Effect of Phase Noise on Parametric Instabilities

Abstract

We report an experimental study on the effect of an external phase noise on the parametric amplification of surface waves. We observe that both the instability growth rate and the wave amplitude above the instability onset are decreased in the presence of noise. We show that all the results can be understood with a deterministic amplitude equation for the wave in which the effect of noise is just to change the forcing term. All the data for the growth rate (respectively the wave amplitude), obtained for different forcing amplitudes and different intensities of the noise, can be collapsed on a single curve using this renormalized forcing in the presence of noise.

Wave-vortex interaction

“…2. Its dependence on the reduced control parameter ǫ = (a − a c )/a c is proportional to ǫ 1/4 , as it has been previously reported elsewhere [13]. No distinguishable hysteresis loop is found in the computed bifurcation diagrams.…”

“…This leads to an increase of threshold. For instance, this type of mechanism explains the increase of threshold observed for parametric forcing in the presence of phase noise [13]. The modification of the exponent can be also ascribed to an effective detuning if it has the correct sign with respect to the nonlinear frequency correction.…”

Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise

“…The curves show a linear dependence on Fr, which indicates the proper choice of a quintic subcritical bifurcation. Moreover, if we consider large values of ϵ in equation (7), and that ν is much smaller than γ for a relatively small bistability region, we obtain ϵ γ ≈ R 4 . From figure 9(b R is close to the mode of R, we can fit both bifurcation curves with the model given by equation (6).…”

“…In general, the existence and stability of the different states in driven systems is affected at different levels by the presence of fluctuations, which can be inherent to the system or added by an external mechanism. Sometimes, the net effect is that of shifting the critical value at which the bifurcation occurs [6,7], whereas in some other cases, the effect of the noise is more drastic and it can even change the nature of the bifurcation (i.e. sub or supercriticality) [8], or the nature of the saturation mechanism [9].…”

Subharmonic resonant excitation of edge waves by breaking surface waves

“…It has been revealed that chaotic phases decrease the effective amplitude of the external force (Petrelis et al, 2005). Suppose that the wave breaking leads to the Gaussian noise; then, the corresponding decrease in the external forcing may be estimated as (Petrelis et al, 2005) e…”