Study on the climbing height of double solitary waves along an oblique embankment around Shantou
city Tsunamis have a vere impact on marine coastal structures.Tsunami is
generally simplified as solitary wave as they propagate,and the prence of the
aftermath of Tsunami is similar to a cond solitary wave.Waveform evolution occurs as
solitary wave propagate down a gentle slope.This paper reveals the propagation of
double solitary waves and slope climbing by numerical simulation where the prototype of
十大旅游胜地
the embankment is around Shantou city in the Guangdong Province,China.It not only
enriches the theory of solitary wave,but also has important implications for the analysis
of tsunami disaster mechanism and the hydrodynamic load characteristics of structures.
Bad on the average Navier-Stokes equation and the VOF approach,numerical
simulation results are given,including changes in the velocity field of the climbing and
falling process species.The results show that the double solitary waves produce a strong秋风清秋月明
reflux effect,which results in the cond solitary wave climbing significantly less than the
height of the first solitary wave without the influence of the current.At the same time,
double solitary waves can have a much stronger effect on the
embankment.
double solitary waves,embankment,run-up height,hydrodynamic characteris-tics
Received on Jul.7,2020
Corresponding auther:********************
Vol.22No.2Marine Science Bulletin Oct.2020WANG Yang 1,HUANG Cheng 1,YI Jiaji 1,FENG Kecong 1,XIA Xiaoyu 2*1.570100,2.
430074,
Tsunamis are generated when extreme ocean conditions such as earthquakes,volcanic eruptions,and submarine landslides cau water bodies to shake.Tsunami wavelengths are extremely long,reaching hundreds of kilometers,and tsunami waves travel with great energy and speed.However,in deep water,tsunami waves are less amplitude and harder to detect.As the tsunami propagates from the deep ocean zone to the offshore zone,the tsunami waves will increa dramatically in wave height,creating huge lapping waves tens of meters high,combined with the extremely high speed,which
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Marine Science Bulletin Vol.22 can be very destructive.In recent years,the Indian Ocean tsunami of2004has caud the most devastation.A9.3magnitude earthquake under the a in northern Suma
tra triggered a tsunami that killed nearly300000people.The tsunami triggered by the Great East Japan Earthquake in2011took away nearly20000lives.When waves from the deep ocean areas are transmitted to offshore areas,due to the influence of topography, islands and environmental flows,the waves undergo changes such as shallowing, refraction,bypassing,deformation and fragmentation,which not only involves the modeling theory and numerical calculation methods of nonlinear water waves,but also needs to take into account the influence of complex factors such as afloor topography and currents.Coastal zone disaster prevention and mitigation and deep-a resource development have created new and urgent needs for rearch on extreme ocean dynamics such as tsunamis and distortion waves,respectively[1-3].
The waveform and motion characteristics of tsunami wave before breaking are clo to tho of solitary wave,and the waveform is stable with little energy loss when propagating in deep water.Solitary wave is characteristically found in shallow waters,has one peak,is waveform stable,and can propagate steadily over long distances.A complete model of tsunami wave generation,propagation and climb has been developed bad on linear shallow water equations.However,as the tsunami wave propagates into the offshore region,the wave amplitude increas and the nonlinear term of the tsunami wave cannot be ignored[4,5].海棠果树
Previously,the studies mentioned were all bad on the single solitary wave slope climbing problem.Although there are many similarities between tsunami waves and solitary waves,it is still not possible to directly replace tsunami wave with single solitary wave.Offshore tsunami waves can be considered as a superposition of wave trains consisting of multiple solitary waves.So it is necessary to conduct multiple solitary wave climbing studies bad on a single solitary wave slope climbing.In the ca of a tsunami, the tsunami wave is not strictly solitary wave,but more like a ries of waves added together[6].Therefore,in order to derive the theoretical equations for tsunami wave,the Korteweg-de Vries equation for solitary wave is commonly ud as the fundamental wave for the superposition of tsunami waves.At the surface of the a at water depth h,the profile of a solitary wave can be reprented as:
