# Coherent Vortical Structures and Their Relation to Hot/Cold Spots in a Thermal Turbulent Channel Flow

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Procedure

## 3. Results

#### 3.1. Mean Velocity and Temperature Field

#### 3.2. Fluctuations of Velocity and Temperature

#### 3.3. Hot Spots Near the Wall

#### 3.4. Turbulent Heat Fluxes

#### 3.5. Generation of Vortex Structures

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Mean streamwise velocity variation and (

**b**) mean temperature variation in the wall normal direction behind the jets.

**Figure 3.**Variation of (

**a**) streamwise velocity fluctuations; (

**b**) wall normal velocity fluctuations; and (

**c**) temperature fluctuations downstream, behind the jets.

**Figure 4.**(

**a**) Instantaneous and (

**b**) mean temperature contours at ${y}^{+}=5$ on the $xz$ plane. Both instantaneous and mean temperatures are normalized by ${\mathsf{\Theta}}_{bw}$ and ${\mathsf{\Theta}}_{tw}$, as shown in Section 2.

**Figure 5.**The variation of turbulent heat fluxes on the $xy$ plane. (

**a**) $\overline{{u}^{\prime}{\theta}^{\prime}}$ along the jets and (

**b**) $\overline{{v}^{\prime}{\theta}^{\prime}}$ along the jets.

**Figure 6.**The two-point correlation of streamwise velocity fluctuations, ${\rho}_{uu}$ (

**a**) behind the jets and (

**b**) between the jets.

**Figure 7.**${\lambda}_{2}$ contours colored with instantaneous temperature. The inset is a zoomed-in view of the flow field near the jets. The dashed white line shows the centerline of the jets. The iso-surfaces are drawn for ${\lambda}_{2}=-3$.

**Figure 8.**Iso-contours of ${\lambda}_{2}$ vortices at (

**a**) $1D$ and (

**b**) $3D$ downstream of the jets. The iso-contours are drawn for ${\lambda}_{2}=-3$. The instantaneous realization corresponds to $t=2200$.

**Figure 9.**A schematic of hairpin vortices generated downstream of blowing. Wall-normal and streamwise velocity fluctuations are shown with respect to the vortex structure generation.

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**MDPI and ACS Style**

Dharmarathne, S.; Pulletikurthi, V.; Castillo, L.
Coherent Vortical Structures and Their Relation to Hot/Cold Spots in a Thermal Turbulent Channel Flow. *Fluids* **2018**, *3*, 14.
https://doi.org/10.3390/fluids3010014

**AMA Style**

Dharmarathne S, Pulletikurthi V, Castillo L.
Coherent Vortical Structures and Their Relation to Hot/Cold Spots in a Thermal Turbulent Channel Flow. *Fluids*. 2018; 3(1):14.
https://doi.org/10.3390/fluids3010014

**Chicago/Turabian Style**

Dharmarathne, Suranga, Venkatesh Pulletikurthi, and Luciano Castillo.
2018. "Coherent Vortical Structures and Their Relation to Hot/Cold Spots in a Thermal Turbulent Channel Flow" *Fluids* 3, no. 1: 14.
https://doi.org/10.3390/fluids3010014