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Journal of Fluids Engineering | Volume 136 | Issue 6 | Special Section Articles
Special Section Articles

Multiscale Nested Simulations of Rayleigh–Taylor Instabilities in Ionospheric Flows

[+] Author and Article Information
Alex Mahalov

The Wilhoit Foundation Dean's
Distinguished Professor
Center for Environmental Fluid Dynamics,
Global Institute of Sustainability,
School of Mathematical and Statistical Sciences,
Arizona State University,
Tempe, AZ 85287-1804
e-mail: mahalov@asu.edu

Mohamed Moustaoui

Associate Professor
Center for Environmental Fluid Dynamics,
Global Institute of Sustainability,
School of Mathematical and Statistical Sciences,
Arizona State University,
Tempe, AZ 85287-1804
e-mail: mohamed.moustaoui@asu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 7, 2013; final manuscript received July 28, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060908 (Apr 28, 2014) (8 pages) Paper No: FE-13-1222; doi: 10.1115/1.4025657 History: Received April 07, 2013; Revised July 28, 2013
Article
References
Figures
Citing Articles

Nested numerical simulations of ionospheric plasma density structures associated with nonlinear evolution of the Rayleigh–Taylor (RT) instability in equatorial spread F (ESF) are presented. The numerical implementation of the nested model uses a spatial discretization with a C grid staggering configuration where normal velocities of ions and electrons are staggered one-half grid length from the density of charged particles. The advection of charged particles is computed with a fifth order accurate in space weighted essentially nonoscillatory (WENO) scheme. The continuity equation is integrated using a third-order Runge–Kutta (RK) time integration scheme. The equation for the electric potential is solved at each time step with a multigrid method. For the limited area and nested simulations, the lateral boundary conditions are treated via implicit relaxation applied in buffer zones where the density of charged particles for each nest is relaxed to that obtained from the parent domain. The high resolution in targeted regions offered by the nested model was able to resolve secondary RT instabilities, and to improve the resolution of the primary RT bubble compared to the coarser large domain model. The computational results are validated by conducting a large domain simulation where the resolution is increased everywhere.
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References

1
Zhou, Y., Remington, B. A., Robey, H. F., Cook, A. W., Glendinning, S. G., Dimits, A., Buckingham, A. C., Zimmerman, G. B., Burke, E. W., Peyser, T. A., Cabot, W., and Eliason, D., 2003, “Progress in Understanding Turbulent Mixing Induced by Rayleigh–Taylor and Richtmyer–Meshkov Instabilities,” Phys. Plasmas, 10, pp. 1883–1896. [CrossRef]
2
Tang, W., and Mahalov, A., 2013, “Stochastic Lagrangian Dynamics for Charged Flows in the E–F Regions of Ionosphere,” Phys. Plasmas Am. Inst. Phys., 20(3), 032305. [CrossRef]
3
Berkner, L. V., and Wells, H. W., 1934, “F Region Ionosphere—Investigation at Low Latitudes,” Terres. Magn., 39, pp. 215–230. [CrossRef]
4
Woodman, R. F., and La Hoz, C., 1976, “Radar Observation of F Region Equatorial Irregularities,” Geophys Res., 81, pp. 5447–5466. [CrossRef]
5
Basu, S., Basu, S., Aarons, J., McClure, J. P., and Cousins, M. D., 1978, “On the Coexistence of Kilometer- and Meter-Scale Irregularities in the Nighttime Equatorial F Region,” J. Geophys Res, 83, pp. 4219–4226. [CrossRef]
6
Fejer, B. G., and Kelley, M. C., 1980, “Ionospheric Irregularities,” Rev. Geophys., 18, pp. 401–454. [CrossRef]
7
Kelley, M. C., Larson, M. F., La Hoz, C., and McClure, J. P., 1981, “Gravity Wave Initiation of Equatorial Spread F: A Case Study,” J. Geophys Res., 86, pp. 9087–9100. [CrossRef]
8
Tsunoda, R. T., 1983, “On the Generation and Growth of Equatorial Backscatter Plume. Structuring of the Westwalls of Upwelling,” J. Geophys. Res., 88, pp. 4869–4874. [CrossRef]
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Scannapieco, A. J., and Ossakow, S. L., 1976, “Nonlinear Equatorial Spread F,” Geophys. Res. Lett., 3, pp. 451–454. [CrossRef]
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Ossakow, S. L., 1981, “Spread F Theories. A Review,” J. Atmos. Terr. Phys., 43, pp. 437–452. [CrossRef]
11
Raghavarao, R., Sekar, R., and Suhasini, R., 1992, “Nonlinear Numerical Simulation of Equatorial Spread F: Effects of Winds and Electric Fields,” Adv. Space Res., 12, pp. 227–230. [CrossRef] [PubMed]
12
Sekar, R., Suhasini, R., and Raghavarao, R., 1994, “Effects of Vertical Winds and Electric Fields in the Nonlinear Evolution of Equatorial Spread F,” J. Geophys. Res., 99, pp. 2205–2213. [CrossRef]
13
Huang, C. S., and Kelley, M. C., 1996, “Nonlinear Evolution of Equatorial Spread F, 2. Gravity Wave Seeding of Rayleigh-Taylor Instability,” J. Geophys. Res., 101, pp. 293–302. [CrossRef]
14
Huang, C. S., and Kelley, M. C., 1996, “Nonlinear Evolution of Equatorial Spread F, 4. Gravity Waves, Velocity Shear and Day-to-Day Variability,” J. Geophys Res, 101, pp. 24521–24532. [CrossRef]
15
Alam, K., de Paula, E. R., and Bertoni, F. C. P., 2004, “Effects of the Fringe Field of Rayleigh–Taylor Instability in the Equatorial E and Valley Regions,” J. Geophys. Res., 109, 12310. [CrossRef]
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Herrmann, M., and Blanquart, G., 2006, “Flux Corrected Finite Volume Scheme for Preserving Scalar Boundedness in Reacting Large-Eddy Simulations,” AIAA J., 44(12), pp. 2879–2886. [CrossRef]
18
Huba, J. D., Joyce, G., and Fedder, J.A., 2000, “Sami2 is Another Model of the Ionosphere (SAMI2): A New Low-latitude Ionosphere Model,” J. Geophys. Res., 105, pp. 23035–23053. [CrossRef]
19
Mahalov, A., and Moustaoui, M., 2009, “Vertically Nested Nonhydrostatic Model for Multi-Scale Resolution of Flows in the Upper Troposphere and Lower Stratosphere,” J. Comput. Phys., 228, pp. 1294–1311. [CrossRef]
20
Jiang, G.-S., and Peng, D., 2000, “Weighted ENO Schemes for Hamilton Jacobi Equations,” SIAM J. Sci. Comput., 21(6), pp. 2126–2143. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The profile of ion-neutral collision frequency as a function of altitude used in the numerical simulations

