CN108664680A - A kind of sandy beach balanced cross section prediction technique under solitary wave effect - Google Patents
A kind of sandy beach balanced cross section prediction technique under solitary wave effect Download PDFInfo
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Abstract
The seabeach balanced cross section prediction technique based on probability analysis that the invention discloses a kind of, belong to coastal evolution analysis field, seabeach balanced cross section is divided into breaker band inner equilibrium section and balanced cross section outside breaker band by the present invention by boundary of breaker line, and the position of wave height, breaker point will be isolated in actual observation（Distance of the wave breaking point away from beach berm section start）The starting gradient with seashore is as known quantity, using equilibrium beach profile curve as object function, assume along journey even dissipation in conjunction with Wave energy, Solitary Wave Propagation smashing principle, with constraintss such as the sediment bypassing conservation of mass, silting probability analyses, the lower seabeach balanced cross section mathematical model of solitary wave effect is established.The method of the present invention has the characteristics that definite conception, computational accuracy are high, can be applied to the improvement and protection at the seabeach after the effect of tsunami wave.
Description
Technical field
The present invention relates to solitary wave act on lower seabeach balanced cross section prediction technique, more particularly to it is a kind of based on probability analysis
Prediction technique belongs to coastal evolution analysis field.
Background technology
Seabeach is the precious natural resources that the Nature assigns the mankind, and pleasant view can be as the leisure trip of people
It swims place and generates economic benefit, special geographical location can obstruct impact of the wave to land building, farmland and road,
Protect the living space of the mankind.But as the mankind are to the excessive exploitation of natural resources and frequently occurring for extreme climate, ocean
Dynamic equilibrium between power and seashore sediment bypassing is broken, and is caused seashore width and is narrowed, gradient steepening, sandy roughening etc.
A series of erosion problem.Running down so that more and more people begin to focus on Coastal erosion problem for coastal ecology, also draws
The extensive concern for having sent out water conservancy and ocean research worker is made sandy beach erosion mechanism and equilibrium beach profile correct pre-
Surveying becomes the research hotspot of coastal engineering field extensive concern, has very important theory significance and practical value.
Tsunami is that energy is concentrated the most in numerous beach erosion elements, a kind of destructive power disaster the most huge, Ke Yi
Permanent destruction is caused to sandy beach, ship and coastal building rapidly within short time.The waveform of tsunami, propagation characteristic,
The motion mode of water body particle and solitary wave are very much like, all isolated by studying in existing domestic and international laboratory research
The characteristic of wave studies tsunami indirectly.
Therefore the equation of the seabeach balanced cross section under correctly predicted solitary wave effect has the disaster formation for recognizing tsunami
Important theory significance.
Invention content
The lower seabeach balanced cross section prediction technique of solitary wave effect that the object of the present invention is to provide a kind of based on probability analysis,
To obtain the beach profile curve after tsunami effect, and the recovery for seashore experience tsunami provides a kind of new ways and means.
The present invention basic principle be：
Beach profile is divided into breaker band with outside breaker band, in breaker band, it is false along journey even dissipation to be based on Wave energy
If outside breaker band, based on Solitary Wave Propagation smashing principle, silting probability analysis method and silt function, shape are introduced
The parameters such as coefficient are steep etc. in conjunction with sediment bypassing mass-conservation equation, sand bar maximum slope using beach profile curve as object function
Constraints establishes the lower seabeach balanced cross section mathematical model of solitary wave effect.
The technical solution of " the sandy beach balanced cross section prediction technique under solitary wave effect " of the present invention is pressed following successively
Step carries out：
1, the calculating parameter of balanced cross section is determined
According to the actual conditions of beach profile, determine that calculating parameter is：The initial gradient before wave actionθ, break-up point positionx b , it is broken
The broken depth of waterh b , silt functionψ, the steep factor sigma in sand bar slope；
2, beach profile is divided into two parts
Beach profile is divided into two parts by boundary of wave breaking point, wave breaking point to water front part is wave in breaker band
Break-up point to deep-sea part is outside breaker band；
3, the lower seabeach balanced cross section mathematical model of solitary wave effect is established
Object function is seabeach balanced cross section curvef(x,h)=0, it is uniform along journey with Wave energy in Theory of Solitary Waves, breaker band
Dissipation is to establish breaker band interior profile model it is assumed that object function is necessary to cross wave breaking point condition in order to control；Pass through breaker band
Outer silting probability analysis, control condition is sediment bypassing mass-conservation equation, sand bar slope is steep, establishes breaker band outer section mould
Type：
（1）Establish breaker band interior profile model
Establish coordinate system as shown in Figure 1（x,h）, with Theory of Solitary Waves, wave breaking energy even dissipation assume, object function must
By wave breaking point condition in order to control, breaker band interior profile model expression is established.
