A linear model for the structure of turbulence beneath surface water waves
A linear model for the structure of turbulence beneath surface water waves
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DOI：
10.1016/j.ocemod.2010.10.007
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发表时间：
2011
期刊：
影响因子：
3.2
通讯作者：
Miguel C. Teixeira
中科院分区：
文献类型：
--
作者：
Miguel C. Teixeira
利用基于快速变形理论的简化半解析模式研究了海洋表层的湍流结构。在这个与湍流呈线性关系的模型中，流动包括平均欧拉剪切流、考虑波动对湍流的不可逆影响的不旋转表面波的Stokes漂移以及湍流本身，并计算了其时间演化。通过分析模型中使用的运动方程--包含涡旋力的Craik-Leibovich方程的线性化版本，发现包含平均切变和斯托克斯漂移的流动形式上等价于包括平均切变和旋转的流动。特别地，Craik和Leibovich关于第一类流线性不稳定性的条件等价于Bradshaw关于第二类流线性不稳定性的条件。然而，目前的研究超越了线性稳定性分析，考虑了有限振幅的流动扰动，这允许计算湍流统计和处理线性稳定性为中性的情况。结果表明，湍流呈现出各向异性和伸长率连续变化的结构，从仅受剪切变形的条状结构，到仅受Stokes漂移变形的类似于朗缪尔环流的流向涡旋。对于相同符号的切变和斯托克斯漂移梯度(与风浪有关的情况)，TKE增长得更快，但在这种情况下，湍流更各向同性(这对朗缪尔环流是线性不稳定的)。
The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).