CN109799065A - A method of wave theory is made based on second order and generates sequential focusing wave - Google Patents
A method of wave theory is made based on second order and generates sequential focusing wave Download PDFInfo
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Abstract
The present invention provides a kind of method for making wave theory generation sequential focusing wave based on second order, it is as follows: to select suitable focus wave target focal position and time, determine the wave amplitude and initial phase of each wave component of focus wave, theory according to wave component makes wave parameter, wave theoretical calculation wave maker moving displacement is made using second order and makes wave in the sink, observes the corrugated time-histories of focal spot and carries out correlation analysis with target corrugated；If waveform is unsatisfactory for requiring, it can reasonably be corrected according to target wave amplitude and phase to wave input parameter is made, by it is revised make wave parameter and bring wave maker displacement into calculate the displacement of equation calculation wave maker and make wave in the sink, it observes focal spot corrugated and is compared with ideal corrugated, is iterated again if being unsatisfactory for requiring.Using wave making method proposed by the invention, it can gather in less iteration and obtain that waveform is good, period specific sequential focusing wave in wave number, improve the efficiency of unrestrained slot hydrodynamic test.
Description
Technical field
The present invention relates to coastal waters, ocean engineering hydrodynamic force wave flume experimental test technology, are specifically exactly that one kind is based on
Second order makes the method that wave theory generates sequential focusing wave.
Background technique
Relate to sea base Infrastructure such as offshore wind generating, offshore oil platform, land-sea interface channel etc. have begun and by
Gradually become the important foundation of coastal waters economic zone development.These infrastructure architecture objects are in complicated marine environment, be faced with wind,
The a series of environmental hazard effect such as wave, ocean current, earthquake, corrosion.Wherein Mechanics of Extreme Wave, which belongs to, safely marine structure
Ocean disaster (the Whittaker et al.2016 seriously threatened；Chien et al.2002).Theory of calamity result of study
Show under the background of Global climate change, the frequency occurs for following Oceanic disasters such as violent typhoon, Mechanics of Extreme Wave, tsunami etc. no
It can obviously increase, but single disaster intensity may significantly increase.If violent typhoon in 2017 " day dove " is with regard to China Pearl River Delta
Greatly society and economic loss, the Mechanics of Extreme Wave that " day dove " is caused is caused to lead to for example anti-wave of offshore area engineering structure in area
The damage such as dike, shore protection.Therefore, deeply generated effect of the understanding Mechanics of Extreme Wave to engineering structure, to raising ocean and coastal waters
Engineering structure safety important in inhibiting.The test of wave hydrodynamic model is made as research offshore engineering structure wave-structure
With the strong means of problem, play the role of pushability in ocean engineering development process.
Mechanics of Extreme Wave is simulated in laboratory at present and generally uses this method of focus wave, and focus wave may be considered multiple frequencies
The wave crest of the regular wave of rate appears in unified place in the same time to which wave crest is superimposed to form the biggish wave of wave amplitude.1990
Year, two scholars of Rapp and Melville generate amplitude wave using the method for wave focusing in the sink, and have observed depth
The broken phenomenon of focused wave in the case of water；Cox and Ortega has observed focused wave in 2002 and has produced in horizontal codes head plate
Raw slamming pressure；Hunt-Raby et al. (2011) has studied more unrestrained phenomenon of the focus wave on bunding；Domestic Liu Shuxue (Ma
Et al.2010), the scholars seminar such as Yang Jianmin (Deng et al.2016) also studied focus wave focusing principle and using poly-
Burnt wave has observed wave-structure function.Although generating amplitude wave using the method for wave focusing has had nearly 30 years
History, but at present used in focused wave there are still moment and focus point is focused to move down phenomenon (Fern á ndez et
al.2014)。
In order to improve test efficiency, applicant proposes the practical approach that sequential focusing wave is generated in sink early period, still
There is also focusing moment and focus point to move down phenomenon for this method.
