Peng et al 2023b - Revision history

Rimni at 14:23, 5 October 2023

2023-10-05T14:23:33Z

Rimni at 14:22, 5 October 2023

2023-10-05T14:22:14Z

Rimni at 14:21, 5 October 2023

2023-10-05T14:21:29Z

Rimni at 14:20, 5 October 2023

2023-10-05T14:20:05Z

Rimni at 11:26, 5 October 2023

2023-10-05T11:26:03Z

Rimni at 14:36, 4 October 2023

2023-10-04T14:36:22Z

Rimni: /* 4 Conclusions */

2023-10-04T14:28:40Z

‎4 Conclusions

Rimni at 14:27, 4 October 2023

2023-10-04T14:27:25Z

Rimni at 14:31, 3 October 2023

2023-10-03T14:31:57Z

Rimni: /* 3.3 Motion parameters */

2023-10-03T14:04:20Z

‎3.3 Motion parameters

@@ Line 254: / Line 254: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-! H（m）<br>  <math display="inline">{\eta }_0</math>（m）!!  style="text-align: center;vertical-align: center;"| 45 !! style="text-align: center;vertical-align: center;" |15
+! H (m)<br>  <math display="inline">{\eta }_0</math> (m)!!  style="text-align: center;vertical-align: center;"| 45 !! style="text-align: center;vertical-align: center;" |15
 |-
 |  style="text-align: center;vertical-align: top;"|10

@@ Line 247: / Line 247: @@
 The submarine is located in the numerical flume and the distance between the gravity center and the flume inlet is 1500 m. The submarine is in a state of equilibrium with its own buoyancy. The power of the submarine is not taken into account, so it has no initial speed and its freedom of motion is not constrained.
-In order to study the interactions between different ISWs and submarine, three ISW amplitudes and two submergence depths are used in this part, which include  <math display="inline">{\eta }_0 =10</math>m, <math display="inline">{\eta }_0=20</math>m,  <math display="inline">{\eta }_0=30</math>m and <math display="inline">H=45</math>m, <math display="inline">H=15</math>m,as shown in [[#tab-1|Table 1]].
+In order to study the interactions between different ISWs and submarine, three ISW amplitudes and two submergence depths are used in this part, which include  <math display="inline">{\eta }_0 =10</math>m, <math display="inline">{\eta }_0=20</math>m,  <math display="inline">{\eta }_0=30</math>m and <math display="inline">H=45</math>m, <math display="inline">H=15</math>m, as shown in [[#tab-1|Table 1]].
 <div class="center" style="font-size: 75%;">'''Table 1'''. Calculation cases</div>

@@ Line 356: / Line 356: @@
 |+
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image62.jpeg|246px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image62.jpeg|266px]]
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image63.jpeg|center|246px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image63.jpeg|center|266px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) 0s
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(b) 50s
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image64.jpeg|246px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image64.jpeg|266px]]
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image65.jpeg|center|246px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image65.jpeg|center|266px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(c) 100s
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(d) 150s
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image66.jpeg|246px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image66.jpeg|266px]]
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image67.jpeg|center|246px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image67.jpeg|center|266px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(c) 200s

@@ Line 391: / Line 391: @@
 |+
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image68.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image68.png|300px]]
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image69.png|center|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image69.png|center|300px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) <math display="inline">H=45</math>m
@@ Line 411: / Line 411: @@
 |+
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image70.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image70.png|300px]]
-|style="text-align: center;padding:10px;"|[[Image:Review_420808633416-image71.png|center|288px]]
+|style="text-align: center;padding:10px;"|[[Image:Review_420808633416-image71.png|center|300px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) <math display="inline">H=45</math>m
@@ Line 431: / Line 431: @@
 |+
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image72.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image72.png|300px]]
-|style="text-align: center;padding:10px;"|[[Image:Review_420808633416-image73.png|center|288px]]
+|style="text-align: center;padding:10px;"|[[Image:Review_420808633416-image73.png|center|300px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) <math display="inline">H=45</math>m
@@ Line 453: / Line 453: @@
 |+
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image74.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image74.png|300px]]
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image75.png|center|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image75.png|center|300px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) Comparison of lateral velocity
@@ Line 469: / Line 469: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image76.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image76.png|300px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 15'''. Comparison of pitch angle at different depths

