湍流与黏性有什么关系?

legolasGG

It';s  a good question. I don';t have definite answer, but I can give some of my thoughts:
   1)viscosity is not equal to dissipation, viscosity can be one kind of dissipation, there are other dissipation mechanisms
   2)viscosity is not mixing/diffusion. Mixing is due to molecular random motion or turbulent oscillation
   3)nonlinearity in general mechanics can be cast into two catalogues: 1)nonlinearity due to the material 2)nonlinearity due to physical law
    For nonlinearity in Euler equation, its the later. It doesn';t really directly relate to turbulence, because if we write the equation in Lagrangian coordinate, the nonlinear convection term dispears, but turbulence is still there.
   4)viscosity concept itself is an assumption. Try to link viscosity or eddy viscosity are models for turbulence, doesn';t answer why turbulence.
   5)Raynolds equation is basically trying to split one equation into two, ofcause it will never be closed by physical grounds. We only have one F=ma equation, if split into two equations, it only makes the problem more difficult. And the split is not based on physics but based on mathematical convenience ( my opinion)
   6)why turbulence then? I guess it has to do with the micro-scopic mechanisms of the flowing materials, the rest of them (viscosity, nonlinearity) only magnify it and make it more developed and harder to track. If there is super fluid, or ideal fluid, shouldn';t have turbulence. Water, gas, granular particles are all particles composed of smaller particles. It';s one general form of how matter exist in this world. There are other matters such as electro-magnatic fields, light, why they don';t have turbulence in those matter? I';m just speculating. I think there is no hope to work on turbulence by mathematics, only physicists someday may reveal it.
legolasGG

assssss6s

粘性是分子无规则运动引起的，湍流相对于层流的特性是由涡体混掺运动引起的。
粘性无穷的小，湍流就永难停息。

coolboy

[这个贴子最后由coolboy在 2005/11/08 08:33am 第 5 次编辑]

legolasGG is quite good but still not good enough to make everything right:

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  3)nonlinearity in general mechanics can be cast into two catalogues: 1)nonlinearity due to the material 2)nonlinearity due to physical law
   For nonlinearity in Euler equation, its the later. It doesn';t really directly relate to turbulence, because if we write the equation in Lagrangian coordinate, the nonlinear convection term dispears, but turbulence is still there.
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The basic notion that the Eulerian description of motion is nonlinear but the Lagrangian description becomes linear is incorrect. I noted that quite a few well-known scientists had made the same mistake in this aspect. The following set of standard Eulerian equations (5 equations with 5 dependent variables, V=(u,v,w),p,rho, written in 4 Eulerian independent variables: t,x,y,z)
@V/@t + V.(Del)V = -(Del)p / rho
@rho/@t + V.(Del)rho + rho(Del).V = 0
p = p(rho)
is nonlinear because it contains many nonlinear terms. However, for an incompressible fluid (rho = constant, such as water that has been studied for more than 200 years) both the pressure gradient term and the continuity equation ((Del).V = 0) become linearized. The only term that makes the whole system still nonlinear under this circumstance is V.(Del)V. The Lagrangian description of the fluid motion eliminates V.(Del)V. However, it does not eliminate the nonlinearity of the system at all. It actually transforms the linear pressure gradient term and continuity equation in the Eulerian description into highly and much more intractable nonlinear terms (Lamb 1932, "Hydrodynamics", pp. 13-14, 5 equations with 5 dependent variables written in 4 Lagrangian independent variables: t,a,b,c)
(@2R/@t2).(@R/@a) = -(@p/@a)/rho
(@2R/@t2).(@R/@b) = -(@p/@b)/rho
(@2R/@t2).(@R/@c) = -(@p/@c)/rho
(@x/@a).(@y/@b).(@z/@c) + ... = rho0/rho
p = p(rho)
where R=(x,y,z). The reason that the Lagrangian description becomes much more intractable is that there are now two types of nonlinear terms. One involves the second derivatives and the other contains the third order nonlinearity. Note that the above two systems are equivalent in the sense that they all describe the same physical process but in different coordinate systems.

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There are other matters such as electro-magnatic fields, light, why they don';t have turbulence in those matter?
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Who told you this? For example, the so-called optical turbulence studies nonlinear Schrodinger equation that describes a light beam propagating in media with a nonlinear refractive index.

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I think there is no hope to work on turbulence by mathematics, only physicists someday may reveal it.
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Partially correct: turbulence and viscosity are related through the Kolmogorov theory that tries to solve the problem from a physical aspect under a special/simple circumstance.

fantasy

对于湍流的定义不大清楚，但是一般来说失稳应该是无粘项的作用，粘性的作用只是破坏这种作用而已，如果有所谓的能量级串，那粘性的存在必然使其不能无穷分下去。从另一方面讲，必须有粘性，因为粘性是流体中类似涡这样的结构能够存在的必要条件（除去一些理论上的没有实际意义的涡之外）。粘性提供了这样的物理基础之后，就都是起破坏性的了，粘性越强就与不可能形成湍流。当然这很难区分，因为一方面要靠那么一点点粘性解决结构问题，一方面又要考虑它的副作用。本人对这个问题没怎么研究，随便说说，好在湍流是世界性难题，也没谁有把握真正懂得。

zulu

没有黏性就没有流体，更无所谓湍流。[br][br]-=-=-=-=- 以下内容由 zulu 在 时添加 -=-=-=-=-
物理学考察的对象必须由“元素”组成，流体力学中叫“微团”。流体微团之间的黏性，也就是微团之间的引力，是流体力学研究中不可以忽略的。否则考察的就不是流体，而是其它的对象，例如流沙、电流等。或者说，只有元素间存在不可忽略的引力，而此引力又不足以维持剪切力下保持形态稳定的物体，才能称之为流体。

飘风

粘性对高波数的耗散比较快,如果要维持这一状态,就需要由低波数来传递能量.
粘性如果越小,则波数的上限会更加大,即能量串级的层次更多.
理论上也可以导出能量由低波数向高波数的传递量.

feiyuzhen

受教了

bo-bo

湍流和层流都符合N-S方程，但表现出的性质差异非常的，于是研究者就将湍流单独分开来研究，研究的终点是否是湍流与层流的统一？

fhq1971

[这个贴子最后由fhq1971在 2006/06/06 00:38am 第 1 次编辑]

fhq1971

    两者应该是有关系的。现实的流体流动都是有粘性的，判断流型的相似数Re计算公式中有粘性一项，因而粘性与流型是有关系的。
   但是应该注意一点，在实际研究过程中，假象了无粘流体（即理想流体）没有粘度，没有粘度怎么计算Re？怎么判断流型？但是理想流体流动可以有湍流模型的，这一点是解释不通的。
   

limon

标哥的论文你看得懂么？

xwz

本人不是研究湍流的，本人认为湍流产生要有旋涡，旋涡的产生离不开粘性，所以说湍流的产生离不开粘性，而湍流一旦出现，直到发展到最终的表现流动形态，也就是达到最终的相对湍流平衡态，同样离不开流体的粘性耗损效应。因此在某种意义上，粘性是湍流重要而且是必备的触发剂之一，同时也是湍流得以维持相对平衡的重要因素。

是不是可以设想一种极限状态，在出现湍流后，如果粘性无穷大，湍流会被粘性耗散成层流吗？若可以，则是否可以说：
湍流因为粘性而产生，同样因为粘性而消失

通流

旋涡的产生离不开粘性，
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这对吗？为什么？无粘流体照样能产生漩涡啊。第一行的逻辑就有问题。

xwz

无粘流体是如何产生旋涡的？？？能举一例吗

通流

会吐烟圈吗？