Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers
Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers
复制标题
强分层剪切层线性最优扰动的非线性演化
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
John Taylor
中科院分区：
文献类型：
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作者：
Alexis Kaminski;Colm‐cille P. Caulfield;John Taylor
Miles-howard定理指出，在并联，无关，稳定的分层剪切流程中，正常模式不稳定性的必要条件是，最小梯度Richardson号码，$ ri_ {g，min} $，小于$ 1/4 $但是，纳维尔 - 斯托克斯和浮力方程的非正常性可能会在有限的时间内实质性地扰动能量增长。最大化稳定分层的剪切层的扰动能量增益，该剪切层由具有特征速度的双曲线切线速度分布组成$ u_ {0}^{ast} $以及具有恒定浮力频率$ n_ {0}^{at ast} $的统一分层。我们更改批量Richardson Number $ ri_ {b} = n_ {0}^{ast 2} h^{ast 2}/u_ {0}^^ast 2} $（对应于$ ri_ {g，min} $）在0.20至0.50和雷诺之间数字$ MATHIT {re} = u_ {0}^{ast} h^{ast}/unicode [stix] {x1d708}^{ast}^{ast} $介于1000和8000之间，prandtl号码固定在$ Mathit {pr} {pr} = 1 $。 $ ri_ {g，min}> 1/4 $。 } $。 $ unicode [stix] {x1d700} _ {p}/（unicode [stix] {x1d700} _ {p}+unicode [stix] {x1d700} _ {k} _ {k} _ {k} _ {k}）$ p} $是密度方差的耗散率，$ unicode [stix] {x1d700} _ {k} $是动能的耗散率，对于最强烈的非线性案例而言约为0.35。
The Miles–Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the minimum gradient Richardson number, $Ri_{g,min}$ , is less than $1/4$ somewhere in the flow. However, the non-normality of the Navier–Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity $U_{0}^{ast }$ and a uniform stratification with constant buoyancy frequency $N_{0}^{ast }$ . We vary the bulk Richardson number $Ri_{b}=N_{0}^{ast 2}h^{ast 2}/U_{0}^{ast 2}$ (corresponding to $Ri_{g,min}$ ) between 0.20 and 0.50 and the Reynolds numbers $mathit{Re}=U_{0}^{ast }h^{ast }/unicode[STIX]{x1D708}^{ast }$ between 1000 and 8000, with the Prandtl number held fixed at $mathit{Pr}=1$ . We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where $Ri_{g,min}>1/4$ . We show that the effects of nonlinearity are more significant for flows with higher $mathit{Re}$ , lower $Ri_{b}$ and higher initial perturbation amplitude $E_{0}$ . Enhanced kinetic energy dissipation is observed for higher- $Re$ and lower- $Ri_{b}$ flows, and the mixing efficiency, quantified here by $unicode[STIX]{x1D700}_{p}/(unicode[STIX]{x1D700}_{p}+unicode[STIX]{x1D700}_{k})$ where $unicode[STIX]{x1D700}_{p}$ is the dissipation rate of density variance and $unicode[STIX]{x1D700}_{k}$ is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases.
随时间变化的混合层中的瞬态扰动增长
影响因子：
3.7
作者：
Arratia C
通讯作者：
Arratia C