@@ Line 493: / Line 493: @@
 ==References==
 <div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-<span id='_nebA1B3473E_F351_4D32_B948_3DA0003B2C7B'></span>[1] Huang X, Chen Z, Zhao W, et al. An extreme internal solitary wave event observed in the northern South China Sea. Scientific Reports, 2016,6(1):30041.
+<span id='_nebDA44E60A_2C14_425A_BBE8_EB5D1EB74680'></span> [2] Guo C., Chen X. A review of internal solitary wave dynamics in the northern South China Sea. Progress in Oceanography, 121:7-23, 2014.
-−
-<span id='_nebDA44E60A_2C14_425A_BBE8_EB5D1EB74680'></span> [2] Guo C, Chen X. A review of internal solitary wave dynamics in the northern South China Sea. Progress in oceanography, 2014,121:7-23.
-<span id='_neb9E7607E2_8CC5_4704_8EDC_65232DC3188C'></span> [3] Cui J, Dong S, Wang Z. Study on applicability of internal solitary wave theories by theoretical and numerical method. Applied Ocean Research, 2021,111:102629.
+<span id='_neb9E7607E2_8CC5_4704_8EDC_65232DC3188C'></span> [3] 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> [4] Alford MH, Lien R, Simmons H, et al. Speed and evolution of nonlinear internal waves transiting the South China Sea. Journal of Physical Oceanography, 2010,40(6):1338-1355.
+<span id='_nebB0B99C6E_F214_49DB_8071_899C36AE0AD7'></span> [4] 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='_nebEA94831D_DAD0_43BF_ADD5_AE940F12B5B4'></span> [5] Chen CY, Hsu RC, Chen HH, et al. Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes. Ocean Engineering, 2007,34(1):157-170.
+<span id='_nebEA94831D_DAD0_43BF_ADD5_AE940F12B5B4'></span> [5] 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.
-<span id='_neb70BE7145_9EDC_4C2E_9BA7_36B1DEEAC8FB'></span> [6] Zou PX, Bricker JD, Uijttewaal WSJ. The impacts of internal solitary waves on a submerged floating tunnel. Ocean Engineering, 2021,238:109762.
+<span id='_neb70BE7145_9EDC_4C2E_9BA7_36B1DEEAC8FB'></span> [6] Zou P.X., Bricker J.D., Uijttewaal W.S.J. The impacts of internal solitary waves on a submerged floating tunnel. Ocean Engineering, 238:109762, 2021.
-<span id='_neb6406592C_E197_46DF_A377_D720346DEC31'></span> [7] Wang X, Zhou J, Wang Z, et al. A numerical and experimental study of internal solitary wave loads on semi-submersible platforms. Ocean engineering, 2018,150:298-308.
+<span id='_neb6406592C_E197_46DF_A377_D720346DEC31'></span> [7] Wang X., Zhou J., Wang Z., et al. A numerical and experimental study of internal solitary wave loads on semi-submersible platforms. Ocean Engineering, 150:298-308, 2018.
-<span id='_neb7E1675DA_6A67_46D0_BD31_11035A3811E1'></span> [8] 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, 2020,12(1):208.
+<span id='_neb7E1675DA_6A67_46D0_BD31_11035A3811E1'></span> [8] 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='_nebC1AB4008_0311_447F_B3B9_585AFCDB0050'></span>[9] Chen J, You YX, Liu X D, et al. Numerical simulation of interaction of internal solitary waves with a moving submarine. Chinese Journal of Hydrodynamics, 2010.
+<span id='_nebC1AB4008_0311_447F_B3B9_585AFCDB0050'></span>[9] 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, 2010.
-<span id='_nebF9F37563_C5E0_47BA_A3E6_AB43CB4808D0'></span>[10] Li J, Zhang Q, Chen T. Numerical investigation of internal solitary wave forces on submarines in continuously stratified fluids. Journal of marine science and engineering, 2021,9(12):1374.
+<span id='_nebF9F37563_C5E0_47BA_A3E6_AB43CB4808D0'></span>[10] Li J., Zhang Q., Chen T. Numerical investigation of internal solitary wave forces on submarines in continuously stratified fluids. Journal of Marine Science and Engineering, 9(12):1374, 2021.
