北太平洋垃圾带的形成与变化Formation and Variation of the Great Pacific Garbage Patch

Formation and Variation of the Great Pacific Garbage PatchXiaoben Liu, Liuwu Shi, Yue ZhaoAbstractWe build four models to do a deep analysis on the formation, variation and distribution of the Great Pacific Garbage Patch. The first two models are created to research the mechanism of how the garbage island comes into existence from a microscopic scale. 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, another is due to damp vibration. Using classic physical theories, we capture main motives propelling trash into the North Pacific Gyre. The third model is a compartment model aiming to find the possible increasing amount of trash in the garbage patch. A function of total garbage amount is extrapolated from the model.We use this model to predict that the number of plastic debris will be more than three times larger in the next 10 years successfully. In our fourth model, we work out a density function. Using the function, we depict the temporal and spatial distribution of garbage in the ocean. We also make a simulation reflecting its distributing rules more obviously. At last, we release some suggestions to prohibit deterioration in the Great Pacific Garbage Patch. IntroductionWhere is the largest landfill in the world? It’s in the Pacific Ocean, about one thousand kilometers near the shore of America, called the Great Pacific Garbage Patch. It’s a specific area between California State and Hawaii, but until now there’s no accurate estimation about its coverage. The Great Pacific Garbage Patch is notorious for its high concentration of littered trash, plastic debris. According to a recent investigation, 80 percent of the trash is from main continents, 10 percent consists of used nets or other fishing tools and the other10 percent of trash is from passing-by ships. Most of the garbage islands are inoceanic gyres.Undoubtedly the accumulation of garbage has already made huge negative influence on the environment. Large amount of oceanic animals die of eating up plastic trash by mistake. It’s a critical moment to release some feasible and practical methods to prevent deterioration.Proper methods involve comprehensive information about the object. We verify many basic parameters characterizing the formation process of the huge landfill. The effect of ocean current is considered as the top factor in transferring garbage to America seashore.We build several models to solve three problems separately: the accumulation and motion of trash on the Pacific Ocean; the increasing ratio of the garbage amount in Great Pacific Garbage Patch; the distribution of the garbage density in Great Pacific Garbage Patch.The first questionThe first section mainly discusses the possible motion track and the way how trash pile in the Pacific Ocean. There are two mechanisms of how trash thrown into the oceanic gyre.Let’s start from the Great Pacific Garbage Patch. In our analysis, main mechanism for formation of this garbage area is due to force reactions on trash.As trash is floating in the current, it has a velocity similar to that of the current.When trash moves out the current, it enters a district where no wind exists.Forced by water resistances, the initial velocity decreases with a certain acceleration. Finally trash stays static in some area in the oceanic gyre. As time goes on, more trash accumulates in the district, forming a garbage patch.AssumptionsVelocity of trash is low enough to calculate resistance given by water using the formula: f kv.All the debris has discrete motion without conglomeration.Oceanic surface out of the currents is considered to be static.Ignore the differences generated by various figures.Glutinosity of sea water is neglected.Our first modelAccording to our discovery, the North Pacific Current doesn’t keep its motion direction as a uniform straight line. As we can see from Figure 1, the North Pacific Current branches near the pacific garbage patch. Consequently trash is conveyed inside the oceanic gyre.Figure 1 Current flow in the North Pacific Gyre.When trash is in the current, its motion is regarded as a static condition relative to the oceanic surface with a communal velocity v , as shown in Figure 2.Figure 2 Trash moving in the current.After moving for a distance, at the crossing where current branches, trash enters the area where no winds blow. As the direction of velocity alters, trash makes a turn and rotates for a certain angel. In