浊（x，t）=H0ch2[k0（x-x0-c0t）](1) where H0is the wave height of solitary wave,k0=（3h0/4h3）1/2denotes the effective wave number,x0is the location of wave crest at t=0,c0=[g（H0+h）]1/2is the wave velocity with the gravitational acceleration value g.According to the N wave theory,tsunami waves can
No.2酸辣粉条的家常做法
be approximated as a ries of positive and negative solitary waves superimpod on each other to form a ries of waves called tsunami-like waves.The parametric control for the superposition of the solitary wave determines whether the tsunami-like wave is in good agreement with the real-world tsunami waves[7].The formula for the wave superposition is:
浊（x，t）=
n
i=1
移着i H0ch2[琢i棕0（x/c0-（x0/c0+t i））](2)
where n is the number of superimpod waves，着i and琢i are scale factors reflecting the wave height,frequency and period of each underlying solitary wave,t i is the start time of different waves.Real tsunami waves can be approximated using equation(2).However, in practical calculations,it is difficult to obtain all the control parameters of the tsunami waves.Subquently,the concept of double solitary waves emerged and experiments were conducted.The correlation experiments show that during double solitary wave climbing,the first wave has a large influence on th
e maximum climbing height value of the cond wave,and the position relationship between the two waves also has an influence on wave climbing[8].Numerical simulations further give the flow field and energy conversion laws of double solitary waves along the straight wall and steep slope climbing process.
In this paper,the numerical simulation of wave climbing process on a slope under the action of double solitary waves is carried out to study the flow of double solitary waves and their climbing characteristics,so as to provide a reference for the design of engineering
embankments.
Numerical simulation is ud to study the climbing characteristics of double solitary waves.It is assumed that the fluid is incompressible,and the basic equations of motion of the fluid and the RNG资-着turbulence equation are ud to clo the group of equations[9,10]
.
The motion of the fluid satisfies the continuity equation,the differential formula for the continuity equation:
鄣籽鄣t+div（籽u軋）=0(3)
where r is the fluid density,t is the time,isthe fluid velocity vector,and div is the differential operator.
WANG Yang,et al.:Study on the climbing height of double solitary (13)
Marine Science Bulletin Vol.
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The momentum equation is derived according to Newton's cond law.The sum of the external combined forces exerted per unit time within a specified fluid micro-element should be consistent with the change in the momentum of the fluid within that microdollar[11,12].Bad on Newton's cond law,the equation of momentum in the three directions x,y,and z can be derived:
鄣（籽u x）鄣t+·（籽u x u軋）=鄣p鄣x+鄣子xx鄣x+鄣子yx鄣y+鄣子zx鄣z+籽f x
鄣（籽u y）鄣t+·（籽u y u軋）=鄣p鄣y+鄣子xy鄣x+鄣子yy鄣y+鄣子zy鄣z+籽f y
鄣（籽u z）鄣t+·（籽u z u軋）=鄣p鄣z+鄣子xz鄣x+鄣子yz鄣y+鄣子zz鄣z+籽f z
(4)
where:p is the pressure on the fluid micromotion,Pa;f x,f y,f z are unit mass force in three directions,m/s2;t xx,t yy,tzz are the components of the viscous stress t acting on the surface of the micromere due to molecular adhesion,
Pa.
自T=C滋k 2 T
着T(5) where k T is the turbulent kinetic energy,the turbulent kinetic energy dissipation rate,and Cu is a constant,which is0.085in the RNG资-着turbulence
model.
Using the similarity principle,the entrance boundary in the model employs a numerical wave-making plate technique to produce double solitary waves.The wave height of the first wave is0.06m,the wave height of the cond wave is0.12m,and the waveform is shown in Fig.1.The length of the calculation area is30m,the height is0.6m and the slope is10degrees.
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No.20.20
0.15
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0.05
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6789t /
迫不得已的意思
s 0.8
0.6
0.4
0.2
-0.2-0.401012345
6789t /s
(a)Horizontal flow velocity
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-0.1
-0.2
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6789t /s
民考汉
(b)Vertical flow
世界上最远的距离
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velocity The temporal curves of the horizontal and vertical flow velocity at the location of the flow velocity monitoring point (2m,0.2m)are shown in Fig.2.
WANG Yang,et al.:Study on the climbing height of double solitary …
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