This presentation is mostly based on the work “The effects of rotation rate on deep

convection in giant planets with small solid cores” by M. Evonuk & G. A. Glatzmaier 2007,

Planetary and Space Science, 55, 407 (post scriptum by J. A. Caballero)

"The Effects of Rotation rate on deep Convection in Giant Planet”

DAVID LÓPEZ FDEZ-NESPRAL

Why to study Rotation?

-Rotation affects the internal structure and dynamics of gaseous bodies.

The strength and nature of convection

How to study Rotation?

VORTICITY

-The strength and pattern of the flow depends rotation rates

-Generated by fluid rising or sinking through the density stratified interior- Effects of angular momentum flux

DIFFERENTIAL ROTATION AND WINDS AT SURFACE

QUESTION?

DOES THE FLUID CHANGE WITH THE PRESENCE OF A SMALL NON-CONVECTING CORE?

This questions is of interest for two reason:

FIRSTGiant planets are believe to have formed through accretion of a solid core followed by the capture of gaseous Hydrogen and Helium or by gravitational instability of gas in the disk.

Giant planets form their cores may erode

Erosion occurs if •The heavy elements are soluble in Hydrogen and Helium •The convective energy us sufficient to overcome the molecular weight barrier

SECOND Models of giant gaseous planets are not able to simulate convection without a solid core

It is important to know if the presence of a non-convecting core causes change in the fluid flow patterns, relative to a fully convective planet.

We study various rotation rates (with and without cores)

For identical size, mass, and heating

MODEL AND NUMERICAL METHODThe model is in 2DAdvantage: To obtain higher resolution and more turbulent flowDisadvantage:To Can not see the internal dynamics of a 3D fluid

FEATURES-It is a simple density-stratified fluid with four density scale heights

•Density-stratified Vs Constant-density

•Density-stratified is needed for the coriolis force to influence the fluid flow

Why a stratified medium?

The equations of momentum (1), heat (2), and mass conservation (3) are solved with the finite volume method on a Cartesian grid.

rurguePuuut ijijijji

2

312)(

srp

trp

t QrT

TC

rS

drTd

TT

TC

SuSSSt

0 u

(1)

(2)

(3)

RESULTS AND DISCUSSIONAT HIGHER ROTATIONIt is difficult to distinguish between the cases with small core and not core

NO CORE SMALL SOLID CORE

(Show a snapshots of the entropy perturbation overlaid with velocity arrows)

The fluid flow is differentiated in two part (On both cases):-Prograde motion (rotation counterclockwise motion from solar north pole) in the outer part of the disk

-Retrograde motion (rotation clockwise motion from solar north pole) in the inner part of the disk

No core: Dashed line ------- Small core: line

This differential rotation is maintained by the generation of vorticity though the density stratification (Coriolis force)

The Coriolis generates:-Negative vorticity (A) by hot material expands in the inner regions of the disk

-Positive vorticity (C): by sinking material in the outer regions of the disk

NO ROTATION

NO CORE

This case forms two symmetric cells with peak flow velocities in the center of the disk

The most efficient flow patterns for removing the heat generates in the central region

The symmetry of these two cells results in mean zonal flows close to zero through out the disk

SMALL SOLID CORE (a)

In this case, the core breaks up the flow through the center into small cells

This configuration produces higher kinetic energies around the core

The prograde zonal flow near the core (figure b) is due to the persistence of a dominant cells (figure a) during the time over which was made

AT SLOW ROTATION

In this case, slow rotation, the convective cell patterns are similar to the case with no rotation.However, The Coriolis force is not null, organizes the flow to maintain a weak differential rotation:

-Prograde motion in the outer part

-Retrograde motion in the inner part As in the high rotation case

NO CORE SMALL SOLID CORE

Although the two cases behave differently at depth, they have a similar zonal velocities at the base of the radiative zone

This suggest that surface observations of the zonal wind velocities would be indistinguishable

How we can distinguish both cases?

• High rotation•Slow rotation• No rotation

Measuring velocities at surface

•Core•No Core Measuring magnetic fields at surface

IN A FUTURE WORK !!!!