this condition, forces imposed on it are completely different. The oceanic surface is static, but trash is floating with a velocity v , so trash will be oppressed by resistances, as shown in Figure 3.Figure 3 Trash moving in the no-wind area.Trash is influenced by three forces: Coriolis Force, and two resistances given by sea water . In our model, we just analyze forces on the direction of v .Obviously the velocity is on a decline. Computations for acceleration:2f dv k v dtmm=-=-k-----constant of resistanceSo we can extrapolate the equation of velocity:0k tmv v e-=k-----constant of resistance0v -----the initial velocityThe distance that trash could float before it stops can be computed like below:S vdt =⎰We ’ve tested many values fork, but Skeeps its value between 600kmand 800km. The result is illustrated by simulation in Figure 4.Figure 4 Distance that trash can float with different values of k .So we reach to the conclusion that, if trash moves with branch currents, entering the no-wind area, the distance that it can float is between 600km and 800km. And there will be a large garbage island about 600km to 800km distant from the North Pacific Current.Out second modelThis model is built to solve problems why there are so much trash accumulating near Japan coastline.In this model, we mainly concentrate on the dissipation effect along the current. It makes the water flow move in a radiating way, though the radiating flow is much thinner comparing with the main stream. As a result, some trash is pulled into the gyre by the radiating stream. We use damp vibration model to explore how the velocity varies in this condition. The basic equation is:v =[1]S vdt =⎰We make computations to verify how far trash could float in the ocean.5Time(s)D i s t a n c e (m )5Time(s)D i s t a n c e (m )5Time(s)D i s t a n c e (m )5Time(s)D i s t a n c e (m )5Time(s)D i s t a n c e (m )5Time(s)D i s t a n c e (m )5Time(s)D i s t a n c e (m)5Time(s)D i s t a n c e (m )Figure 5 Distances that trash could float with different values of β.We can see from the pictures that trash travels at a distance varying as theβ changes. If value of β increases, the damped effect enhances obviously, sothe distance that trash travels at become shorter . But even β is designated to be very small, the travelling distance still keeps on a relative low level from 60km to 180km. So we conclude that the dissipation effect is quite feeble. Trash thrown by dissipation effect will not form in a garbage patch.So garbage accumulation mainly occurs in the gyre (currents junction) between Hawaii and California. But near Japan coastline, as the main motion form is damp vibration, no piling area exists.The second questionHow the amount of garbage increasing in the pacific gyre is the second question. We build a compartment model to resolve the problem. We reckon the increasing tendency can be depicted with the compartment model.The mechanism of compartment is illustrated in Figure 6. Compartment model is consistent with the dynamic variation of the garbage amount in the Great Pacific Garbage Patch. The garbage island is regarded as a central room and the oceanic is regarded as an absorbing room.Time(year)D i s t a n c e (k m )beta=0.15Time(year)D i s t a n c e (k m )Time(year)D i s t a n c e (k m )Time(year)D i s t a n c e (k m )beta=0.3Time(year)D i s t a n c e (k m )beta=0.35Time(year)D i s t a n c e (k m )beta=0.4Time(year)D i s t a n c e (k m )beta=0.45Time(year)D i s t a n c e (k m )beta=0.5Figure 6 Compartment model.1Q -----amount of trash carried by the oceanic current per yearQ -----amount of trash in the Great Pacific Garbage Patch1k -----amount of trash thrown in the area by oceanic current k-----amount of trash removed or eliminated from the area1Qis the value of garbage inflow from Asia and America. In our model, it ’sonly related to the growth of society and economy. So its tendency is best described as an exponent function.10m tQ Q e=0Q -----the initial amount of garbage carried by the oceanic current per yearm -----a constant determined by realityDifferential coefficient equation:10m tdQ k Q ekQ dt=-After solving the equation, we can get:102ktm tk Q Q C eek m-=++Giving an initial value to the equation, it ’s varied into:1010(300)mtktk Q ek Q Q ek mk m-=--++According to data from the Internet, garbage amount in America increases three times in ten years, we calculate out the value of m is approximately 0.1387.Every year there is half of the garbage adding to