Oscillatory force generation in nonequilibrium systems from peaked energy spectra.*

A key to force generation in non-equilibrium systems is encoded in their energy fluctuation spectra. A non-equipartition of energy, which is only possible in active or forced systems, can lead to a non-monotonic fluctuation spectrum. Recently, it has been shown that for a narrow, unimodal spectrum, the force exerted by a non-equilibrium system on two walls embedded in a system with such a spectrum oscillates between repulsion and attraction as a function of wall separation [1]. These results are consistent with the Maritime Casimir effect, which is driven by wind-water interactions, and with recent simulations of active Brownian particles. The spectrum is believed to be the solution of a specific class of Fokker-Planck equations. Taking a hydrodynamic perspective of Janssen [2], we construct a theory and a numerical basis for the observed Pierson and Moskovitz spectrum, which underlies the Maritime Casimir effect.

[1] A. A. Lee, D. Vella and J.S. Wettlaufer, Fluctuation spectra and force generation in nonequilibrium systems, Proc. Nat. Acad. Sci. USA. 114, 9255 (2017).
[2] P. Janssen, Quasilinear approximation for the spectrum of wind-generated water waves, J. Fluid Mech. 117, 493 (1982).