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1、Formation and Variation of the Great Pacific Garbage PatchAbstract In this paper, we build a model by utilize dynamic analog to expound the formation of the ocean garbage patch. Our destination is to track the litter debris and forecast its future conditions to help managing it. After the analysis,
2、we find that the velocity of trash alleviates as time goes on. Trash does its motion in two probable ways, one is due to resistances given by sea water, and another is due to damped vibration. By using classic physical theories, we capture main motives propelling trash into the South Pacific Gyre. T
3、hats how the great garbage patch forms.According to the model and the its result, we formulate the monitoring program.Compared with the physical truth, the model also has some unsatisfactory aspects, but it has some reference.IntroductionWhere ever is the worlds largest dump? It is located in the Pa
4、cific Ocean, about one thousand six hundred kilometers west of California, called the Great Pacific Ocean Garbage Patch. According to pertinent data 1, it is ten million tons of debris litter that is piling up there, like a plastic soup when people are looking ahead. And 80 percent of the trash is f
5、rom main continents, 10 percent consists of used nets or other fishing tools and the other 10 percent of trash is from passing-by ships. Most of the garbage islands are in oceanic gyres. Nowadays, a wide variety of technical and scientific problems associated with this debris mass are coming to ligh
6、t. But until now, no one can reason out its coverage area exactly and the great economic losses ecological impact and the Pacific Ocean Gyre has caused.Long-term effective methods are searched to objectively characterize the Gyre. The ocean current is the mechanism of the Great Pacific Ocean Garbage
7、 Patch. In our paper, we will take the south pacific ocean garbage patch for example, focusing on how the debris litter drifts in the fluid, assembles in quantity, distributes under the effect of ocean currents in. Afterwards, in accordance with our model, we project process reasonable suggestions t
8、o monitor the Gyre, tracking its growth.Assumptions1. Regardless of time and geographical positions impacts on the speed of the ocean currents, we consider the speed as constant value.2. According to the datum2, we designate the speed of the west wind drift vp1 as 1.4 km/h, that of Peru Current vp2
9、as 1 km/h, that of the south equatorial warm current as vp3 3 km/h, that of the north Australia current as vp4 1.4 km/h.3. Regard the flow of the currents as stationary flow and the seawater as Newtonian fluid, which means the viscosity of the seawater is constant.4. Consider the level of the sea is
10、 in laminar flow.5. The mass points motion in the sea can be influenced by the ocean current no matter how far the mall point is away from it.6. The mass points motion is synthesized by the sub-movement of per ocean current regardless of effects of other factors.The ModelIn our model, we will utiliz
11、e dynamic analog to expound the formation of the ocean garbage patch. The model substitutes straight lines for ocean currents which form the gyre, in the model the orientation of the straight line representative of the flow direction and the speed value retrospect to the assumption No.4. Sequentiall
12、y, we simplify the physical truth as that shown in the figure 1. (Due to the change of the direction of the Peru Current on passage, the simplified model replaces tow straight lines, which are of the same speed but different direction, of the Peru Current. ) Figure 1: the Distribution of the Ocean C
13、urrents in the South Pacific OceanThen, our model talks over how the ocean current effect the mass points movement, more specifically, the effect on the velocity of the direction parallel to the line and perpendicular to the line.Lets discuss the effect on the mass points velocity of the direction p
14、arallel to the line firstly.According to the assumption No.3 and No.4 and the relative information 3, we can describe the ocean current flow as one-dimensional steady flow. On the basis of Navier-Stokes Equation show belowY means the mass force of the direction Y-axis, in our model ; means the densi
15、ty of sea water; means the kinematic viscosity of sea water, , means the dynamic viscosity of sea water. We can simplify the equation above and get the one belowIntegrate and get (1)So we plug tow boundary conditions (2) shown below into the formula (1) integral constant is determined , Since , so (