the island [2]. There arealso some other factors influencing the value of k : the ratio of photo degradation, clean-up work done by human. Details are neglected, we only emphasize the synthesis effect of these factors. So we adjust the value of k to be 0.3.Here is a sheet showing proportions of garbage from different sources [3] & [4]:So the value of 0Q is 1631.The value of 1k is uncertain. But we know that in 2008 the value of Q is 7000. We use the equation 1010(300)mtktk Q ek Q Q ek mk m-=--++ to simulate so as tofind a proper 1k . Results of simulation:50010001500Time(year)M a s s (t e n t h o u s a n d t o n )k1=0.2Time(year)M a s s (t e n t h o u s a n d t o n )k1=0.3Time(year)M a s s (t e n t h o u s a n d t o n )k1=0.4100020003000Time(year)M a s s (t e n t h o u s a n d t o n )k1=0.5Time(year)M a s s (t e n t h o u s a n d t o n )k1=0.6Time(year)M a s s (t e n t h o u s a n d t o n )k1=0.7Figure 7 Simulation results.In this group of pictures, i t’s discovered that the best choice for 1k is 0.45.Figure 8 When 1k is 0.45, how the amount of trash grows.Conclusion is that if no effective control is launched, the amount of garbage will grow to 26000 thousand tons.The third questionIn this section, we aim to work out the distribution of garbage density in the North Pacific. Trash floats into the area propelled by currents, its velocity decreases continuously. So trash is trapped in the area. The density of garbage becomes larger as distance from the centre of the Great Pacific Garbage Patch decreases. Finally several rings with same trash density on them exist.On this condition, the main trapping forces are thought to be reactions due to collisions between different plastic debris. From Figure 9, we can see how trash enters the garbage piling area.Figure 902468101214161820Time(year)M a s s 0fT r a s h (t e n t h o u s a n d t o n )k1=0.45There may be an illegible boundary of the specific area. The outline of the boundary is very complicated, for convenient analysis, we postulate that the boundary is a uniform circularity. And the direction of the currents is perpendicular to the boundary. Trash enters the garbage area through the direction of the currents. In the area, trash is repelled by other plastic debris accumulating in the area. The nearer as to the center of the garbage piling area, the stronger the forces become. Influenced by resistances, finally trash stops moving in the sea and stays static in a certain spot.The density of garbage piling in this district can be calculated by equations below.()()nlf l lf l eρρ-∂=⨯∂=So we get a formula:l n1neCeρ⨯-=l ----- distance from trash to the boundary of the garbage piling arean ---- an attenuating constant of density.From the picture given in the subject, we capture several points to simulate the garbage density distribution.Sheet 2145 39 4.5 145 40 1.5 145 41 0.01 Simulation results are shown in Figure 10.Figure 10 Distribution of garbage density.The tendency of the varying garbage density:Distance(km)d e n s i t y (p l a s t i c c o u n t o f c u b i c m e t e r o f w a t e r )Figure 11 Tendency of the varying garbage density.Trash density in central part is much larger than that of the outer ring. ConclusionTrash covers every oceanic gyre. Trash accumulation mainly happens in currents junctions, such as near the west America coastline. In other areas, the major motion form is damp vibration, so garbage density is lower.Trash inflow brought by currents contributes to the increasing garbage amount. If no control methods launched, the amount of garbage will triple in the coming ten years.The distribution of trash density in a gyre is convergent, closer to the center of trash area, the density grows larger.World citizens should keep a concept that less use of plastic stuffs contributes to the decline of garbage in the ocean. It’s urgent to tight consumption of plastic products. If using plastic products is necessary, the material should have a character of high photo degradation ratio. More cleaning-up projects are needed in the North Pacific Gyre. The accumulated garbage should be removed as soon as possible.References[1] Dynamic simulation based on damp vibration of formation of the GreatPacific Garbage Patch. By Haizhuo Lin, Zhe Yang, Bo Xin, Haiming Zhan. 2010 9(16)[2] Economic losses generated by the Great Pacific Garbage Patch. By ChenBin. 2010 (6)[3] Economic losses generated by the Great Pacific Garbage Patch. By ChenBin. 2010 (6)[4] /Html/epr/30_1296.html。