1. Theory of Solitary Waves：
Solitary wave wave energy density expression formula is
Wave height and the depth of water are directly proportional after wave breaking, and proportionality coefficient isγ b , i.e.,：
Solitary wave velocity of wave expression formula is：
2. wave breaking energy even dissipation assumes：
It is assumed that when seabeach is in stable state, the unit of water body wave energy loss of balanced cross section is constantD *, Then have：
3. object function is necessary to cross wave breaking point
f(x
b
,h
b
)=0
Above-mentioned simultaneous can be obtained breaker band interior profile model expression
Wherein,；
（2）The reckoning of neutrality point and silting erosion amount
By breaker band interior profile model expression neutral point is solved with starting cross-section expression formula simultaneous（x 0 ,h 0 ）, and calculate mud extraction
Husky erosion amount：
Neutrality is put to the sediment siltation amount of wave breaking pointS d0 For：
The silting amount of wave breaking point offshore sideS d1 It can be expressed as：
；
（3）Establish breaker band outer section model
Establish coordinate system as shown in Figure 1（x’,h’）By silting probability analysis outside breaker band, with the sediment bypassing conservation of mass
Equation, sand bar slope suddenly in order to control condition, object function it is necessary cross wave breaking point, establish breaker band outer section model
1. silting probability analysis
The main reason for experience according to previous studies, hydraulic jump is siltation sand bar formation.The generation of hydraulic jump is two kinds of different directions
Water body collision generates, one is along the bottom current that inclined-plane onshore moves, silt is made to be ramped up movement；The second is wave
It climbs and terminates to fall the reflux generated after rise, silt is made to be moved downward along inclined-plane, the two meets to form hydraulic jump near wave breaking point,
Two kinds of component along inclined-plane is offset at this time, silt straight bevel facet deposition.The deposition probability of silt is about perpendicular to starting inclined-plane
Line L is introduced at normal distributionAThere is beach profile shape expression formula for form parameter for controlling the shape of balanced cross section：
2. sediment bypassing mass-conservation equation
The outer silting amount of breaker band is provided by net erosion sediment in breaker band, and erosion amountS e , accumulating amountS d It is proportionalψ：
3. sand bar slope is steep
The steep factor sigma in siltation sand bar slope formed after due to the presence of silt underwater information warfare solitary wave being acted on is definite value：
σ=constant;
（4）It solves and draws the lower seabeach balanced cross section of solitary wave effect：The lower seabeach balanced cross section model of solution solitary wave effect simultaneously will
Breaker band outer section model coordinate systems（x’,h’）It is transformed into original coordinate system（x,h）, coordinate transform expression is：
Mathematical model in breaker band
The outer mathematical model of breaker band
Coordinate transform formula
Mathematical model derived above is a beach profile prediction model.Back beach section shape is acted on for tsunami at present
Prediction, not yet someone to solitary wave act under balanced cross section curvilinear equation carried out technique study.The present invention proposes a kind of
The result of calculation of the new prediction technique based on probability analysis seabeach balanced cross section, the mathematical model established by this method is sea
Beach balanced cross section curvef(x,h)=0Expression formula.
The technology path of the method for the present invention is as shown in Figure 2.
It is characteristic of the invention that：Based on neutral line hypothesis, by seabeach balanced cross section curvef(x,h)=0Expression formula is as mesh
Beach profile is divided into breaker band with outside breaker band, in breaker band, is based on Wave energy along journey even dissipation by scalar functions
It is assumed that outside breaker band, silt function, form factor are introduced based on Solitary Wave Propagation smashing principle, silting probability analysis
Equal parameters, using beach profile curve as object function, in conjunction with the constraints such as suddenly of sediment bypassing mass-conservation equation, sand bar maximum slope
Condition establishes the lower seabeach balanced cross section mathematical model of solitary wave effect.This method can be accurate, easy calculating predict tsunami
Balanced cross section after effect has the characteristics that definite conception, computational accuracy are high.
The invention has the advantages that：
1, the sandy equilibrium beach profile equation under solitary wave effect is proposed, before this, not yet someone acts on solitary wave
Under balanced cross section curvilinear equation carried out technique study.
2, this method has been put forward for the first time by analyzing locomotory mechanism of the silt after solitary wave effect with probability analysis
Method studies balanced cross section, and method is reasonable and feasibility is strong, and verification accuracy is high.
3, the method for the present invention definite conception, computational accuracy are high, engineer application is easy, can be applied to the effect of tsunami wave
The improvement at seabeach afterwards and Protection Analysis.
