标题： 引力波湍流中的非对称双级联 显示英文标题

标题： Asymmetric dual cascade in gravitational wave turbulence

摘要： 我们在强制和衰减两种情况下，对从强局部四次相互作用极限下引力波湍流的运动方程推导出的四阶非线性扩散方程进行了数值模拟。 当在中间波数$k_i$施加强迫时，我们观察到能量和波作用量的双重级联。 在稳态下，相关的通量比与$k_i$成正比，并恢复了Kolmogorov-Zakharov谱。 在衰减湍流中，研究显示波作用量谱可以扩展到大于初始激发波数$k_i$的范围，且具有恒定的负通量，而能量通量为正，并与$k$呈幂律依赖关系。 这导致了一个意外的结果：一个单一的惯性范围，其Kolmogorov-Zakharov波作用量谱逐渐扩展到大于$k_i$的波数。 我们还观察到在$t^{-1/3}$时波作用量随时间衰减，而能量谱的前沿则按照$t^{1/3}$法则传播。 这些特性可以通过简单的理论论证来理解。 显示英文摘要

摘要： We numerically simulate, in both the forced and decay regimes, a fourth-order nonlinear diffusion equation derived from the kinetic equation of gravitational wave turbulence in the limit of strongly local quartic interactions. When a forcing is applied to an intermediate wavenumber $k_i$, we observe a dual cascade of energy and wave action. In the stationary state, the associated flux ratio is proportional to $k_i$, and the Kolmogorov-Zakharov spectra are recovered. In decaying turbulence, the study reveals that the wave action spectrum can extend to wavenumbers greater than the initial excitation $k_i$ with constant negative flux, while the energy flux is positive with a power law dependence in $k$. This leads to an unexpected result: a single inertial range with a Kolmogorov-Zakharov wave action spectrum extending progressively to wavenumbers larger than $k_i$. We also observe a wave action decay in time in $t^{-1/3}$ while the front of the energy spectrum progresses according to a $t^{1/3}$ law. These properties can be understood with simple theoretical arguments.