Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence
Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence
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DOI：
10.1016/s0167-2789(02)00391-3
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发表时间：
2002-05-15
影响因子：
4
通讯作者：
Shepherd, TG
中科院分区：
文献类型：
--
作者：
Tran, CV;Shepherd, TG
我们研究二维（2D）湍流的双周期域驱动的单尺度强迫和阻尼的各种形式的耗散机制uppermum（μ）（-Delta）（μ）。所谓“单尺度类”，我们的意思是强迫作用在有限的波数范围内，k（min）小于或等于k小于或等于k（max），涡度拟能注入eta大于或等于0与能量注入eta大于或等于0的比率由k（min）（2）n小于或等于eta小于或等于k（max）（2）n限制。这种强迫在二维湍流的理论和数值研究中经常被考虑。当μ大于或等于0时，渐近行为满足平行touparallel to（1）（2）小于或等于k（max）（2）平行touparallel to（2），其中平行touparallel to（2）和平行touparallel to（1）（2）分别是能量和拟能.如果类单尺度强迫的条件仅在时间平均意义上成立，则不等式在时间平均意义上成立。对于Navier-Stokes湍流（mu = 1），时间平均涡度拟能耗散率从上到下的界为2upperm（1）k（max）（2）。这些结果的能量和涡度拟能的谱分布和它们的耗散，从而对能量和涡度拟能级联的存在，在这样的系统中的强烈约束。特别是，经典的双叶栅图片被证明是无效的强制二维Navier-Stokes湍流（mu = 1）时，它是被迫以这种方式。包含Ekman阻力（mu = 0）沿着分子粘度允许双重级联，但与能谱在拟能级联惯性范围内的对数修正幂律不相容。为了实现后者，需要调用逆粘度（mu < 0）。这些对容许幂律的限制适用于任何光谱定域强迫，而不仅仅是单尺度强迫。(C)2002 Elsevier Science B. V.保留所有权利。
We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form upsilon(mu) (-Delta)(mu). By "monoscale-like" we mean that the forcing is applied over a finite range of wavenumbers k(min) less than or equal to k less than or equal to k(max), and that the ratio of enstrophy injection eta greater than or equal to 0 to energy injection epsilon greater than or equal to 0 is bounded by k(min)(2)epsilon less than or equal to eta less than or equal to k(max)(2)epsilon. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for mu greater than or equal to 0 the asymptotic behaviour satisfies parallel touparallel to(1)(2) less than or equal to k(max)(2)parallel touparallel to(2), where parallel touparallel to(2) and parallel touparallel to(1)(2) are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier-Stokes turbulence (mu = 1), the time-mean enstrophy dissipation rate is bounded from above by 2upsilon(1)k(max)(2). These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier-Stokes turbulence (mu = 1) when it is forced in this manner. Inclusion of Ekman drag (mu = 0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified -3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (mu < 0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing. (C) 2002 Elsevier Science B.V. All rights reserved.