+The profile of ion-neutral collision frequency as a function of altitude used in the numerical simulations
View Large  |  Save Figure  |  Download Slide (.ppt)
The profile of ion-neutral collision frequency as a function of altitude used in the numerical simulations
Grahic Jump Location
Fig. 2

The profile of recombination rate as a function of altitude used in the numerical simulations

+The profile of recombination rate as a function of altitude used in the numerical simulations
View Large  |  Save Figure  |  Download Slide (.ppt)
The profile of recombination rate as a function of altitude used in the numerical simulations
Grahic Jump Location
Fig. 3

The background electron density (10-5 cm-3) profile as a function of altitude used in the numerical simulations

+The background electron density (10-5 cm-3) profile as a function of altitude used in the numerical simulations
View Large  |  Save Figure  |  Download Slide (.ppt)
The background electron density (10-5 cm-3) profile as a function of altitude used in the numerical simulations
Grahic Jump Location
Fig. 4

The field of the iso-density contours after 2000 s obtained from the large domain simulation. The simulation is initialized with a small density perturbation superimposed to the background density profile. The two dashed vertical lines represent the horizontal boundary of the domain used in the limited area and the nested simulations (Figs. 5 and 6).

+The field of the iso-density contours after 2000 s obtained from the large domain simulation. The simulation is initialized with a small density perturbation superimposed to the background density profile. The two dashed vertical lines represent the horizontal boundary of the domain used in the limited area and the nested simulations (Figs. 5 and 6).
View Large  |  Save Figure  |  Download Slide (.ppt)
The field of the iso-density contours after 2000 s obtained from the large domain simulation. The simulation is initialized with a small density perturbation superimposed to the background density profile. The two dashed vertical lines represent the horizontal boundary of the domain used in the limited area and the nested simulations (Figs. 5 and 6).
Grahic Jump Location
Fig. 5

The field of the iso-density contours after 2000 s obtained from the limited area simulation. The simulation uses specified boundary conditions in the horizontal and open boundary conditions in the vertical. The lateral boundary conditions use the implicit relaxation applied in buffer zones where the density of charged particles is relaxed to that obtained from the parent domain (Fig. 4).

+The field of the iso-density contours after 2000 s obtained from the limited area simulation. The simulation uses specified boundary conditions in the horizontal and open boundary conditions in the vertical. The lateral boundary conditions use the implicit relaxation applied in buffer zones where the density of charged particles is relaxed to that obtained from the parent domain (Fig. 4).
View Large  |  Save Figure  |  Download Slide (.ppt)
The field of the iso-density contours after 2000 s obtained from the limited area simulation. The simulation uses specified boundary conditions in the horizontal and open boundary conditions in the vertical. The lateral boundary conditions use the implicit relaxation applied in buffer zones where the density of charged particles is relaxed to that obtained from the parent domain (Fig. 4).
Grahic Jump Location
Fig. 6

The field of the iso-density contours after 2000 s obtained from the nested simulation. The simulation uses specified boundary conditions in the horizontal and open boundary conditions in the vertical. The lateral boundary conditions use the implicit relaxation applied in buffer zones where the density of charged particles is relaxed to that obtained from the parent domain (Fig. 4).

+The field of the iso-density contours after 2000 s obtained from the nested simulation. The simulation uses specified boundary conditions in the horizontal and open boundary conditions in the vertical. The lateral boundary conditions use the implicit relaxation applied in buffer zones where the density of charged particles is relaxed to that obtained from the parent domain (Fig. 4).
View Large  |  Save Figure  |  Download Slide (.ppt)
The field of the iso-density contours after 2000 s obtained from the nested simulation. The simulation uses specified boundary conditions in the horizontal and open boundary conditions in the vertical. The lateral boundary conditions use the implicit relaxation applied in buffer zones where the density of charged particles is relaxed to that obtained from the parent domain (Fig. 4).
Grahic Jump Location
Fig. 7

The field of the iso-density contours after 2000 s obtained from the large domain simulation after doubling the horizontal resolutions everywhere. The simulation is initialized with a small density perturbation superimposed to the background density profile.

+The field of the iso-density contours after 2000 s obtained from the large domain simulation after doubling the horizontal resolutions everywhere. The simulation is initialized with a small density perturbation superimposed to the background density profile.
View Large  |  Save Figure  |  Download Slide (.ppt)
The field of the iso-density contours after 2000 s obtained from the large domain simulation after doubling the horizontal resolutions everywhere. The simulation is initialized with a small density perturbation superimposed to the background density profile.

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