# Scaling and excitation of combined convection in a rapidly rotating plane layer

## Abstract

The optimum (to my mind) scaling of the combined thermal and compositional convection in a rapidly rotating plane layer is proposed.This scaling follows from self-consistent estimates of typical physical quantities. Similarity coefficients are introduced for the ratio convection dissipation/convection generation (s) and the ratio thermal convection/compositional convection (r). The third new and most important coefficient δ is the ratio of the characteristic size normal to the axis of rotation to the layer thickness. The faster the rotation, the lower δ. In the case of the liquid Earth core, δ ~ 10{sup –3} substitutes for the generally accepted Ekman number (E ~ 10{sup –15}) and s ~ 10{sup –6} substitutes for the inverse Rayleigh number 1/Ra ~ 10{sup –30}. It is found that, at turbulent transport coefficients, number s and the Prandtl number are on the order of unity for any objects and δ is independent of transport coefficients. As a result of expansion in powers of δ, an initially 3D system of six variables is simplified to an almost 2D system of four variables without δ. The problem of convection excitation in the main volume is algebraically solved and this problem for critical values is analytically solved. Dispersion relations andmore »

- Authors:

- Russian Academy of Sciences, Pushkov Institute of Terrestrial Magnesium, Ionosphere and Radio Wave Propagation (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22617059

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 124; Journal Issue: 2; Other Information: Copyright (c) 2017 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CONVECTION; DISPERSION RELATIONS; DISPERSIONS; EXCITATION; EXPANSION; LAYERS; LIQUIDS; PLANETS; PRANDTL NUMBER; RAYLEIGH NUMBER; ROTATION; STARS; THICKNESS

### Citation Formats

```
Starchenko, S. V., E-mail: sstarchenko@mail.ru.
```*Scaling and excitation of combined convection in a rapidly rotating plane layer*. United States: N. p., 2017.
Web. doi:10.1134/S1063776117020091.

```
Starchenko, S. V., E-mail: sstarchenko@mail.ru.
```*Scaling and excitation of combined convection in a rapidly rotating plane layer*. United States. doi:10.1134/S1063776117020091.

```
Starchenko, S. V., E-mail: sstarchenko@mail.ru. Wed .
"Scaling and excitation of combined convection in a rapidly rotating plane layer". United States.
doi:10.1134/S1063776117020091.
```

```
@article{osti_22617059,
```

title = {Scaling and excitation of combined convection in a rapidly rotating plane layer},

author = {Starchenko, S. V., E-mail: sstarchenko@mail.ru},

abstractNote = {The optimum (to my mind) scaling of the combined thermal and compositional convection in a rapidly rotating plane layer is proposed.This scaling follows from self-consistent estimates of typical physical quantities. Similarity coefficients are introduced for the ratio convection dissipation/convection generation (s) and the ratio thermal convection/compositional convection (r). The third new and most important coefficient δ is the ratio of the characteristic size normal to the axis of rotation to the layer thickness. The faster the rotation, the lower δ. In the case of the liquid Earth core, δ ~ 10{sup –3} substitutes for the generally accepted Ekman number (E ~ 10{sup –15}) and s ~ 10{sup –6} substitutes for the inverse Rayleigh number 1/Ra ~ 10{sup –30}. It is found that, at turbulent transport coefficients, number s and the Prandtl number are on the order of unity for any objects and δ is independent of transport coefficients. As a result of expansion in powers of δ, an initially 3D system of six variables is simplified to an almost 2D system of four variables without δ. The problem of convection excitation in the main volume is algebraically solved and this problem for critical values is analytically solved. Dispersion relations and general expressions for critical wavenumbers, numbers s (which determine Rayleigh numbers), other critical parameters, and asymptotic solutions are derived. Numerical estimates are made for the liquid cores in the planets that resemble the Earth. Further possible applications of the results obtained are proposed for the interior of planets, moons, their oceans, stars, and experimental objects.},

doi = {10.1134/S1063776117020091},

journal = {Journal of Experimental and Theoretical Physics},

number = 2,

volume = 124,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2017},

month = {Wed Feb 15 00:00:00 EST 2017}

}