Maximum drag enhancement asymptote in spanwise-rotating viscoelastic plane Couette flow of dilute polymeric solutions

Abstract

The existence of a maximum drag enhancement (MDE) asymptote at high rotation ( $Ro$ ) and Weissenberg ( $Wi$ ) numbers in turbulent viscoelastic spanwise-rotating plane Couette flow has been demonstrated. Specifically, it is shown that above a critical $Wi$ , drag enhancement plateaus and the MDE asymptote is realized in a broad range of $Ro$ . The mean velocity profiles at MDE appear to closely follow a log-law profile that has a nearly identical slope but different intercepts as a function of $Ro$ . Much like the maximum drag reduction (MDR) asymptote, the logarithmic function in MDE is closely followed if the mean velocity is plotted using the traditional inner variable scaling; however, the logarithmic function is not well defined when examined by the indicator function. Hence, in this study, we have used the logarithmic fit as a visual guide for the mean velocity profile. Last and perhaps the most intriguing finding of this study is that MDE occurs in the elasto-inertial turbulence (EIT) flow state; hence, it is mainly sustained by elastic forces much like the MDR flow state. To that end, a universal picture of elastically induced drag modification asymptotes is emerging, namely these asymptotic states are an inherent property of the elastically sustained EIT flow state.