Nonlinear scalings emerge in a linear regime: an observation in electrokinetic flow
In nonlinear systems, small perturbations are conventionally attributed to negligible nonlinearity, justifying linear approximations. Here, we uncover a notable exception to this paradigm in an electrokinetic (EK) flow. Using a novel dual frequency excitation scheme with two high frequency AC electric fields ($> 10^{5}$ Hz), we efficiently excite flow perturbations at a difference frequency ($Δf$) four orders of magnitude lower. This approach reveals a strong nonlocal energy transfer mechanism mediated purely by the nonlinearity of the electric body force, enabling precise, clean flow control free from electrode polarization artifacts. Unexpectedly, these small, nominally linear velocity and electric conductivity fluctuations exhibit power law spectra. With increasing electric Rayleigh number, the scaling exponents agree quantitatively with predictions for fully developed EK turbulence by the Quad cascade process theory. This observation not only implies multiple flow state transitions even at low excitations, but also indicates that intrinsic nonlinearity regulates perturbations even in the linear regime, necessitating a fundamental re examination of linear approximations in electrohydrodynamics and other nonlinear systems.