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# Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence

Abstract : 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, $gij≡gii(x,y,t)δij$, 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 wave number 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 wave numbers. The wave number and frequency-wave-number spectra are found to be compatible with the theory of weak wave turbulence and the characteristic timescale 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 $g11$ and $g22$.
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Journal articles

https://hal.archives-ouvertes.fr/hal-03326816
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Submitted on : Thursday, August 26, 2021 - 2:50:10 PM
Last modification on : Sunday, May 1, 2022 - 3:17:29 AM

### Citation

Sebastien Galtier, Sergey V. Nazarenko. Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence. Phys.Rev.Lett., 2021, 127 (13), pp.131101. ⟨10.1103/PhysRevLett.127.131101⟩. ⟨hal-03326816⟩

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