-[11] Guan H, Wei G, Hui DU. Hydrodynamic properties of interactions of three-dimensional internal solitary waves with submarine. Journal of PLA University of Science and Technology (Natural Science Edition), 2012,13(05):577-582.
+[11] Guan H., Wei G., Hui D.U. Hydrodynamic properties of interactions of three-dimensional internal solitary waves with submarine. Journal of PLA University of Science and Technology (Natural Science Edition), 13(05):577-582, 2012.
-[12] Groves NC, Huang TT, Chang MS. Geometric characteristics of DARPA SUBOFF models (DTRC Model Nos. 5470 and 5471). 1989, Technical Report (No.DTRC/SHD-1298-01).
+[12] Groves N.C., Huang T.T., Chang M.S. Geometric characteristics of DARPA SUBOFF models (DTRC Model Nos. 5470 and 5471).  Technical Report (No.DTRC/SHD-1298-01), 1989.
-[13] Du H , Wei G , Zeng WH , et al. Experimental investigation on the kinematics characteristic of submerged slender body under internal solitary wave of depression. Journal of Ship Mechanics, 2017, 21(10):1210-1217.
+[13] Du H., Wei G., Zeng W.H., et al. Experimental investigation on the kinematics characteristic of submerged slender body under internal solitary wave of depression. Journal of Ship Mechanics, 21(10):1210-1217, 2017.
-<span id='_neb0F8BB81C_4ACB_4A46_A5D8_18B1A98389B0'></span>[14] Cui J, Dong S, Wang Z, et al. Kinematic response of submerged structures under the action of internal solitary waves. Ocean Engineering, 2020,196:106814.
+<span id='_neb0F8BB81C_4ACB_4A46_A5D8_18B1A98389B0'></span>[14] Cui J., Dong S., Wang Z., et al. Kinematic response of submerged structures under the action of internal solitary waves. Ocean Engineering, 196:106814, 2020.
-<span id='_nebEC3BF0DB_6ED8_4811_B654_126EBF70E930'></span>[15] Koop CG, Butler G. An investigation of internal solitary waves in a two-fluid system. Journal of Fluid Mechanics, 1981,112(-1):225.
+<span id='_nebEC3BF0DB_6ED8_4811_B654_126EBF70E930'></span>[15] Koop C.G., Butler G. An investigation of internal solitary waves in a two-fluid system. Journal of Fluid Mechanics, 112:225-251, 1981.
-<span id='_neb5D2BFFF9_2F16_43A6_AB2F_57B09F6E6048'></span>[16] Korteweg DJ, de Vries G. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1895,39(240):422-443.
+<span id='_neb5D2BFFF9_2F16_43A6_AB2F_57B09F6E6048'></span>[16] Korteweg D.J., de Vries G. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 39(240):422-443, 1895.
-<span id='_neb7CE8CB30_1770_4BDA_8C4F_A16DCD76F9E1'></span>[17] Ostrovsky LA, Stepanyants YA. Do internal solitons exist in the ocean?. Reviews of Geophysics, 1989,27(3):293, 310.
+<span id='_neb7CE8CB30_1770_4BDA_8C4F_A16DCD76F9E1'></span>[17] Ostrovsky L.A., Stepanyants Y.A. Do internal solitons exist in the ocean?. Reviews of Geophysics, 27(3):293-310, 1989.
-<span id='_neb84F0F059_30BA_4914_B0DA_14413D389C9F'></span>[18] Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 1981,39(1):201-225.
+<span id='_neb84F0F059_30BA_4914_B0DA_14413D389C9F'></span>[18] Hirt C.W., Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1):201-225, 1981.
-<span id='_nebD785F48B_4786_4E6C_9DEE_7ABA5D7FCD5E'></span>[19] Ma W, Li Y, Ding Y, et al. Numerical investigation of internal wave and free surface wave induced by the DARPA SUBOFF moving in a strongly stratified fluid. Ships and offshore structures, 2020,15(6):587-604.
+<span id='_nebD785F48B_4786_4E6C_9DEE_7ABA5D7FCD5E'></span>[19] Ma W., Li Y., Ding Y., et al. Numerical investigation of internal wave and free surface wave induced by the DARPA SUBOFF moving in a strongly stratified fluid. Ships and Offshore Structures, 15(6):587-604, 2020.

