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Journal Articles Physical Review Letters Year : 2021

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, gijgii(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.

Dates and versions

hal-03326816 , version 1 (26-08-2021)

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