# The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows

## Abstract

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolmogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large-scale radiative hydrodynamic simulations. We reach two primary conclusions. (1) The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. (2) Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large-scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data onmore »

- Authors:

- Department of Astrophysical and Planetary Sciences, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309 (United States)
- Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany)
- High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80307 (United States)
- Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, Centre national de la recherche scientifique (CNRS), F-31400 Toulouse (France)

- Publication Date:

- OSTI Identifier:
- 22365025

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 793; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; CONTINUITY EQUATIONS; CONVECTION; CORRELATIONS; DENSITY; EQUATIONS OF STATE; GRANULATION; HEAT FLUX; HYDRODYNAMIC MODEL; IONIZATION; LUMINOSITY; NONLINEAR PROBLEMS; PHOTOSPHERE; SIMULATION; SOLAR GRANULATION; SPECTRA; SUN; THREE-DIMENSIONAL CALCULATIONS; TURBULENCE

### Citation Formats

```
Lord, J. W., Rast, M. P., Cameron, R. H., Rempel, M., and Roudier, T., E-mail: mark.rast@lasp.colorado.edu.
```*The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows*. United States: N. p., 2014.
Web. doi:10.1088/0004-637X/793/1/24.

```
Lord, J. W., Rast, M. P., Cameron, R. H., Rempel, M., & Roudier, T., E-mail: mark.rast@lasp.colorado.edu.
```*The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows*. United States. doi:10.1088/0004-637X/793/1/24.

```
Lord, J. W., Rast, M. P., Cameron, R. H., Rempel, M., and Roudier, T., E-mail: mark.rast@lasp.colorado.edu. Sat .
"The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows". United States. doi:10.1088/0004-637X/793/1/24.
```

```
@article{osti_22365025,
```

title = {The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows},

author = {Lord, J. W. and Rast, M. P. and Cameron, R. H. and Rempel, M. and Roudier, T., E-mail: mark.rast@lasp.colorado.edu},

abstractNote = {We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolmogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large-scale radiative hydrodynamic simulations. We reach two primary conclusions. (1) The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. (2) Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large-scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large-scale modes in the deep layers are artificially reduced. Since the large-scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small-scale convective correlations are maintained through the bulk of the solar convection zone.},

doi = {10.1088/0004-637X/793/1/24},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 1,

volume = 793,

place = {United States},

year = {2014},

month = {9}

}