On the competition of transverse and longitudinal modes of Marangoni convection in a three-dimensional layer of viscoelastic fluid

Abstract

Within the vast array of applications encompassed by viscoelastic fluids, some lack of knowledge seems to affect the non-linear behavior of Marangoni convection when its typical initial unicellular and steady states are taken over by more complex flow configurations. These still hide a not-fully understood competition of complex and diverse physical mechanisms that determine the prevailing macroscopic behavior. In the present study, relevant insights are sought from consideration of the classical differentially heated rectangular layer of liquid with adiabatic bottom and top free surface. It is shown that, for increasing values of the Marangoni number and/or the elasticity parameter, this problem offers a multifaceted spectrum of different outcomes depending on the non-trivial interplay established between two distinct categories of disturbances (transverse and longitudinal). These are studied using a diversity of model types in which some processes are on or off to discern selectively their effect in the laminar state and their contribution to the evolution of the system toward chaos. The characteristic marks by which the ensuing elastic turbulence can be distinguished from the companion Kolmogorov counterpart are highlighted through analysis of the emerging scaling laws in the velocity spectrum and the sensitivity of these to the intensity of the driving force and the considered elasticity level. It is shown that these two forms of turbulence can coexist in the considered problem.