引力波Turbulence对偶级联的直接证据
Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence
摘要：
本文首次对引力波湍流进行了直接数值模拟。广义相对论方程的数值求解周期框与对角度量张量取决于两个空间坐标，$g_{ij} \equiv g_{ii}(x,y,t) δ_{ij}$，并与一个额外的小尺度耗散项。我们只限于弱引力波和自由衰减的湍流。我们发现，在中间波数的初始度规激发导致能量和波作用的双重级联。当直接能量级联达到耗散尺度时，在能量从平台到幂律衰减的时间演化中观察到过渡，而逆级联前沿继续向低波数传播。的波数和频率-波数谱被发现是兼容的弱波湍流理论和双级联的特征时间尺度是预期的四波共振相互作用。模拟结果表明，一个最初弱的引力波湍流往往会变得强大的波动作用的逆级联的进展与选择性放大的波动$g_{11}$和$g_{22}$。
英文摘要：
We present the first direct numerical simulation of gravitational wave turbulence. General relativity equations are solved numerically in a periodic box with a diagonal metric tensor depending on two space coordinates only, $g_{ij} \equiv g_{ii}(x,y,t) δ_{ij}$, and with an additional small-scale dissipative term. We limit ourselves to weak gravitational waves and to a freely decaying turbulence. We find that an initial metric excitation at intermediate wavenumber leads to a dual cascade of energy and wave action. When the direct energy cascade reaches the dissipative scales, a transition is observed in the temporal evolution of energy from a plateau to a power-law decay, while the inverse cascade front continues to propagate toward low wavenumbers. The wavenumber and frequency-wavenumber spectra are found to be compatible with the theory of weak wave turbulence and the characteristic time-scale of the dual cascade is that expected for four-wave resonant interactions. The simulation reveals that an initially weak gravitational wave turbulence tends to become strong as the inverse cascade of wave action progresses with a selective amplification of the fluctuations $g_{11}$ and $g_{22}$.
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