16、2)We can make a conclusion that the mass points velocity in the direction parallel to the ocean current is the same as that of the ocean current.Secondly we focus on the mass point velocity in the direction perpendicular to the ocean currents direction.Having consulted some materials 4, we decide th
17、at the ocean currents impact on floaters in the direction perpendicular to the ocean currents direction is equivalent to wave damped oscillation. The farther away from the wave source, the weaker the oscillation is, which means in our model that the smaller the floaters velocity in the direction per
18、pendicular to the ocean currents direction is. And the velocity value is (3)A means oscillation range, ; means the damping coefficient, ; d means the distance the point from the source or the line; the evolution means velocity is the energys evolution.The distance d is determined by the formula belo
19、w (4) Then we should decide the equations of the straight lines of the ocean currents. According to the figure 1 and our estimation of the intercepts, the equations are shown belowSo the distances that any point away from the lines are Substituting d1, d2, d3, d4, d5 for d in the formula (3), we can
20、 get the velocities in the direction perpendicular to the ocean currents directions vc1, vc2, vc3 , vc4 ,vc5. Because the farther the points away from the ocean current the smaller its velocity in the perpendicular direction is, we realize the smaller its velocity is the bigger its pressure is accor
21、ding to Bernoulli Equation 4. Therefore, in the direction perpendicular to the ocean currents flowing direction, the force direction is opposite to the velocity gradient, directing to the line.Now for any point in the coordinate, the velocity is known. When it moves to another new position, the velo
22、city at this time, which keeps the mass point moving, is determined by the new relationship between the position and the line. We establish the coordinate based on the latitude and longitude, the original point located in the point of intersection of eastern longitude 150 degrees and southern latitu
23、de 60 degrees, illustrated in the figure 1. v1, v2, v3, v4 and v5 are the velocities of the currents, and () are counterclockwise angles between the directions of velocity and the X-axis axle as shown in the figure 1. We discuss how every ocean current impacts a mass point separately. A mass point u
24、nder the west wind drifts impact, the sub-velocities in the direction of X-axis and Y-axis are (5)v1x means the mass points velocity in the direction of X-axis; v1y means the mass points velocity in the direction of Y-axis. Similarly available formula can be got below (6) (7) (8) (9) So under the ac
25、tion of the five streams of ocean currents, the velocity of X-axis is (10)and the velocity of X-axis is (11) Assuming that the initial position of any point is , we have testified the velocity at any time is available, so the position of the point at any time is also doubtless. We can solve the valu
26、e by integral. (12) When the number of points is big enough to simulate the track of the litter debris, we can use matlab to illustrate the positions of points, the tendency of litter accumulation, which benefits design and implement our plans to monitor the ocean garbage patch. At last, we simulate
27、 the process of the accumulation as shown in the figure 2 below.Figure 2: the Tendency of the Accumulation of the Litter DebrisLitter debris is far away from the Gyre at the beginning, for example, the litter dumped from the South America floats in the place near A. With the effect of the currents a
28、nd time going, it keeps moving , following the law we analyzed before, along determined eye locus shown in the figure 2 until it reach the area E where the resultant force on the litter is near to zero. It is the same as the litter in the area of B and D. But for C, our model seems appropriate to th
29、e place C, and we will analyze the reason later.Monitoring Program1. In the area off the shore of the north of Australia (the zone shown in the figure 2 whose x ranges from -2000 to 0 and y ranges from 0 to 4000) and of the western coast of the South America (the zone shown in the figure 2 whose x r
30、anges from 8000 to 10000 and y ranges from 0 to 4000 ), where litter debris accumulates in a large amount or the district people highly amass, we can set fifty monitoring platforms in all, which are under the control of experts and scholars who will do measurement termly to master the density and th
