On the Origin of Turbulence
On the Origin of Turbulence
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论湍流的起源
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发表时间：
2007
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通讯作者：
E. Casuso
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作者：
E. Casuso
我们都熟悉的事实是，只有当速度低于某一临界极限时，管内的水才能获得线性流动，当速度超过这个极限时，层流就停止了，开始了复杂的、不规则的和起伏的运动。与管中流动相比，更一般的情况是，当一个称为雷诺数的无量纲常数超过1000个数量级的特定值时，由Stokes和Navier方程支配的运动就会转变为湍流运动(P.Bradshaw，1978)。这个雷诺数取决于系统的线性尺寸L、粘滞系数μ、密度ρ和速度v，其形式如下：$R=FRAC{
HO VL}{MU}$$。接下来(S.Chandrasekhar(1949)，APJ 110,329)，我们可以提出一个问题：像湍流这样的现象发生的原因到底是什么？我们把流体中的湍流描述为物质固有的不连续性的结果。我们从将物质密度描述为不连续的Dirichlet积分函数入手，通过物质守恒的欧拉方程，我们得到了一个微分方程，它意味着速度(然后能量)从一个涡旋转移到另一个涡旋，即从一个尺度到另一个尺度，这是湍流的主要观测特征之一。
We are all familiar with the fact that a linear flow of water in a tube can be obtained only for velocities below a certain critical limit and that, when the velocity exceeds this limit, laminar flow ceases and a complex, irregular, and fluctuating motion sets in. More generally than in this context of flow through a tube, it is known that motions governed by the equations of Stokes and Navier change into turbulent motion when a certain nondimensional constant called the Reynolds number exceeds a certain value of the order of 1000 (P. Bradshaw, 1978). This Reynolds number depends upon the linear dimension, L, of the system, the coefficient of viscosity μ, the density ρ, and the velocity v in the following manner $$R = frac{
ho vL}{mu}$$. Following (S. Chandrasekhar (1949), ApJ 110, 329) we can make us the question: What is the reason that a phenomenon like turbulence can occur at all?. We describe the turbulence in fluids as a consequence of the inherent discontinuity of matter. We start with the description of matter density as a discontinuous Dirichlet integral function, and through the Euler equation for matter conservation, we obtain a differential equation which implies a transference of velocity (and then energy) from one eddys to others, i.e. from one scale to another, which is one of the main observational features of turbulence.