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In recent years, scale-by-scale energy transport in wall turbulence has been intensively studied, and the complex spatial and interscale transfer of turbulent energy has been investigated. As the enhancement of heat transfer is one of the most important aspects of turbulence from an engineering perspective, it is also important to study how turbulent heat fluxes are transported in space and in scale by nonlinear multi-scale interactions in wall turbulence as well as turbulent energy. In the present study, the spectral transport budgets of turbulent heat fluxes are investigated based on direct numerical simulation data of a turbulent plane Couette flow with a passive scalar heat transfer. The transport budgets of spanwise spectra of temperature fluctuation and velocity-temperature correlations are investigated in detail in comparison to those of the corresponding Reynolds stress spectra. The similarity and difference between those scale-by-scale transports are discussed, with a particular focus on the roles of interscale transport and spatial turbulent diffusion. As a result, it is found that the spectral transport of the temperature-related statistics is quite similar to those of the Reynolds stresses, and in particular inverse interscale transfer is commonly observed throughout the channel in both transport of the Reynolds shear stress and wall-normal turbulent heat flux

Nonlinear interaction between different scales in turbulence results in both interscale and spatial transport of turbulent energy, and the role of such scale interactions in turbulent heat transfer mechanism is also of practical importance from the engineering viewpoint. In the present study, we investigate a turbulent plane Couette flow with passive-scalar heat transfer at the Prandtl number 0.71, in order to address the similarity/difference between the scale interactions in the velocity and temperature fields. The constant-temperature-difference boundary condition is used so that the mean velocity and temperature profiles are similar, and then the roles of interscale and spatial transports are compared for the spectral transport budgets of the turbulent energies and temperature-related statistics. We show that turbulent heat transfer occurs at relatively small streamwise length scales compared to momentum transfer, although molecular diffusion is more significant in the temperature field as the Prandtl number is less than 1. Detailed analysis on the transport budgets of the temperature-related spectra shows that scale interactions in temperature field supply more energy to small scales than those in velocity field. Such significant temperature cascade leads to more energetic temperature fluctuation at small scales, which eventually results in the dissimilarity between the spectra of turbulent heat and momentum transfers.

Interscale energy transfer in wall turbulence has been intensively studied in recent years, and both the forward (i.e. from larger to smaller scales) and reversed transfers of turbulent energy have been found whereas their corresponding physical phenomena have not been revealed. In the present study, we perform DNS of turbulent plane Couette flow with reduced-size computational domains, where either the streamwise or spanwise domain size is reduced to their minimal lengths, aiming at elucidating the role of scale interactions in each direction. Our computational results with the streamwise-minimal domain suggest that the interplays between streamwise-elongated streaks and vortices smaller than the streamwise minimal length are the essential scale interactions for both the inner and outer structures. We further show that these streamwise-independent and smaller-scale structures exchange energy through forward and reversed interscale energy transfers, and the reversed energy transfer maintains the energy production at larger scales. Based on the resemblance of the observed Reynolds-stress transport and the scenario of the self-sustaining cycle, we conjecture that the forward and reversed energy transfers mainly represent the streak instabilities and regeneration of streamwise vortices, respectively. Furthermore, the computation with the spanwise-minimal domain indicates that the interscale energy transfers observed by one-dimensional spanwise spectral analysis are likely related to individual dynamics of each inner and outer structure, rather than represent their interactions.

For the clarification of the routes to elasto-inertial turbulence (EIT), it is essential to understand how viscoelasticity modulates coherent flow structures including the longitudinal vortices. We focused on a rotating plane Couette flow that provides two-dimensional (2D) roll cells for the steady laminar Newtonian-fluid case, and we investigated how the steady longitudinal vortices are modulated by viscoelasticity at different Weissenberg numbers. The viscoelasticity was found to induce an unsteady flow state where the 2D roll-cell structure was periodically enhanced and damped with a constant period, keeping the homogeneity in the streamwise direction. This pulsatile motion of the roll cell was caused by a time lag in the response of the viscoelastic force to the vortex development. Both the pulsation period and time lag were found to be scaled by the turnover time of cell rotation rather than by the relaxation time, despite the viscoelasticity-induced instability. We also discuss the counter torque on the roll cell and the net energy balance, considering their relevance to polymer drag reduction and EIT., Comment: 26 pages, 18 figures

An alternative step in understanding the flows of near wall drag-reducing turbulence can be examining the flow in a well-organized streamwise vortex with a laminar background. Herein, we studied the flow behaviors of the Giesekus viscoelastic fluid in a rotating plane Couette flow system, which is accompanied by steady roll cell structures. By fixing the Reynolds and rotation numbers at values that provide as steady wavy roll cell, i.e., an array of meandering streamwise vortices, the Weissenberg number was increased up to 2000 (where the relaxation time was normalized by the wall speed and the kinematic viscosity). We observed that, in the viscoelastic flows, the secondary flow (wall-normal and spanwise velocity fluctuations) are suppressed while the streamwise component is maintained, and the wavy roll cells are modulated into streamwise-independent straight roll cells. The kinetic energy transports among the mean shear flow, Reynolds stresses due to the roll cell, and viscoelastic stress are investigated in the non-turbulent background. We further discussed the modulation mechanism and its relevance to the drag reduction phenomenon in the viscoelastic wall turbulence., Comment: 24 pages, 15 figures

A counter-rotating Taylor-Couette flow with relatively small radius ratios of $\eta$ = 0.2--0.5 was investigated over a wide range of the Reynolds number, from laminar to turbulent regime, by means of three-dimensional direct numerical simulations. We investigated the $\eta$ dependence of the flow structure and determined a critical value between $\eta$ = 0.2 and 0.3, below which, the stable outer cylinder side exhibited a modal structure that was different from the Taylor-vortex flow on the inner side. At $\eta \geq$ 0.3, the Taylor-vortex on the unstable inner side dominated the entire flow field between the cylinders, whose footprints were observed in the vicinity of the outer cylinder wall. However, for $\eta$ = 0.2, the influence from the inner side was limited up to the centre of the cylinder gap. Moreover, on the stable outer cylinder side, there appeared a modal structure that was axially homogeneous, azimuthally periodic, and similar to the Tollmien-Schlichting (TS) instability wave. As the Reynolds number increased with a fixed $\eta$ = 0.2, the modal structure changed its azimuthal wavenumber and thickened radially in the wall unit. Although the Reynolds shear stress on the outer side remained approximately zero, the intensity of the velocity fluctuations was comparable to the Taylor-vortex flows in the central part., Comment: 14 pages, 13 figures