点源惯性粒子弥散
Point-source inertial particle dispersion
摘要：
在小惯性极限下，解析地研究了点源连续发射的惯性粒子的弥散问题。我们的重点是粒子联合概率密度函数p（x，v，t）的演化方程，x和v分别是粒子的位置和速度。对于有限的惯性，位置和速度变量是耦合的，结果是p（x，v，t）可以通过求解2d空间中的偏微分方程来确定，d是物理空间维度。对于小惯量，（x，v）变量解耦，p（x，v，t）的确定归结为求解空间变量x上的两个标准强迫对流扩散方程组。后一个方程在这里从第一原理导出，即从众所周知的位置和粒子速度的拉格朗日演化方程导出。
英文摘要：
The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x and v being the particle position and velocity, respectively. For finite inertia, position and velocity variables are coupled, with the result that p(x,v,t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced to solve a system of two standard forced advection-diffusion equations in the space variable x. The latter equations are derived here from first principles, i.e. from the well-known Lagrangian evolution equations for position and particle velocity.
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