Direct Numerical Simulation of Air Heated Cylinder Wake in Transitional State, Part III: Temperature T* in Turbulence Anisotropy (TA), Turbulence of T*, Discontinuity and Dislocation B, and Their Causes in T* with Laminar PSD Gradient, PSD Oscillation, and Strongly Active Scalar

Abstract

The discontinuity (DC) and dislocation (DL) in a physical property, e.g., temperature T*, besides vortex spiral (SP) [1, 2], are extremely important for wake elucidation, but have not been studied yet. The power spectrum density (PSD) of T* always has a laminar (LA) gradient. Therefore a generation mechanism of DC and DL of T* is extremely different from that in SP [1, 2], and is first elucidated in the present study. Thus a need for presenting the present study is extremely strong. The air-heated wake (HW) at Reynolds number Re = 300 and Richardson number Ri = 0.3 is generated by three-dimensional (3-D), time-dependent direct numerical simulation (DNS), and arises above a heated horizontal circular cylinder in upward mainstream.

1. The PSD of T* in the HW is composed of the LA-PSD gradient and PSD oscillation. The former cannot generate extreme instability in T*, which arises only in the latter, but is weak.

2. T* has the motion of spanwise velocity w with turbulence. The PSD of T* therefore has PSD oscillation, slight turbulence, and an LA-like state that is PSD with LA gradient and PSD oscillation [with turbulence triggered by strong turbulence anisotropy (strong TA, STA) with w] arising only in the scalar field.

3. “Generation of DL in the LA-like state” is as follows. A role of STA and w is the turbulence generation in PSD oscillation in T* triggered by STA and w. DL in T* does not arise in LA fluctuation but arises due to turbulence in T* in PSD oscillation.

4. DL is of two kinds. One is DL-A, arising in the transitional region [1, 2] in the SP [2], and having vortex dislocation (VD) [2] in the vector field. The other is DL-B, arising in the LA-like T* due to PSD oscillation in T* in the scalar field.

5. Ri = 0.3 is an extremely slight heating rate. The isothermal wake (IW) and HW have similar PSDs of u and v. The T* at Ri = 0.3 is a strongly active scalar, and leads to the extremely different PSD of only w from the IW and the suppression of 3-D in the wake.