Title: Two-dimensional turbulent condensates without bottom drag Show Chinese title

Title: 二维湍流凝聚体无底部拖曳

Abstract: The extent to which statistical equilibrium theory is applicable to driven dissipative dynamics remains an important open question in many systems. We use extensive direct numerical simulations of the incompressible two-dimensional (2D) Navier-Stokes equation to examine the steady state of large-scale condensates in 2D turbulence at finite Reynolds number $Re$ in the absence of bottom drag. Large-scale condensates appear above a critical Reynolds number $Re_c\approx 4.19$. Close to this onset, we find a power-law scaling of the energy with $Re-Re_c$, with the energy spectrum at large scales following the absolute equilibrium form proposed by Kraichnan. At larger $Re$, the energy spectrum deviates from this form, displaying a steep power-law range at low wave numbers with exponent $-5$, with most of the energy dissipation occurring within the condensate at large scales. We show that this spectral exponent is consistent with the logarithmic radial vorticity profile of the condensate vortices predicted by quasi-linear theory for a viscously saturated condensate. Our findings shed new light on the classical problem of large-scale turbulent condensation in forced dissipative 2D flows in finite domains, showing that the large scales are close to equilibrium dynamics in weakly turbulent flows but not in the strong condensate regime with $Re\gg1$. Show Chinese abstract

Abstract: 统计平衡理论在驱动耗散动力学中的适用程度仍然是许多系统中的一个重要开放问题。 我们使用不可压缩二维(2D)纳维-斯托克斯方程的大量直接数值模拟，来研究在无底部阻力的情况下，有限雷诺数$Re$下二维湍流中大尺度凝聚体的稳态。 大尺度凝聚体出现在临界雷诺数$Re_c\approx 4.19$以上。 在接近这一阈值时，我们发现能量与$Re-Re_c$呈现幂律标度，大尺度的能量谱遵循Kraichnan提出的绝对平衡形式。 在较大的$Re$时，能量谱偏离此形式，在低波数处表现出陡峭的幂律范围，指数为$-5$，大部分能量耗散发生在大尺度的凝聚体中。 我们表明，这种谱指数与粘性饱和凝聚体的准线性理论预测的凝聚体涡旋的对数径向涡度分布是一致的。 我们的发现为有限区域内强制耗散二维流动中的经典大尺度湍流凝聚问题提供了新的见解，表明在弱湍流中大尺度接近平衡动力学，但在具有$Re\gg1$的强凝聚体区域则不然。