The Tilting Mechanism of a Longitudinal Vortical Structure in a Homogeneous Shear Flow with and Without Spanwise Rotation

Abstract

A longitudinal vortical structure is typically observed in near-wall turbulence. This vortical structure is elongated in the streamwise direction, though it is also tilted in the spanwise direction. The sense of this spanwise tilting is determined by the sign of the streamwise vorticity associated with the vortex, and longitudinal vortical structures with a different streamwise vorticity become asymmetric (mirror symmetric). The tilting must be due to the combined effects of the non-linear terms and mean spanwise vorticity associated with the mean shear. However, the detailed mechanism of the tilting is not well known. To study the tilting in detail, we performed direct numerical simulations of a homogeneous shear flow where the longitudinal vortical structures similar to those in the near-wall region are observed. In particular, the effects of spanwise system rotation as well as the Reynolds number on the vortical structure are studied. As a result, we found that spanwise system rotation has more marked effects on the vortical structure than the Reynolds number. When the system rotation is imposed in the same direction as the mean spanwise vorticity, the tilting is enhanced, while the system rotation of the opposite direction attenuates it. We also found that when the longitudinal vortical structure is tilted in the spanwise direction, it is sandwiched between the streamwise vorticity of the opposite sign. The cyclonic rotation enhances the streamwise vorticity of the opposite sign, though the longitudinal vortical structure at the center is attenuated. In the anticyclonic case, the streamwise vorticity of the opposite sign almost disappears and the longitudinal vortical structure is isolated from the surrounding flow.

Computer Experiments on Rapidly Rotating Plane Couette Flow

“…In practice the computational grid often moves with the mean flow in the latter case. The inevitable skewing of the grid cells thus calls upon a re-meshing at regular time intervals [9,16]. Another attractive feature of the present flow is the fact that the imposed system rotation vector is consistently anti-parallel with the mean flow vorticity vector and the flow field is everywhere exposed to anti-cyclonic rotation.…”

“…The central core region of a rotating Couette flow bears some resemblances with homogeneous shear flow subjected to system rotation. Rotating homogeneous shear flows have been considered both theoretically and numerically, including the computer simulations by Bartello et al [5], Salhi and Cambon [35], Yanase et al [40], Brethouwer [9] and Iida et al [16]. Rotating homogeneous shear flows are known to be neutrally stable if the vorticity ratio S = −1.0 [11,35].…”

“…Yanase et al [40] and Brethouwer [9] found that the flow field was dominated by very elongated and intense streamwise vortex tubes. Iida et al [16] focused on S = ±0.5 with the view to investigate the tilting mechanism of the longitudinal vortex structures. Here, anti-cyclonic rotation S = −1/2 corresponds to zero-tilting vorticity and maximum destabilization (B = −1/4) according to Cambon et al [11].…”

“…Here, anti-cyclonic rotation S = −1/2 corresponds to zero-tilting vorticity and maximum destabilization (B = −1/4) according to Cambon et al [11]. Iida et al [16] examined the influence of spanwise system rotation on the vertical flow structures and observed that the spanwise tilting of the structures was reduced whereas their inclination with respect to the mean flow direction was increased.…”