure,  <math display="inline">p^'\mbox{=}p+\frac{2}{3}\rho k</math>, <math display="inline">{\mu }_{\mbox{eff}}</math> is the effective viscosity accounting for turbulence and expressed as <math display="inline">{\mu }_{\mbox{eff}}\mbox{=}\mu \mbox{+}{\mu }_t</math>,  <math display="inline">{\mu }_t</math> is the turbulence viscosity, <math display="inline">{\mu }_t{\mbox{=C}}_{\mu }\rho \frac{k}{{\epsilon }^2}</math>,  <math display="inline">{C}_{\mu }</math> is a constant,  and <math display="inline">{C}_{\mu }=0.09</math> in this paper.
+where  <math display="inline">S_M</math> is the sum of body forces; <math display="inline">p^'</math> is the modified pressure,  <math display="inline">p^'\mbox{=}p+\frac{2}{3}\rho k</math>, <math display="inline">{\mu }_{\mbox{eff}}</math> is the effective viscosity accounting for turbulence and expressed as <math display="inline">{\mu }_{\mbox{eff}}\mbox{=}\mu \mbox{+}{\mu }_t</math>,  <math display="inline">{\mu }_t</math> is the turbulence viscosity, <math display="inline">{\mu }_t = C_{\mu }\rho \frac{k}{{\epsilon }^2}</math>,  <math display="inline">{C}_{\mu }</math> is a constant,  and <math display="inline">{C}_{\mu }=0.09</math> in this paper.
 The  <math display="inline">k-\epsilon </math> model introduces two new variables in the system of equations.  <math display="inline">k</math> and  <math display="inline">\epsilon </math> can obtained from the following transport equations:

@@ Line 214: / Line 214: @@
 |}
-where  <math display="inline">S_M</math> is the sum of body forces; <math display="inline">p^'</math> is the modified pressure,  <math display="inline">p^'\mbox{=}p+\frac{2}{3}\rho k</math>; <math display="inline">{\mu }_{\mbox{eff}}</math> is the effective viscosity accounting for turbulence and expressed as <math display="inline">{\mu }_{\mbox{eff}}\mbox{=}\mu \mbox{+}{\mu }_t</math>;  <math display="inline">{\mu }_t</math> is the turbulence viscosity, <math display="inline">{\mu }_t{\mbox{=C}}_{\mu }\rho \frac{k}{{\epsilon }^2}</math>;  <math display="inline">\mbox{C}_{\mu }</math> is a constant,  <math display="inline">\mbox{C}_{\mu }\mbox{=}0.09</math> in this paper.
+where  <math display="inline">S_M</math> is the sum of body forces; <math display="inline">p^'</math> is the modified pressure,  <math display="inline">p^'\mbox{=}p+\frac{2}{3}\rho k</math>, <math display="inline">{\mu }_{\mbox{eff}}</math> is the effective viscosity accounting for turbulence and expressed as <math display="inline">{\mu }_{\mbox{eff}}\mbox{=}\mu \mbox{+}{\mu }_t</math>,  <math display="inline">{\mu }_t</math> is the turbulence viscosity, <math display="inline">{\mu }_t{\mbox{=C}}_{\mu }\rho \frac{k}{{\epsilon }^2}</math>,  <math display="inline">\mbox{C}_{\mu }</math> is a constant,  and <math display="inline">\mbox{C}_{\mu }=0.09</math> in this paper.
 The  <math display="inline">k-\epsilon </math> model introduces two new variables in the system of equations.  <math display="inline">k</math> and  <math display="inline">\epsilon </math> can obtained from the following transport equations:
@@ Line 238: / Line 238: @@
 |}
-where  <math display="inline">P_k</math> is the turbulence production due to viscous forces. <math display="inline">{\sigma }_k</math>,  <math display="inline">{\sigma }_{\epsilon }</math>, <math display="inline">C_{\epsilon 1}</math> and <math display="inline">C_{\epsilon 2}</math> are constants and having the values:  <math display="inline">{\sigma }_k=1.0</math>, <math display="inline">{\sigma }_{\epsilon }\mbox{=}1.3</math>, <math display="inline">C_{\epsilon 1}=1.44</math>, and <math display="inline">C_{\epsilon 2}=1.92</math>.
+where  <math display="inline">P_k</math> is the turbulence production due to viscous forces, <math display="inline">{\sigma }_k</math>,  <math display="inline">{\sigma }_{\epsilon }</math>, <math display="inline">C_{\epsilon 1}</math> and <math display="inline">C_{\epsilon 2}</math> are constants and having the values:  <math display="inline">{\sigma }_k=1.0</math>, <math display="inline">{\sigma }_{\epsilon }\mbox{=}1.3</math>, <math display="inline">C_{\epsilon 1}=1.44</math>, and <math display="inline">C_{\epsilon 2}=1.92</math>.
 ===2.3 Numerical flume model===

