Pressure-strain redistribution as the mechanism for dissimilar heat transfer under spanwise wall oscillation waveforms

Abstract

Spanwise wall oscillation can enhance convective heat transfer disproportionately to its drag penalty, a departure from the Reynolds analogy termed dissimilar heat transfer (DHT). The companion study of Gu'erin et al. (2026) established that an optimised quasi-plateau waveform attains an analogy factor $\overline{A}n \approx 1.09$ at $Pr = 1$ and attributed this preferential thermal enhancement to the absence of a pressure-strain redistribution channel in the temperature variance equation, but the mechanism had not been quantitatively verified. The present study addresses this gap through phase-resolved variance transport budget analysis from direct numerical simulation of turbulent channel flow at $Reτ= 200$, $Pr = 1$. Two complementary pressure-mediated mechanisms are identified. At the Stokes-strain reversal, the pressure-strain redistribution $Π_{uu}$ imposes a pronounced drain on the streamwise velocity variance with no counterpart in the temperature variance equation: the divergence-free constraint redistributes momentum variance among velocity components but has no scalar analogue. During the quasi-steady plateau phases, the pressure-temperature-gradient correlation $Π_{vθ}$ preferentially enhances the wall-normal scalar flux relative to the momentum flux. The concentration of both mechanisms within the reversal and plateau phases, rather than at the Stokes-layer penetration maxima, identifies the duration of the quasi-steady phases as the controlling parameter for DHT enhancement, resolving the paradox whereby increased penetration depth does not produce increased dissimilarity.