Mathematical modeling offers an avenue to predict distributions of microplastics in the ocean. With this goal in mind this study presents a simple analytic model describing the deterministic dynamics of long-time vertical motion of buoyant microplastics that have succumbed to biofouling in a quiescent ocean. The model couples equations governing vertical particle position and algal population dynamics and is formulated in a nondimensional frame work to determine the minimum number of system parameters. We present results which give a comprehensive understanding of the system's key dynamics when varying four parameters. Previous studies have shown that biofouling causes microplastic particles to oscillate below the ocean's surface; however, for the first time we are able to identify the fundamental processes that govern the microplastic trajectories. The model demonstrates that plastic particle properties are the biggest factor in determining the period and characteristics of the oscillation profile, while the algal population dynamics determine the maximum depth reached. As the fouled particles cross the pycnocline their long-term behavior is to become trapped within a subsurface layer, bounded by the depth of the euphotic zone and the seasonal pycnocline. The smallest particles are extremely sensitive to algal cell attachment and growth suggesting they are always submerged at depths surrounding the base of the euphotic zone or could become trapped in large algal colonies. In general, the results suggest that a higher concentration of biofouled microplastic is expected to be found subsurface, trapped close to the euphotic zone depth rather than at the ocean's surface.

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受藻类生物污染的漂浮微塑料的地下动力学

数学建模提供了一条预测海洋中微塑料分布的途径。考虑到这一目标，本研究提出了一个简单的分析模型，该模型描述了在静止海洋中因生物污垢而死亡的漂浮微塑料的长期垂直运动的确定性动力学。该模型耦合了控制垂直粒子位置和藻类种群动态的方程，并在无量纲框架中制定，以确定系统参数的最小数量。我们提供的结果可以全面了解系统在改变四个参数时的关键动态。先前的研究表明，生物污垢会导致微塑料颗粒在海洋表面以下振荡；然而，我们第一次能够确定控制微塑料轨迹的基本过程。该模型表明，塑料颗粒特性是决定振荡剖面周期和特征的最大因素，而藻类种群动态决定了所达到的最大深度。当被污染的颗粒穿过火山灰层时，它们的长期行为是被困在地下层，受透光区深度和季节性火山灰层的限制。最小的颗粒对藻类细胞的附着和生长极为敏感，这表明它们总是淹没在透光区底部周围的深处，或者可能被困在大型藻类群落中。一般来说，