← Older revision		Revision as of 14:36, 4 October 2023
Line 493:		Line 493:

	==References==		==References==
		+
		+	<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
		+

	<span id='_nebA1B3473E_F351_4D32_B948_3DA0003B2C7B'></span>[1] Huang X, Chen Z, Zhao W, et al. An extreme internal solitary wave event observed in the northern South China Sea. Scientific Reports, 2016,6(1):30041.		<span id='_nebA1B3473E_F351_4D32_B948_3DA0003B2C7B'></span>[1] Huang X, Chen Z, Zhao W, et al. An extreme internal solitary wave event observed in the northern South China Sea. Scientific Reports, 2016,6(1):30041.

@@ Line 474: / Line 474: @@
 |}
-==4 Conclusions==
+==4. Conclusions==
 The dynamic response of large submarine induced by ISWs was simulated by establishing the ISWs numerical flume. The flume was a stratified fluid of two layers, and the fluid density varied with the depth which was more in line with the actual ocean. The track of gravity center, variations in lateral, longitudinal and pitch motion are studied. The conclusions of this study are listed as follows:

@@ Line 402: / Line 402: @@
-The longitudinal velocity of the submarine under different depths is shown in [[#img-12|Figure 12]] . Similar to the lateral velocity, the longitudinal velocity increased along the negative y-direction, and the change of longitudinal velocity was one order of magnitude larger than that of the lateral velocity. Before t=180s, the submarine was accelerating longitudinally. After t=180s, the longitudinal velocity began to keep basically stable at about -2.5m/s.
+The longitudinal velocity of the submarine under different depths is shown in [[#img-12|Figure 12]] . Similar to the lateral velocity, the longitudinal velocity increased along the negative y-direction, and the change of longitudinal velocity was one order of magnitude larger than that of the lateral velocity. Before <math>t=180</math>s, the submarine was accelerating longitudinally. After <math>t=180</math>s, the longitudinal velocity began to keep basically stable at about -2.5m/s.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-12'></div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-{|
+|-style="background:white;"
 |-
-| [[Image:Review_420808633416-image70.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image70.png|288px]]
-| [[Image:Review_420808633416-image71.png|center|288px]]
+|style="text-align: center;padding:10px;"|[[Image:Review_420808633416-image71.png|center|288px]]
 |}
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+The pitch angle of the submarine under different ISW amplitudes is shown in [[#img-13|Figure 13]]. When the submergence depth was 45m, as shown in [[#img-13|Figure 13]](a), the submarine basically keeps level without pitching before <math>t=180</math>s; after <math>t=180</math>s, the submarine began to pitch. The pitch angle gradually increased with time, and the pitch angle variation decreased with the increase of ISW amplitudes. When <math>t=260</math>s, the pitch angles of C11, C21 and C31 were -21.10°, -17.16° and -14.50°, respectively. When the submergence depth <math display="inline">H=15</math>m, the changes of pitch angle were similar to <math display="inline">H=45</math>m.
-Figure 12 Longitudinal velocity at different ISW amplitudes</div>
-The pitch angle of the submarine under different ISW amplitudes is shown in Figure 13. When the submergence depth was 45m, as shown in Figure 13(a), the submarine basically keeps level without pitching before t=180s; after t=180s, the submarine began to pitch. The pitch angle gradually increased with time, and the pitch angle variation decreased with the increase of ISW amplitudes. When t=260s, the pitch angles of C11, C21 and C31 were -21.10°, -17.16° and -14.50°, respectively. When the submergence depth H=15m, the changes of pitch angle were similar to H=45m.
+<div id='img-13'></div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+|-style="background:white;"
