VISCOELASTIC PROPERTIES OF FINE-GRAINED INCOMPRESSIBLE TURBULENCE
VISCOELASTIC PROPERTIES OF FINE-GRAINED INCOMPRESSIBLE TURBULENCE
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DOI：
10.1017/s0022112068002314
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发表时间：
1968-01-01
影响因子：
3.7
通讯作者：
CROW, SC
中科院分区：
文献类型：
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作者：
CROW, SC
如果把湍流看作是一种连续的粘弹性介质，就其对平均场的作用而言，许多剪切流现象可以得到定性的解释。条件下寻求的类比是定量的，它被发现，湍流必须是细粒度和平均场弱。为了几何上的方便，湍流被假定为近似均匀和各向同性的，因此需要体积力来维持它。湍流被发现最初响应于作为弹性介质的任意变形，其中雷诺应力与应变成线性比例。三个过程，导致所产生的雷诺应力放松区分：粘性扩散，体力搅拌和非线性扰。有人认为，无论哪个过程占主导地位，雷诺应力在一个不断变化的平均场根据粘弹性本构关系，有关应力变形历史的标量记忆函数的装置。通过分析弱湍流的参数，其中非线性扰频可以忽略不计，和记忆函数计算的背景湍流的波数频谱。在分析过程中，出现了一种新的雷诺应力，它与湍流通过其体积力的维持环境有关。据发现，平均场必须是令人惊讶的弱，这种“平移应力”可以忽略不计。本文讨论了在不存在体积力和平移应力的情况下，湍流剪切流粘弹性理论的应用。
A number of shear-flow phenomena can be explained qualitatively if turbulence is regarded as a continuous viscoelastic medium with respect to its action on a mean field. Conditions are sought under which the analogy is quantitative, and it is found that the turbulence must be fine-grained and the mean field weak. For geometrical convenience the turbulence is assumed to be nearly homogeneous and isotropic so that body forces are required to maintain it. The turbulence is found to respond initially to an arbitrary deformation as an elastic medium, in which Reynolds stress is linearly proportional to strain. Three processes that cause the resulting Reynolds stress to relax are distinguished: viscous diffusion, body-force agitation and non-linear scrambling. It is argued that, regardless of which process dominates, Reynolds stress evolves in a continuously changing mean field according to a viscoelastic constitutive law, relating stress to deformation history by means of a scalar memory function. The argument is carried through analytically for weak turbulence, in which non-linear scrambling is negligible, and the memory function is computed in terms of the wave-number-frequency spectrum of the background turbulence. In the course of the analysis, a new type of Reynolds stress arises related to the passage of the turbulence through its sustaining environment of body forces. It is found that the mean field must be surprisingly weak for this ‘translation stress’ to be negligible. Applications of the viscoelasticity theory of turbulent shear flow are discussed in which body forces and therefore translation stress are absent.