Summary of the invention
This problem is moved down for the sequential focusing wave focus point generated in sink, the purpose of the present invention is to provide one kind
It, can be in the short time in the wave making method for making the theoretical sequential focusing wave for generating ideal waveform in the sink of wave based on high-order
The ideal focused wave of the multiple waveforms of the stable generation of interior repetition reduces the number of iterations, improves test efficiency, for practical unrestrained slot
Test improves the precision of wave simulation as input wave.
To achieve the above object, technical scheme is as follows: one kind making wave theory based on second order and generates sequential focusing
The method of wave is as follows: firstly, selecting suitable focus wave target focal position and time, to determine each wave component of focus wave
Wave amplitude and initial phase, the theory according to wave component make wave parameter, make wave theoretical calculation wave maker moving displacement simultaneously using second order
Wave is made in the sink, observes the corrugated time-histories of focal spot and carries out correlation analysis with target corrugated；If waveform is unsatisfactory for wanting
It asks, can reasonably be corrected according to target wave amplitude and phase to wave input parameter is made, revised wave parameter of making is brought into
Wave maker displacement calculates equation calculation wave maker and is displaced and makes wave in the sink, observation focal spot corrugated and with ideal corrugated pair
Than being iterated until meeting the requirements again if being unsatisfactory for requiring.
The focus wave institute of generation good waveforms can rapidly be obtained by making wave theory using second order during iterated revision
What is needed makes wave parameter, substitutes into both available generation sequential focusings in the corresponding unique accounting equation of sequential focusing wave wave maker
The displacement of wave maker required for wave, displacement is loaded into wave maker control program can be preferably continuous in focus point acquisition waveform
Focused wave；It can be obtained after less iterated revision number using this method and can be used for wave flume generation wave
The push plate wave maker displacement signal of the good sequential focusing wave of shape.
The present invention also has following technical characteristic
1, the specific method is as follows for required wave maker displacement data:
Using wave steepness ε=H/L as small parameter, perturbation expansion is carried out to corrugated η, accurate expression to second order:
η=ε η(1)+ε2η(2) (1)
In formula:
ε --- small parameter, wave steepness；
η(1)--- single order corrugated；
η(2)--- second order corrugated；
Linear wave-making theory only considers single order ingredient i.e. η(1), the push plate displacement based on linear wave-making theory is X(1)；Make wave
Machine push plate linear displacement X(1)It is calculated by following formula:
In formula:
Nf--- composition harmonic wave sum；
I --- empty unit；
fn--- n-th of wave frequencies ingredient；
T --- the time；
Xan--- composition wave frequency rate fnSingle order wave paddle complex amplitude；
C.c. --- the conjugate complex number of preceding paragraph expression formula, in order to convert real expression for complex expression；
Corresponding single order corrugated are as follows:
In formula:
kj--- wave number, including real wave number k0With empty wave number kj(j >=1), the respectively real root and imaginary root of dispersion equation, it is right
Answer the propagation mode and non-propagating mode in single order corrugated；
X --- spatial position；
cjn--- first-order transfer function is found out by linear water waves theory direct derivation；
Dispersion equation are as follows:
ωn 2=gkjntanh(kjnh) (4)
In formula:
ωn--- composition angular frequency, ωn=2 π fn；
H --- the depth of water；
Form wave frequency rate fnPropagation mode complex wave width AnComplex amplitude X is moved with wave paddleanThere are following relationships:
An=cn0Xan (5)
Wherein complex wave width AnContain composition wave frequency rate fnWave component amplitude anWith initial phase φnInformation, by following formula
It determines:
The generation good sequential focusing wave of waveform generally requires in the sink attempts to make wave for several times, and amplitude is corrected on acquisition corrugated
anWith initial phase φnProcess；When wave is made in first examination, according to theoretical focus position xbWith focusing moment tbDetermine initial phase φn:
φn=-k0nxb+2πfntb (7)
In formula:
xb--- target focus position；
tb--- target focuses point moment；
