# Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Governing Equations and Boundary Conditions

^{1/2}. These conditions, as well as the Beavers-Joseph conditions, include an empirical parameter — the stress jump coefficient. The influence of the stress jump coefficient on the onset of thermal buoyancy convection in horizontal stratified fluid/porous layers was studied in Reference [14]. It was shown that the increase of the stress jump coefficient strongly influences the fluid mode, inducing a more unstable situation at large wave numbers, whereas the porous mode remains unchanged. In Reference [15], the onset of thermal buoyancy convection in a system consisting of a fluid layer overlying a homogeneous porous medium was studied in the framework of the model including the Brinkman term, in a two-domain approach. A comparison of neutral curves with those obtained in the one-domain approach and in the framework of the Darcy model with the two-domain approach shows that the inclusion of the Brinkman term plays a secondary role in the stability results.

## 3. Numerical Results

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**The dependences of stationary flow intensity on the parameter C for various values of $k$: ■—$k=1.0$, ▲—$k=1.2$, ●—$k=0.8$, ♦—$k=1.4$.

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**MDPI and ACS Style**

Lyubimova, T.P.; Muratov, I.D.
Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers. *Fluids* **2017**, *2*, 39.
https://doi.org/10.3390/fluids2030039

**AMA Style**

Lyubimova TP, Muratov ID.
Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers. *Fluids*. 2017; 2(3):39.
https://doi.org/10.3390/fluids2030039

**Chicago/Turabian Style**

Lyubimova, Tatyana P., and Igor D. Muratov.
2017. "Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers" *Fluids* 2, no. 3: 39.
https://doi.org/10.3390/fluids2030039