# Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Physics-Based Approach

#### Physical Setup: Channel Flow with Low Prandtl Number Fluid

#### Energy Cascading

## 3. Theory–Statistics-Based Projection

#### Equivalence to the Advection–Diffusion Equation

## 4. Results and Discussion

#### 4.1. Data Learning: Estimating Moments

#### 4.2. Velocity Data and Surrogate

#### 4.3. Temperature Data and Surrogate

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Power Spectral Density (PSD) and probability density functions (PDF) comparison of the velocity fluctuations obtained from direct numerical simulations (DNS) data and model solution.

**Figure 10.**Spectrum of velocity and temperature data showing a significant difference in the scalar turbulence in liquid metal flow.

**Figure 11.**PSD and PDF comparison of the temperature fluctuations obtained from DNS data and model solution.

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**MDPI and ACS Style**

Ross, M.; Bindra, H. Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow. *Fluids* **2021**, *6*, 79.
https://doi.org/10.3390/fluids6020079

**AMA Style**

Ross M, Bindra H. Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow. *Fluids*. 2021; 6(2):79.
https://doi.org/10.3390/fluids6020079

**Chicago/Turabian Style**

Ross, Molly, and Hitesh Bindra. 2021. "Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow" *Fluids* 6, no. 2: 79.
https://doi.org/10.3390/fluids6020079