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* Flow over a [[golf ball]]. (This can be best understood by considering the golf ball to be stationary, with air flowing over it.) If the golf ball were smooth, the [[boundary layer]] flow over the front of the sphere would be laminar at typical conditions. However, the boundary layer would separate early, as the pressure gradient switched from favorable (pressure decreasing in the flow direction) to unfavorable (pressure increasing in the flow direction), creating a large region of low pressure behind the ball that creates high [[form drag]].  To prevent this, the surface is dimpled to perturb the boundary layer and promote turbulence. This results in higher skin friction, but it moves the point of boundary layer separation further along, resulting in lower drag.

* Flow over a [[golf ball]]. (This can be best understood by considering the golf ball to be stationary, with air flowing over it.) If the golf ball were smooth, the [[boundary layer]] flow over the front of the sphere would be laminar at typical conditions. However, the boundary layer would separate early, as the pressure gradient switched from favorable (pressure decreasing in the flow direction) to unfavorable (pressure increasing in the flow direction), creating a large region of low pressure behind the ball that creates high [[form drag]].  To prevent this, the surface is dimpled to perturb the boundary layer and promote turbulence. This results in higher skin friction, but it moves the point of boundary layer separation further along, resulting in lower drag.

流体流过高尔夫球。 （假设高尔夫球是静止的，而空气在上面流动是最好的理解方式。）如果高尔夫球是光滑的，则在典型条件下，典型情况下球体前部的'''<font color="#ff8000"> 边界层boundary layer</font>'''会出现层流。 但是，边界层会快速分离，因为压力梯度会从顺压（沿流动方向的压力减小）切换到逆压（沿流动方向的压力增大），从而在球后产生较大的低压区域，从而产生较高的形式阻力。 在球的表面加上凹槽以扰动边界层并促进湍流。 这会导致较高的皮肤摩擦，但会进一步移动边界层分离点，从而导致阻力减少。

* 流体流过高尔夫球。 （假设高尔夫球是静止的，而空气在上面流动是最好的理解方式。）如果高尔夫球是光滑的，则在典型条件下，典型情况下球体前部的'''<font color="#ff8000"> 边界层boundary layer</font>'''会出现层流。 但是，边界层会快速分离，因为压力梯度会从顺压（沿流动方向的压力减小）切换到逆压（沿流动方向的压力增大），从而在球后产生较大的低压区域，从而产生较高的形式阻力。 在球的表面加上凹槽以扰动边界层并促进湍流。 这会导致较高的皮肤摩擦，但会进一步移动边界层分离点，从而导致阻力减少。

*[[Clear-air turbulence]] experienced during airplane flight, as well as poor [[astronomical seeing]] (the blurring of images seen through the atmosphere).

*[[Clear-air turbulence]] experienced during airplane flight, as well as poor [[astronomical seeing]] (the blurring of images seen through the atmosphere).

  Irregularity : Turbulent flows are always highly irregular. For this reason, turbulence problems are normally treated statistically rather than deterministically. Turbulent flow is chaotic. However, not all chaotic flows are turbulent.

  Irregularity : Turbulent flows are always highly irregular. For this reason, turbulence problems are normally treated statistically rather than deterministically. Turbulent flow is chaotic. However, not all chaotic flows are turbulent.

不规则性: 湍流总是高度不规则的。由于这个原因，湍流问题通常在统计上而不是决定性地处理。湍流是混沌的。然而，并非所有的混乱流都是紊乱的。

不规则性: 湍流总是高度不规则的。由于这个原因，湍流问题通常用统计的方法而不是决定性地处理。湍流是紊乱的。然而，并非所有的混乱流都是如此。

 

 

 

  Diffusivity :The readily available supply of energy in turbulent flows tends to accelerate the homogenization (mixing) of fluid mixtures.  The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is called "diffusivity".

  Diffusivity :The readily available supply of energy in turbulent flows tends to accelerate the homogenization (mixing) of fluid mixtures.  The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is called "diffusivity".

扩散系数: 在湍流中容易获得的能量供应趋向于加速流体混合物的均匀化(混合)。在流动中，增强混合和提高质量、动量和能量输送速率的特性称为“扩散系数”。

扩散系数: 在湍流中能轻易获得稳定的能量供应，这种能量会加速流体混合物的均匀化(混合)。在流动中，增强混合和提高质量、动量和能量输送速率的特性称为“扩散系数”。

Turbulent diffusion is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle.  In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula.

Turbulent diffusion is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle.  In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula.