Convective stability of turbulent Boussinesq flow in the dissipative range and flow around small particles.
Convective stability of turbulent Boussinesq flow in the dissipative range and flow around small particles.
复制标题
耗散范围内的湍流 Boussinesq 流和小颗粒周围流动的对流稳定性。
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Leshansky
中科院分区：
文献类型：
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作者：
I. Fouxon;A. Leshansky
我们考虑任意的，可能是湍流的，在耗散尺度l_{d}以下平滑的Boussinesq流。证明了流动相对于尺度小于l_{d}的波动增长的稳定性导致了一个非平凡约束。这涉及标量在重力Fl和瑞利标度L方向上的梯度波动的无因次强度，这取决于瑞利数Ra、努塞尔数Nu和l_{d}。该约束表明，静止的层状流体是线性稳定的，在大Ra的极限下发展为不稳定。这限制了在L尺度上具有封闭流线的静止分层流体中小游泳者周围流动的溶液的可观察性[A]。M. Ardekani和R. Stocker，物理学家。通讯学报，105,084502 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.084502。相应地，要研究L尺度下的流动，就必须考虑湍流。我们证明了小颗粒或游泳者周围的湍流可以用标量积分-微分平流-扩散方程来描述。描述解，我们证明了闭流线以有限概率持续存在。我们的研究结果似乎是理解自然海洋环境中小颗粒和游泳者周围流动的必要基础。
We consider arbitrary, possibly turbulent, Boussinesq flow which is smooth below a dissipative scale l_{d}. It is demonstrated that the stability of the flow with respect to growth of fluctuations with scale smaller than l_{d} leads to a nontrivial constraint. That involves the dimensionless strength of fluctuations of the gradients of the scalar in the direction of gravity Fl and the Rayleigh scale L depending on the Rayleigh number Ra, the Nusselt number Nu, and l_{d}. The constraint implies that the stratified fluid at rest, which is linearly stable, develops instability in the limit of large Ra. This limits observability of solution for the flow around small swimmer in quiescent stratified fluid that has closed streamlines at scale L [A. M. Ardekani and R. Stocker, Phys. Rev. Lett. 105, 084502 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.084502]. Correspondingly, to study the flow at scale L one has to take turbulence into account. We demonstrate that the resulting turbulent flow around small particles or swimmers can be described by a scalar integro-differential advection-diffusion equation. Describing the solutions, we show that closed streamlines persist with finite probability. Our results seem to be the necessary basis in understanding flows around small particles and swimmers in natural marine environments.