The constraint harmonic wave caused by single order wave component interacts and wave paddle leave mean place single order and pass
It broadcasts modal velocity gesture and goes out free pseudo- harmonic wave caused by the mismatch of boundary in wave paddle, cause wave paddle by single order displacement movement
When, generated corrugated actually contains above two high-order harmonic wave ingredient in wave flume, is denoted as η respectively(21)And η(22),
η is existed simultaneously in sink(1)+η(21)+η(22)；
η(21)It is to be generated since single order wave component interacts, can not be corrected by manual method, η(22)Be due to
Wave paddle boundary, which mismatches, to be generated, and is displaced X by adding additional wave paddle(2)It is corrected, and passes through addition wave paddle second order
It is displaced X(2)Generate free harmonic wave η(23)To offset freely pseudo- harmonic wave η(22)Influence, thus obtain in the sink corrugated be η(1)+
η(21)；
Wave theory generation focused wave is made using second order to need for every a pair of of wave frequencies (fn,fm) component analyzed,
Obtain corresponding second order wave paddle displacement Xnm (2), expression formula is as follows:
In formula:
F±--- order transfer function；
: * --- representative is constant for complex expression and frequency item, and difference frequency term takes its conjugate complex number；
Its expression formula of order transfer function are as follows:
In formula:
--- j and l, n and m are exchanged to preceding paragraph expression formula；
Kp ±--- broad sense dispersion equation (ωn±ωm)2=gKp ±tanh(Kp ±Real root (p=0) h) and imaginary root solution (p >=
1)；
So generating sequential focusing wave using linear wave-making theory only needs to calculate push plate single order displacement X(1), i.e. formula
(2), wave theory generation sequential focusing wave is made using second order need to calculate single order displacement X(1)With Second Order Displacements X(2)±And displacement
X2nd:
Sequential focusing wave is generated in the sink only needs to be arranged multiple focusing moment (tb1,tb2,tb3,tb4...), generation respectively
Enter formula (10) be calculated second order make wave push plate displacement X2nd 1, X2nd 2, X2nd 3, X2nd 4..., then superposition summation:
X=X2nd 1+X2nd 2+X2nd 3+X2nd 4+… (11)
When being equipped with push plate wave maker in experimental tank, in formula (9)
M2(kjn,K0 ±)=0 (12)
Wherein:
If push plate wave maker is located in sink at x=0m, the expected wave focusing moment is set as tb, focus point x=xb,
Need to select suitable wave spectrum according to user so that it is determined that each wave frequencies ingredient wave amplitude an 1。
Each wave frequencies ingredient initial phase φ required for making wave for the first time is calculated according to formula (7)n 1:
φi 1=-kixb+ωitb
By initial phase φn 1With wave amplitude an 1It substitutes into formula (10) and (11) and the push plate displacement X for making wave for the first time is calculated1,
Starting wave maker carries out making wave, and acquires corrugated time-histories η at place1；
To the corrugated time-histories η collected1Correlation analysis is carried out with theoretical corrugated, waveform is evaluated, if discontented
Foot requires, just to corrugated time-histories η1Fast Fourier variation is carried out, obtains making wave actual measurement initial phase φ for the first timen 1,measuredAnd wave
Width an 1,measured, φ will be inputtedn 1, an 1With actual measurement φn 1,measured, an 1,measuredSubstitute into formula:
φi,new=φi,old+(φi,target-φi,measured) (15)
The input initial phase φ of wave is made for the second timen 2With wave amplitude an 2；
The initial phase φ that will be obtainedi 2With wave amplitude ai 2It substitutes into formula (10) and (11), repeats the above process, until focusing
Until the corrugated measured at point is met the requirements, made required for the good sequential focusing wave of wave direction to obtain and generate in the sink
Wave machine push plate displacement.
2, when being equipped with flap type wave generator in experimental tank, in formula (9), E±And M2(kjn,K0 ±) two parameter difference
It is determined by formula (17) and (18):
Beneficial effects of the present invention and advantage are as follows: wave making method proposed by the invention is applied, it can be in a short time
The good sequential focusing wave of waveform that can be lived by less iterative steps improves the focused wave for generating good waveforms
Test efficiency, improve wave-structure function hydrodynamic test input wave simulation precision and repeatability and stablize
Property, so that focus wave repeats test and becomes feasible program, improve test efficiency.
