# Convective Flow in an Aquifer Layer

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## Abstract

**:**

## 1. Introduction

## 2. Governing Systems and Solutions

#### 2.1. Basic State Solutions

#### 2.2. Linear Problem (Order ${\u03f5}^{1}{\delta}^{0}$ and ${\u03f5}^{1}{\delta}^{1}$)

#### 2.2.1. Zeroth Order

#### 2.2.2. Order of $\u03f5\delta $

## 3. Nonlinear Problem

#### 3.1. Order of ${\u03f5}^{2}{\delta}^{0}$

#### 3.2. Order of ${\u03f5}^{2}{\delta}^{1}$

## 4. Results

#### 4.1. One-Dimensional Results for the Vertical Dependence of Linear Solutions:

#### 4.2. Two-Dimensional Results for ${W}_{10}(x.z),{\theta}_{10}(x,z),{W}_{11}(x,z),{\theta}_{11}(x,z),{W}_{20}(x,z):$

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Linear 1D solution for $W$, i.e., $\u03f5\left({W}_{10}\left(z\right)+\delta {W}_{11}\left(z\right)\right)$.

**Figure 7.**Linear 1D solution for $\theta $, i.e., $\u03f5\left({\theta}_{10}\left(z\right)+\delta {\theta}_{11}\left(z\right)\right)$.

**Figure 8.**Linear 1D solution for $W$, i.e., $\u03f5\left({W}_{10}\left(z\right)+\delta {W}_{11}\left(z\right)\right)$.

**Figure 9.**Linear 1D solution for $\theta $ i.e., $\u03f5\left({\theta}_{10}\left(z\right)+\delta {\theta}_{11}\left(z\right)\right)$.

**Figure 12.**Linear 2D solution for $W,$ i.e., $\u03f5\left({W}_{10}(x,z)+\delta {W}_{11}(x,z)\right)$.

**Figure 13.**Linear 2D solution for $\theta ,$ i.e., $\u03f5\left({\theta}_{10}(x,z)+\delta {\theta}_{11}(x,z)\right)$.

**Figure 14.**Linear 2D solution for $W$, i.e., $\u03f5\left({W}_{10}(x,z)+\delta {W}_{11}(x,z)\right)$.

**Figure 15.**Linear 2D solution for $\theta $, i.e., $\u03f5\left({\theta}_{10}(x,z)+\delta {\theta}_{11}(x,z)\right)$.

**Figure 16.**Nonlinear 2D solution for $W$, i.e., $\u03f5\left({W}_{10}(x,z)+\delta {W}_{11}(x,z)+\u03f5{W}_{20}(x,z)\right)$.

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**MDPI and ACS Style**

Bhatta, D.; Riahi, D.
Convective Flow in an Aquifer Layer. *Fluids* **2017**, *2*, 52.
https://doi.org/10.3390/fluids2040052

**AMA Style**

Bhatta D, Riahi D.
Convective Flow in an Aquifer Layer. *Fluids*. 2017; 2(4):52.
https://doi.org/10.3390/fluids2040052

**Chicago/Turabian Style**

Bhatta, Dambaru, and Daniel Riahi.
2017. "Convective Flow in an Aquifer Layer" *Fluids* 2, no. 4: 52.
https://doi.org/10.3390/fluids2040052