Description of the drawings
Fig. 1 is establishment of coordinate system schematic diagram of the present invention；
Fig. 2 is the Technology Roadmap of the present invention；
Fig. 3 is that the present invention implements prediction section and measured section comparison diagram.
Specific implementation mode
Below by drawings and examples, invention is further described in detail, but protection scope of the present invention is not limited to
In the content.
Embodiment 1：A kind of sandy beach balanced cross section prediction technique under solitary wave effect
We are existed using Yin Lu Young《Hydro- and morpho-dynamic modeling of breaking
solitary waves over a finesand beach. Part I: Experimental study》In experiment other side
Method is specifically described and verifies, and particular content is as follows：
1, the calculating parameter of balanced cross section is determined
According to the actual conditions of beach profile, determine that calculating parameter is：The initial gradient 1/15, break-up point position before wave action
10.24m, break-up point depth of water 0.53m, silt function 0.8, the steep coefficient in sand bar slope 1.82.
2, beach profile is divided into two parts
As shown in Figure 3 by beach profile with wave breaking pointx b =10.24 are divided into two parts, wave breaking point to water front portion for boundary
It is divided into breaker band, wave breaking point to deep-sea part is outside breaker band.
3, the lower seabeach balanced cross section mathematical model of solitary wave effect is established
Mathematical model in breaker band
Coordinate transform formula
The outer mathematical model of breaker band
4, it solves and draws seabeach balanced cross section mathematical model
Above-mentioned mathematical model function form is complex, and general is difficult to solve parameter by formulaA, B, uValue, because of Matlab etc.
Numerical software have the function of the complicated equation of solution and Complicated Function Curve can be drawn thus recommend its to model solve with
Image Rendering, two formula predictions section of figure, that is, Matlab solve the section curve drawn.Matlab solvers are as follows：
X_b=input (' break-up point position please be input：');
H_b=input (' the break-up point depth of water please be input：');
Theta_tan=input (' initial slope foot please be input：');
Fai=input (' silt function please be input：');
Sigma=input (' the steep coefficient in sand bar slope please be input：');
A_1=h_b/x_b^0.4;
syms x y;
eq_1=A_1*x^0.4-theta_tan*x;
x_0=max(double(solve(eq_1)));%x_0 is coastal line point
s_chong=double(int(A_1*x^0.4-theta_tan*x,x,0,x_0));
s_yu=fai*s_chong;
s_yu1=double(int(theta_tan*x-A_1*x^0.4,x,x_0,x_b));%s_yu1 is coastal line point to breaker point siltation volume
s_yu2=s_yu-s_yu1;%s_yu2 is the siltation volume after breaker point
theta=atan(theta_tan);
x_e=x_b*cos(theta)+h_b*sin(theta);
h_e=h_b*cos(theta)-x_b*sin(theta);% coordinate transforms
for A_2=1.4:0.001:If 1.5% domain without solution changeable shape coefficient
h=-1/(A_2*sigma*sqrt(2*pi))*exp((x_e*A_2-x)^2/(-2*sigma^2))-h_e;
u=max(double(solve(h)));
f=1/(A_2*sigma*sqrt(2*pi))*exp((x*A_2-u)^2/(-2*sigma^2));
s=double(int(f, x, x_e, inf));
if abs(s-s_yu2)<=0.001
break
end
end
z=x*cos(theta)+y*sin(theta);
t=y*cos(theta)-x*sin(theta);
g=t+(1/(A_2*sqrt(2*pi)*sigma))*exp((A_2*z-u)^2/(-2*sigma^2));
F1=ezplot (g, [x_b, 13, h_b, 1]) % are according to actually taking drawing range
set(f1,'Color','b','LineWidth',2)
set(gca,'ydir','reverse')
hold on
f1=ezplot(y-A_1*x^0.4,[0,x_b,0,h_b])
set(f1,'Color','b','LineWidth',2)
axis([0 13 -infinf])
set(gca,'xdir','reverse')
Title (' inquire into section ')
By result it is found that the beach profile obtained by the method for the present invention tests the section shape measured with Yin Lu Young more
Close, which can be applied in the prediction of the lower equilibrium beach profile of solitary wave effect.
Claims (2)
1. the sandy beach balanced cross section prediction technique under a kind of solitary wave effect, it is characterised in that：It, will based on neutral line hypothesis
Beach profile is divided into breaker band with outside breaker band, in breaker band, is based on Wave energy along journey even dissipation it is assumed that broken
Outside wavestrip, the parameters such as silt function, form factor are introduced based on Theory of Solitary Waves, silting probability analysis, with beach profile
Curve in conjunction with the constraintss such as sediment bypassing mass-conservation equation, sand bar maximum slope be steep, establishes solitary wave work as object function
With lower seabeach balanced cross section mathematical model.