Detailed description of the invention
Fig. 1 is the ideal corrugated corrugated step 1 iteration corrugated that linear wave making method generates in the sink, crest frequency fp=
0.6Hz, target maximum amplitude Amax=11.0cm；Surveying corrugated and theoretical corrugated related coefficient is 0.9530；
Fig. 2 is the ideal corrugated corrugated step 3 iteration corrugated that linear wave making method generates in the sink, crest frequency fp=
0.6Hz, target maximum amplitude Amax=11.0cm；Surveying corrugated and theoretical corrugated related coefficient is 0.9562；
Fig. 3 is the ideal corrugated corrugated step 6 iteration corrugated that linear wave making method generates in the sink, crest frequency fp=
0.6Hz, target maximum amplitude Amax=11.0cm；Surveying corrugated and theoretical corrugated related coefficient is 0.9607；
Fig. 4 is the ideal corrugated corrugated step 1 iteration corrugated that second order wave making method generates in the sink, crest frequency fp=
0.6Hz, target maximum amplitude Amax=11.0cm；Surveying corrugated and theoretical corrugated related coefficient is 0.9726；
Fig. 5 is the ideal corrugated corrugated step 2 iteration corrugated that second order wave making method generates in the sink, crest frequency fp=
0.6Hz, target maximum amplitude Amax=11.0cm；Surveying corrugated and theoretical corrugated related coefficient is 0.9758；
Fig. 6 is the ideal corrugated corrugated step 3 iteration corrugated that second order wave making method generates in the sink, crest frequency fp=
0.6Hz, target maximum amplitude Amax=11.0cm；Surveying corrugated and theoretical corrugated related coefficient is 0.9764；
Specific embodiment
The invention patent specific derivation process and embodiment are described further below, it is succinct in order to describe, it derives
Process is stated with plural form:
Embodiment 1
Using wave steepness ε=H/L as small parameter, perturbation expansion is carried out to corrugated η, accurate expression to second order:
η=ε η(1)+ε2η(2) (19)
In formula:
ε --- small parameter, wave steepness；
η(1)--- single order corrugated；
η(2)--- second order corrugated；
Linear wave-making theory only considers single order ingredient i.e. η(1), the push plate displacement based on linear wave-making theory is X(1).Make wave
Machine push plate linear displacement X(1)It can be calculated by following formula:
In formula:
Nf--- composition harmonic wave sum；
I --- empty unit；
fn--- n-th of wave frequencies ingredient；
T --- the time；
Xan--- composition wave frequency rate fnSingle order wave paddle complex amplitude；
C.c. --- the conjugate complex number of preceding paragraph expression formula, in order to convert real expression for complex expression；
Corresponding single order corrugated is
In formula:
kj--- wave number, including real wave number k0With empty wave number kj(j >=1), the respectively real root and imaginary root of dispersion equation, it is right
Answer the propagation mode and non-propagating mode in single order corrugated；
X --- spatial position；
cjn--- first-order transfer function can be found out by linear water waves theory direct derivation；
Dispersion equation are as follows:
ωn 2=gkjntanh(kjnh) (22)
In formula:
ωn--- composition angular frequency, ωn=2 π fn；
H --- the depth of water.
Form wave frequency rate fnPropagation mode (small amplitude wave i.e. on conversational implication) complex wave width AnMultiple vibration is moved with wave paddle
Width XanThere are following relationships:
An=cn0Xan (23)
Wherein complex wave width AnContain composition wave frequency rate fnWave component amplitude anWith initial phase φnInformation, Ke Yiyou
Following formula determines:
The generation good sequential focusing wave of waveform generally requires in the sink attempts to make wave for several times, and amplitude is corrected on acquisition corrugated
anWith initial phase φnProcess.It, can be according to theoretical focus position x when wave is made in first examinationbWith focusing moment tbDetermine first phase
Position φn:
φn=-k0nxb+2πfntb (25)
In formula:
xb--- target focus position；
tb--- target focuses point moment.