+|align="center" |
-{|
+{|style="margin: 0em auto 0.1em auto;width:auto;"
 |-
-| [[Image:Review_420808633416-image72.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image72.png|288px]]
-| [[Image:Review_420808633416-image73.png|center|288px]]
+|style="text-align: center;padding:10px;"|[[Image:Review_420808633416-image73.png|center|288px]]
 |}
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+'''(2) The effect of submergence depths'''
-Figure 13 Pitch angle at different ISW amplitudes</div>
-（2）The effect of submergence depths
+[[#img-14|Figure 14]] shows the comparison of the submarine velocity under different submergence depths. When the wave amplitude was constant, the influence of the submergence depth on the change of the lateral velocity and longitudinal velocity can be ignored.
-Figure 14 shows the comparison of the submarine velocity under different submergence depths. When the wave amplitude was constant, the influence of the submergence depth on the change of the lateral velocity and longitudinal velocity can be ignored.
+<div id='img-1'></div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+|-style="background:white;"
+|align="center" |
-{|
+{|style="margin: 0em auto 0.1em auto;width:auto;"
 |-
-| [[Image:Review_420808633416-image74.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image74.png|288px]]
-| [[Image:Review_420808633416-image75.png|center|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image75.png|center|288px]]
 |}
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+The variations of pitch angle with time at the same wave amplitude but different submergence depths are shown in [[#img-15|Figure 15]]. As shown in the figure, submergence depths had little influence on the variation of pitch angle.
-Figure 14 Comparison of velocity at different depths</div>
-The variations of pitch angle with time at the same wave amplitude but different submergence depths are shown in Figure 15. As shown in the figure, submergence depths had little influence on the variation of pitch angle.
+<div id='img-15'></div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+|-style="background:white;"
- [[Image:Review_420808633416-image76.png|288px]] </div>
+|style="text-align: center;padding:10px;"| [[Image:Review_420808633416-image76.png|288px]]
+|-
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 15'''. Comparison of pitch angle at different depths
-Figure15 Comparison of pitch angle at different depths</div>
+|}
 ==4 Conclusions==

@@ Line 380: / Line 380: @@
 ===3.3 Motion parameters===
-(1)The effect of different ISWs amplitudes
+'''(1) The effect of different ISWs amplitudes'''
-The lateral velocity of the submarine under different ISW amplitudes is shown in Figure 11. After t=100 s, the absolute lateral value of velocity increased along the negative x-direction. Under the same submergence depth, lateral acceleration decreased with the increase of wave amplitude. When H=45 m and t=260 s, the lateral velocities of C11, C21 and C31 were -0.51 m/s, -0.41 m/s and -0.39 m/s, respectively. By comparison with Figure11 (a) and Figure 11 (b), it is found that the submergence depth has little influence on the lateral velocity variation trend.
+The lateral velocity of the submarine under different ISW amplitudes is shown in [[#img-11|Figure 11]]. After <math>t=100</math> s, the absolute lateral value of velocity increased along the negative <math>x</math>-direction. Under the same submergence depth, lateral acceleration decreased with the increase of wave amplitude. When <math>H=45</math>m and <math>t=260</math>s, the lateral velocities of C11, C21 and C31 were -0.51 m/s, -0.41 m/s and -0.39 m/s, respectively. By comparison with [[#img-11|Figure 11]](a) and [[#img-11|Figure 11]](b), it is found that the submergence depth has little influence on the lateral velocity variation trend.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">