@@ Line 466: / Line 466: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|  style="text-align: center;padding:10px;"| [[Image:Draft_Lai_342303871-image84.jpeg|288px]]
+|  style="text-align: center;padding:10px;"| [[Image:Draft_Lai_342303871-image84.png|288px]]
-|  style="text-align: center;padding:10px;"| [[Image:Draft_Lai_342303871-image85.jpeg|center|288px]]
+|  style="text-align: center;padding:10px;"| [[Image:Draft_Lai_342303871-image85.png|center|288px]]
 |-
 |  style="text-align: center;font-size: 75%;"|(a) <math>t = 320</math>s
 |  style="text-align: center;font-size: 75%;"|(b) <math>t = 400</math>s
 |-
-|  colspan='2' style="text-align: center;padding:10px;"|[[Image:Draft_Lai_342303871-image86.jpeg|288px]]
+|  colspan='2' style="text-align: center;padding:10px;"|[[Image:Draft_Lai_342303871-image86.png|288px]]
 |-
 |  colspan='2' style="text-align: center;font-size: 75%;"|(c) <math>t = 480</math>s
@@ Line 478: / Line 478: @@
 | colspan="2" style="padding:10px;"| '''Figure 10'''. Velocity vectors around the SUBOFF when it encounters the ISW
 |}
 ====='''(3) Effect of submergence depth (below the wave surface)'''=====

@@ Line 427: / Line 427: @@
 |  style="text-align: center;padding:10px;"| [[Image:Draft_Lai_342303871-image79.jpeg|center|288px]]
 |-
-|  style="text-align: center;font-size: 75%;"|(a)
+|  style="text-align: center;font-size: 75%;"|(a) Horizontal force
-|  style="text-align: center;font-size: 75%;"|(b)
+|  style="text-align: center;font-size: 75%;"|(b) Vertical force
 |-
 |  colspan='2' style="text-align: center;padding:10px;"|[[Image:Draft_Lai_342303871-image80.jpeg|288px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" style="padding:10px;"| '''Figure 8'''. Forces and torques on the SUBOFF at different submergence depths
@@ Line 436: / Line 438: @@
-{|
+The above research shows that the force of the SUBOFF has the greatest influence when submerged body passes through the wave surface. Therefore, in order to investigate the influence of the ISW amplitude on the submerged body when submerged body cross the wave surface, the submergence depth is chosen to be 15m, and the wave amplitude are  <math display="inline">{\eta }_0=20\mbox{m}</math> and <math display="inline">{\eta }_0=30\mbox{m}</math> respectively, namely Case A21 and Case A31.
 |-
-| [[Image:Draft_Lai_342303871-image78.jpeg|288px]]
+|  style="text-align: center;font-size: 75%;"|(a) Horizontal force
-| [[Image:Draft_Lai_342303871-image79.jpeg|center|288px]]
+|  style="text-align: center;font-size: 75%;"|(b) Vertical force
 |}
 {|
@@ Line 468: / Line 465: @@
 | [[Image:Draft_Lai_342303871-image82.jpeg|center|288px]]
 |}
-</div>
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
@@ Line 505: / Line 502: @@
-=====(3) Effect of submergence depth (below the wave surface)=====
+====='''(3) Effect of submergence depth (below the wave surface)'''=====
 When the submerged body is completely below the ISW, in order to study the influence of the distance between the submerged body and the wave peak, the wave amplitude is selected as  <math display="inline">{\eta }_0\mbox{=20m}</math> , and the submergence depths are 30m and 45m respectively, namely Case A22 and CaseA23, as shown in Figure 11.