Acceleration model in Turbulent flows

난류에서 나타나는 가속도의 간헐성을 회전에 의해 나타나는 가속도와 소산에 의해 나타나는 가속도로 분리함으로써 해석하고자 하였다.

Compare the Lamb vortex model and real turbulent flow

It is well known that fluid acceleration in turbulence is highly intermittent. Source of the intermittency was found to be closely related to the rotational motion of coherent vortical structures. From the Poisson equation for pressure, acceleration, which is mostly the negative of pressure gradient, can be expressed as a sum of acceleration-like below.
$$\frac{\partial u}{\partial t} + u\cdot\nabla u = -\frac{1}{\rho} \nabla P + \nu \nabla^{2}u = a^{I} + a^{S}$$
$$a=-(\nabla^2)^{-1} \nabla \Omega + (\nabla^2)^{-1} \frac{\nabla \epsilon}{2\nu} =a^{\Omega} + a^{\epsilon}$$

They are acceleration due to rotational motion of eddy and acceleration due to irrotational strain field, respectively. We investigated the statistical characteristics of those accelerations by using direct numerical simulation of isotropic turbulence. Flatness of acceleration is of order of 10 but flatness of new defined acceleration terms are 3~5 which represents less intermittency in the range of moderate Reynolds number. Numerical and experimental results do not show clear slope since the Reynolds number is relatively low, but an asymptotic behavior is observed.

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