A prescribed wave probe reveals phase hidden vortex force memory in turbulence

Guoqiang Liu, Maryam AlShehhi

Phase averaging closes the equations of multi scale flows by removing bilinear couplings with vanishing one time means. Their two time correlations can still survive. We test this distinction for waves passing through turbulence. We study the stochastic vortex force in direct numerical simulation of homogeneous isotropic turbulence. This wave vorticity coupling is removed by classical phase averaging at one time. A prescribed analytic carrier and a modal projection fix the channel before any closure is applied. The resulting two time autocorrelation is finite and integrable. The fixed point measurement tests estimator selectivity. Three lock in controls suppress mismatched alternatives by up to four orders of magnitude. The trajectory measurement tests scale and geometry. In the audited clean support branch, the normalized response is concentrated near the wavelength matched eddy scale. A geometry control replaces the transverse SVF projection with the longitudinal vorticity component. The response peak then moves to a wavelength mismatched shell. In that channel, the mismatched shell is eighteen times stronger than the wavelength matched shell. This rules out a generic vorticity explanation. Sampling along the wave group velocity trajectory gives much faster decorrelation than the matched stationary baseline. The shortening is at least an order of magnitude. This contrast combines scale selection with moving frame sampling.The measurement recovers a real two time object inside a coupling that traditional averaging removes at one time. The same prescribed probe protocol can extract channel resolved memory from other phase suppressed bilinear couplings.