Inverse cascade in film flows

Abstract

Developed interfacial dynamics of thin film flows with moderate Reynolds numbers exhibits a remarkable feature: the evolution is dominated by solitary-like pulses with a natural large wavelength between them. This phenomenon is robust and resembles the inverse energy cascade in two-dimensional turbulence. A new simple evolution equation is proposed to describe the film flow dynamics which captures such an inverse cascade. The equation combines the simplest kinematic nonlinearity with the exact linear term. The spectral kernel of the linear term is found from the numerical solution of the associated linear stability problem.