Inherent nonlinearity of fluid motion and acoustic gravitational wave memory

Analogue gravitational field from nonlinear fluid dynamics

“…This can be analytically shown from the method of characteristics to solve the Riemann wave equation [55]. For a simple wave with initial profile (at t = 0) v = A cos kx, t shock = 2 (γ+1)Ak [56].…”

“…If the observation time in any experiment fulfills t obs < t lin , then the solution of the Riemann wave equation can be considered as a massless field over the background (i). Writing the originally 3 + 1D metric in a quasi-1D system in 1 + 1D form [56], we simply have (omitting a constant conformal factor ρ 0 /c s0 )…”

“…As a first option (1), for t < t lin , the Riemann wave is considered as a massless scalar field; for t t lin , background (i) is reverted to background (ii), and one defines a new perturbation Φ (1) , which again varies faster than the Riemann wave. The background is redefined, the Riemann wave is itself the background, leading to the new acoustic 1 + 1D metric of type (ii), again taking over the conformal factors from the 3 + 1D embedding space of a quasi-1D system [56],…”

“…From equation (56), we also have For a non-simple wave, we have to consider both δJ + and δJ − which are related to h tx and h xx by equation (61). Therefore, we only look at the source terms for the h tx and h xx components, note h tt is not an independent quantity, but is related to h xt and h xx via equation (60).…”