The constraint harmonic wave caused by single order wave component interacts and wave paddle leave mean place single order and pass
It broadcasts modal velocity gesture and goes out free pseudo- harmonic wave caused by the mismatch of boundary in wave paddle, cause wave paddle by single order displacement movement
When, generated corrugated actually contains above two high-order harmonic wave ingredient in wave flume, is denoted as η respectively(21)And η(22),
η is existed simultaneously in sink(1)+η(21)+η(22)。
η(21)It is to be generated since single order wave component interacts, can not be corrected by manual method, η(22)Be due to
Wave paddle boundary, which mismatches, to be generated, and can be displaced X by adding additional wave paddle(2)It is corrected, and passes through addition wave paddle
Second Order Displacements X(2)Generate free harmonic wave η(23)To offset freely pseudo- harmonic wave η(22)Influence, to obtain corrugated in the sink and be
η(1)+η(21)。
Wave theory generation focused wave is made using second order to need for every a pair of of wave frequencies (fn,fm) component analyzed,
Obtain corresponding second order wave paddle displacement Xnm (2), expression formula is as follows:
In formula:
F±--- order transfer function；
: * --- representative is constant for complex expression and frequency item, and difference frequency term takes its conjugate complex number.
Order transfer function is that second order makes the theoretical mostly important achievement of wave, expression formula are as follows:
In formula:
--- j and l, n and m are exchanged to preceding paragraph expression formula；
Kp ±--- broad sense dispersion equation (ωn±ωm)2=gKp ±tanh(Kp ±Real root (p=0) h) and imaginary root solution (p >=
1)；
E±And M2(kjn,K0 ±) two parameters are related to wave maker type, it is seen that specific embodiment 2-3.
So generating sequential focusing wave using linear wave-making theory only needs to calculate push plate single order displacement X(1), i.e. formula
(20), wave theory generation sequential focusing wave is made using second order need to calculate single order displacement X(1)With Second Order Displacements X(2)±And displacement
X2nd:
Sequential focusing wave is generated in the sink only needs to be arranged multiple focusing moment (tb1,tb2,tb3,tb4...), generation respectively
Enter formula (28) be calculated second order make wave push plate displacement X2nd 1, X2nd 2, X2nd 3, X2nd 4..., then superposition summation:
X=X2nd 1+X2nd 2+X2nd 3+X2nd 4+… (29)
When generating sequential focusing wave in laboratory, when using linear wave-making theory, generally requiring 5~8 times can just be obtained
The ideal focus wave of waveform is obtained, using second order focus wave wave making method set forth in the present invention, obtains the good focus wave of waveform
Required iteration is made wave number and will be reduced to 2~3 times, to improve hydrodynamic test efficiency.
Embodiment 2
If being equipped with push plate wave maker in experimental tank, in formula (27)
M2(kjn,K0 ±)=0 (30)
Wherein:
If push plate wave maker is located in sink at x=0m, the expected wave focusing moment is set as tb, focus point x=xb,
Need to select suitable wave spectrum according to user so that it is determined that each wave frequencies ingredient wave amplitude an 1。
Each wave frequencies ingredient initial phase φ required for making wave for the first time is calculated according to formula (25)n 1:
φi 1=-kixb+ωitb
By initial phase φn 1With wave amplitude an 1It substitutes into formula (28) and (29) and the push plate displacement X for making wave for the first time is calculated1,
Starting wave maker carries out making wave, and acquires corrugated time-histories η at place1。
To the corrugated time-histories η collected1Correlation analysis is carried out with theoretical corrugated, waveform is evaluated, if discontented
Foot requires, just to corrugated time-histories η1Fast Fourier variation is carried out, obtains making wave actual measurement initial phase φ for the first timen 1,measuredAnd wave
Width an 1,measured, φ will be inputtedn 1, an 1With actual measurement φn 1,measured, an 1,measuredSubstitute into formula:
φi,new=φi,old+(φi,target-φi,measured) (33)
The input initial phase φ of wave is made for the second timen 2With wave amplitude an 2。
The initial phase φ that will be obtainedi 2With wave amplitude ai 2It substitutes into formula (28) and (29), repeats the above process, until focusing
Until the corrugated measured at point is met the requirements, made required for the good sequential focusing wave of wave direction to obtain and generate in the sink
Wave machine push plate displacement.