31、e distribution of the great garbage patch gyre in the pacific ocean.2. In the zone between the south equatorial warm current, whose x ranges from 0 to 8000 and y ranges from 3000 to 5000, and the west wind drift, whose x ranges from 0 to 8000 and y ranges from -1000 to 1000, we can set certain drogu
32、es in every unit area, in order to measure the amount of the litter.3. In addition to the items, the monitoring ships should be arranged to the Gyre to collect samples, which involve the density, to forecast variation tendency by data statistics.4. With the development of the technology, some high a
33、dvanced tools can be deploied in this field to monitor or handle the litter.The resourcing the monitoring program needs is offshore platforms, drogues, the monitoring ships and so on, the monitoring instruments consisting of sensor units, and units for collecting and storing data, units for processi
34、ng data, units for communication and relative auxiliary equipments. In addition, a large quantity of and excellent manpower resource is in demand. It is not only high tech testing facilities and the talent of high quality but also environmental philosophy that can monitor or even save the human bein
35、gs.Model EvaluatingAdvantages1. Through the analysis of the main reason which causes the litter debris to move in the sea, our model ascertains that it is the Gyre that drives the litter debris. Then we find out the solution to the problem how to determine the velocity of mass points. By integral, i
36、t is easy to describe the track of litter debris movement and its position at any time. That is convenient for us to forecast the extend , density and distribution.2. Compared with the physical truth illustrated in the figure 3 in the position in which the litter accumulates, it is obviously that ou
37、r model approaches to the physical truth.Figure 3: the Physical Truth of the Pacific Ocean Garbage Patch3. Our model can forecast the whole garbage patchs driftage, and otherwise can simulate a mass points. That will be economical to track some mass points to gain the whole garbage patch information
38、.Limitations By analysis in detail, there are also some deviations can be found between the results of our model and the physical truth. To some degree, our models accuracy is low, and the reasons are listed below.1. In our model, we take the datum of the some main ocean currents, but the complex co
39、nditions are changeable in the sea, the source of the datum may be unfaithful.2. Our model gets rid of the effect caused by typhoons , rainstorms and other factors, but in fact, it is more complicated than that we consider in the model.3. Be restricted by the datum and our team members abilities, we
40、 dont take the Australian continents effect on the north Australian current into account deeply. Hence, the track of the litter debris is widely divergent with the physical truth.References1 2 3Shuren Yang, Zhiming Wang, Guangyu He, Haiqing Cui, Engineering Fluid Mechanics, Petroleum Industry Press.
41、4Haizhou Lin, Zhe Yang, Bo Xin, Haiming Zhan, the Cause of the Central Pacific Garbage Patch based on the damped oscillation and dynamic analog, published on Theoretical Reserch 2010-8, 108-109.Appendixclc;clear;close all x0=8000;y0=2000;syms t for n1=-100:50:1000 for n2=-2000:100:2000 vp1=2;vp2=1;v
42、p3=3;vp4=2;vp5=1; s1=10*(2*pi)/360; s2=95*(2*pi)/360; s3=180*(2*pi)/360; s4=275*(2*pi)/360; s5=85*(2*pi)/360; x=0:1000:8000; y1=0:100:500; y1=tan(s1)*x plot(x,y1) hold on x=7700:100:8080; y2=2000:100:4000; y2=tan(s2)*(x-8200); plot(x,y2); hold on x=0:100:8000; y3=7500:100:8000; y3=tan(s3)*x+4000; pl
43、ot(x,y3); hold on x=-400:100:100; y4=0:100:4000; y4=tan(s4)*x; plot(x,y4) hold on x=7700:10:8000; y5=0:100:2000; y5=tan(s5)*(x-7700); plot(x,y5) hold on d1=abs(tan(s1).*(x0+n1)-(y0+n2)/(tan(s1)2+1)(1/2); d2=abs(abs(tan(s2)*(x0+n1)-(y0+n2)-8500.*tan(s2)/(tan(s2)2+1)(1/2); d3=abs(abs(tan(s3)*(x0+n1)-(
44、y0+n2)+4000)/(tan(s3)2+1)(1/2); d4=abs(abs(tan(s4)*(x0+n1)-(y0+n2)/(tan(s4)2+1)(1/2); d5=abs(abs(tan(s5)*(x0+n1)-(y0+n2)-7700*tan(s5)/(tan(s5)2+1)(1/2); vc1=(exp(-0.2*d1)(1/2); vc2=(exp(-0.2*d2)(1/2); vc3=(exp(-0.2*d3)(1/2); vc4=(exp(-0.2*d4)(1/2); vc5=(exp(-0.2*d5)(1/2); vx1=vp1*cos(s1)-vc1*sin(s1)
45、; vx2=vp2*cos(s2)-vc2*sin(s2); vx3=-vp3; vx4=vp4*cos(s4)-vc4*sin(s4); vx5=vp5*cos(s5)-vc5*sin(s5); vy1=vp1*sin(s1)+vc1*cos(s1); vy2=vp2*sin(s2)+vc2*cos(s2); vy3=-vc3; vy4=vp4*sin(s4)+vc4*cos(s4); vy5=vp5*sin(s5)+vc5*cos(s5); vx=vx1+vx2+vx3+vx4+vx5; vy=vy1+vy2+vy3+vy4+vy5; %x=solve(y2=y5,x) %t=0:100:3000; x=x0+n1+int(vx*t,t,0,50); y=y0+n2+int(vy*t,t,0,50); plot(x,y,o) hold on end end hold on