2. according to the sandy beach balanced cross section prediction technique under solitary wave effect described in claims 1, it is characterised in that press
Following steps carry out：
（1）Determine the calculating parameter of balanced cross section
According to the actual conditions of beach profile, determine that calculating parameter is：The initial gradient before wave actionθ, break-up point positionx b , it is broken
The broken depth of waterh b , silt functionψ, the steep factor sigma in sand bar slope；
（2）Beach profile is divided into two parts
Beach profile is divided into two parts by boundary of wave breaking point, wave breaking point to water front part is wave in breaker band
Break-up point to deep-sea part is outside breaker band；
（3）Establish the lower seabeach balanced cross section mathematical model of solitary wave effect
Object function is seabeach balanced cross section curvef(x,h)=0, uniform along journey with Wave energy in Theory of Solitary Waves, breaker band
Dissipation is to establish breaker band interior profile model it is assumed that object function is necessary to cross wave breaking point condition in order to control；Pass through breaker band
Outer silting probability analysis, control condition is sediment bypassing mass-conservation equation, sand bar slope is steep, establishes breaker band outer section mould
Type：
Establish breaker band interior profile model
Establish coordinate system as shown in Figure 1（x,h）, with Theory of Solitary Waves, wave breaking energy even dissipation assume, object function must
By wave breaking point condition in order to control, breaker band interior profile model expression is established：
Wherein, A is parameter, is defined as follows
D*For unit water body wave energy loss,γ b For breaker wave heightHAnd the depth of waterhProportionality coefficient；
The reckoning of neutrality point and silting erosion amount
The section model expression formula obtained by above formula solves neutral point with starting cross-section expression formula simultaneous（x 0 ,h 0 ）, and calculate mud extraction
Husky erosion amount：
Neutrality is put to the sediment siltation amount of wave breaking pointS d0 For：
The silting amount of wave breaking point offshore sideS d1 It can be expressed as：
；
Establish breaker band outer section model
Establish coordinate system as shown in Figure 1（x’,h’）, by silting probability analysis outside breaker band, kept with sediment bypassing quality
Permanent equation, sand bar slope are steep, object function is necessary crosses wave breaking point condition in order to control, establishes breaker band outer section model：
1. silting probability analysis
The deposition probability of silt, at normal distribution, is introduced about the line L perpendicular to starting inclined-planeBFor form parameter, for controlling
The shape of balanced cross section has beach profile shape expression formula：
2. sediment bypassing mass-conservation equation
Net erosion sediment provides in the equal breaker band of the outer silting amount of breaker band, and erosion amountS e , accumulating amountS d It is proportionalψ：
S
d=
ψS
e=
S
d0+
S
d1
；
3. sand bar slope is steep
The steep factor sigma in siltation sand bar slope formed after due to the presence of silt underwater information warfare solitary wave being acted on is definite value：
σ=constant;
（4）It solves and draws the lower seabeach balanced cross section of solitary wave effect：The lower seabeach balanced cross section model of solution solitary wave effect simultaneously will
Breaker band outer section model coordinate systems（x’,h’）It is transformed into original coordinate system（x,h）, the equilibrium state of beach profile is drawn, number
Learning model expression is：
Mathematical model in breaker band
The outer mathematical model of breaker band
Coordinate transform formula。
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| CN110110654A (en) * | 2019-05-06 | 2019-08-09 | 中国科学院遥感与数字地球研究所 | A kind of amplitude inversion method and device for down type ocean interior estimates |
| CN111553069A (en) * | 2020-04-23 | 2020-08-18 | 河海大学 | Method for measuring balance degree of terrain profile under wave action |
| CN113219481A (en) * | 2021-03-29 | 2021-08-06 | 河海大学 | Wave band breaking wave water power monitoring method and system based on three-dimensional laser radar |
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| CN110110654B (en) * | 2019-05-06 | 2021-03-02 | 中国科学院遥感与数字地球研究所 | Amplitude inversion method and device for descending ocean isolated waves |
| CN111553069A (en) * | 2020-04-23 | 2020-08-18 | 河海大学 | Method for measuring balance degree of terrain profile under wave action |
| CN111553069B (en) * | 2020-04-23 | 2022-11-04 | 河海大学 | Method for measuring balance degree of terrain profile under wave action |
| CN113219481A (en) * | 2021-03-29 | 2021-08-06 | 河海大学 | Wave band breaking wave water power monitoring method and system based on three-dimensional laser radar |
| CN113219481B (en) * | 2021-03-29 | 2022-02-18 | 河海大学 | Wave band breaking wave water power monitoring method and system based on three-dimensional laser radar |
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