Embodiment 3
For being articulated with the flap type wave generator of pool bottom, it is generally used for generating the focus wave of deepwater environment.If necessary
The sequential focusing wave under deepwater environment is simulated, basic step of the invention is identical as specific embodiment 2, the difference is that formula
(27) in, E±And M2(kjn,K0 ±) two parameters determine by formula (17) and (18) respectively:
Claims (3)
1. a kind of make the method that wave theory generates sequential focusing wave based on second order, which is characterized in that method is as follows: selection is suitable
Focus wave target focal position and time determine the wave amplitude and initial phase of each wave component of focus wave, the reason according to wave component
By making wave parameter, making wave theoretical calculation wave maker moving displacement using second order and making wave in the sink, the wave of focal spot is observed
Face time-histories simultaneously carries out correlation analysis with target corrugated；It, can be according to target wave amplitude and phase to making if waveform is unsatisfactory for requiring
Wave input parameter is reasonably corrected, and brings revised wave parameter of making into wave maker displacement calculating equation calculation wave maker position
Wave is moved and made in the sink, focal spot corrugated is observed and is compared with ideal corrugated, is iterated again if being unsatisfactory for requiring
Until meeting the requirements.
2. a kind of method for making wave theory generation sequential focusing wave based on second order according to claim 1, which is characterized in that
The specific method is as follows for required wave maker displacement data:
Using wave steepness ε=H/L as small parameter, perturbation expansion is carried out to corrugated η, accurate expression to second order:
η=ε η(1)+ε2η(2) (1)
In formula:
ε --- small parameter, wave steepness；
η(1)--- single order corrugated；
η(2)--- second order corrugated；
Linear wave-making theory only considers single order ingredient i.e. η(1), the push plate displacement based on linear wave-making theory is X(1)；Wave maker pushes away
Plate linear displacement X(1)It is calculated by following formula:
In formula:
Nf--- composition harmonic wave sum；
I --- empty unit；
fn--- n-th of wave frequencies ingredient；
T --- the time；
Xan--- composition wave frequency rate fnSingle order wave paddle complex amplitude；
C.c. --- the conjugate complex number of preceding paragraph expression formula, in order to convert real expression for complex expression；
Corresponding single order corrugated are as follows:
In formula:
kj--- wave number, including real wave number k0With empty wave number kj(j >=1), the respectively real root and imaginary root of dispersion equation, corresponding one
Propagation mode and non-propagating mode in rank corrugated；
X --- spatial position；
cjn--- first-order transfer function is found out by linear water waves theory direct derivation；
Dispersion equation are as follows:
ωn 2=gkjntanh(kjnh) (4)
In formula:
ωn--- composition angular frequency, ωn=2 π fn；
H --- the depth of water；
Form wave frequency rate fnPropagation mode complex wave width AnComplex amplitude X is moved with wave paddleanThere are following relationships:
An=cn0Xan (5)
Wherein complex wave width AnContain composition wave frequency rate fnWave component amplitude anWith initial phase φnInformation is determined by following formula:
The generation good sequential focusing wave of waveform generally requires in the sink attempts to make wave for several times, and amplitude a is corrected on acquisition corrugatednWith
Initial phase φnProcess；When wave is made in first examination, according to theoretical focus position xbWith focusing moment tbDetermine initial phase φn:
φn=-k0nxb+2πfntb (7)
In formula:
xb--- target focus position；
tb--- target focuses point moment；
The constraint harmonic wave caused by single order wave component interacts and wave paddle leave mean place single order propagating mode
State velocity potential goes out boundary in wave paddle and mismatches generated freely pseudo- harmonic wave, when leading to wave paddle by single order displacement movement, wave
Generated corrugated actually contains above two high-order harmonic wave ingredient in unrestrained sink, is denoted as η respectively(21)And η(22), i.e. sink
In exist simultaneously η(1)+η(21)+η(22)；
η(21)It is to be generated since single order wave component interacts, can not be corrected by manual method, η(22)It is due to making wave
Edges of boards circle, which mismatch, to be generated, and is displaced X by adding additional wave paddle(2)It is corrected, and passes through addition wave paddle Second Order Displacements
X(2)Generate free harmonic wave η(23)To offset freely pseudo- harmonic wave η(22)Influence, thus obtain in the sink corrugated be η(1)+
η(21)；
Wave theory generation focused wave is made using second order to need for every a pair of of wave frequencies (fn,fm) component analyzed, obtained
Corresponding second order wave paddle is displaced Xnm (2), expression formula is as follows:
In formula:
F±--- order transfer function；
: * --- representative is constant for complex expression and frequency item, and difference frequency term takes its conjugate complex number；
Its expression formula of order transfer function are as follows:
In formula:
--- j and l, n and m are exchanged to preceding paragraph expression formula；
Kp ±--- broad sense dispersion equationReal root (p=0) and imaginary root solution (p >=1)；
So generating sequential focusing wave using linear wave-making theory only needs to calculate push plate single order displacement X(1), i.e. formula (2), benefit
Wave theory generation sequential focusing wave, which is made, with second order needs to calculate single order displacement X(1)With Second Order Displacements X(2)±And displacement X2nd:
Sequential focusing wave is generated in the sink only needs to be arranged multiple focusing moment (tb1,tb2,tb3,tb4...), it substitutes into respectively public
Formula (10) is calculated second order and makes wave push plate displacement X2nd 1, X2nd 2, X2nd 3, X2nd 4..., then superposition summation:
X=X2nd 1+X2nd 2+X2nd 3+X2nd 4+… (11)
When being equipped with push plate wave maker in experimental tank, in formula (9)
M2(kjn,K0 ±)=0 (12)
Wherein:
If push plate wave maker is located in sink at x=0m, the expected wave focusing moment is set as tb, focus point x=xb, according to
User need to select suitable wave spectrum so that it is determined that each wave frequencies ingredient wave amplitude an 1。
Each wave frequencies ingredient initial phase φ required for making wave for the first time is calculated according to formula (7)n 1:
φi 1=-kixb+ωitb
By initial phase φn 1With wave amplitude an 1It substitutes into formula (10) and (11) and the push plate displacement X for making wave for the first time is calculated1,
Starting wave maker carries out making wave, and acquires corrugated time-histories η at place1；
To the corrugated time-histories η collected1Correlation analysis is carried out with theoretical corrugated, waveform is evaluated, if being unsatisfactory for wanting
It asks, just to corrugated time-histories η1Fast Fourier variation is carried out, obtains making wave actual measurement initial phase φ for the first timen 1,measuredAnd wave amplitude
an 1,measured, φ will be inputtedn 1, an 1With actual measurement φn 1,measured, an 1,measuredSubstitute into formula:
φi,new=φi,old+(φi,target-φi,measured) (15)
The input initial phase φ of wave is made for the second timen 2With wave amplitude an 2；
The initial phase φ that will be obtainedi 2With wave amplitude ai 2It substitutes into formula (10) and (11), repeats the above process, until being surveyed in focal spot
To corrugated meet the requirements until, thus obtain in the sink generate the good sequential focusing wave of wave direction required for wave maker push away
Plate displacement.
3. a kind of method for making wave theory generation sequential focusing wave based on second order according to claim 2, which is characterized in that
When being equipped with flap type wave generator in experimental tank, in formula (9), E±And M2(kjn,K0 ±) two parameters are respectively by formula (17)
(18) it determines:
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN112014066A (en) * | 2020-08-25 | 2020-12-01 | 中国海洋大学 | Vertical push plate wave-making method and vertical push plate wave-making water tank |
| CN114323555A (en) * | 2021-11-30 | 2022-04-12 | 中国人民解放军国防科技大学 | Experimental method for simulating solitary waves in ocean |
| CN114323555B (en) * | 2021-11-30 | 2023-09-15 | 中国人民解放军国防科技大学 | Experimental method for simulating ocean solitary waves |
| CN117288420A (en) * | 2023-08-30 | 2023-12-26 | 华南理工大学 | Wave-making flow-making method for generating double wave clusters Jiao Bo in uniform flow |
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