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Mantle Convection Tutorial: Effect of temperature- and depth-dependent rheology, Rayleigh number, and internal heating.

This tutorial deals with understanding the effect of changing the more-important parameters controlling mantle convection. Like most materials, mantle rock has a viscosity which is dependent upon its temperature. Hot rock has a lower viscosity than cold rock. The first part of this tutorial examines this. Furthermore, the lower mantle has a different mineral assemblage than the upper mantle due to phase transitions that occur between 410-660 km depth. It is generally accepted that lower mantle minerals have a higher intrinsic viscosity than upper mantle minerals. The second part of the tutorial examines the effect of a discontinuous viscosity jump across the lower boundary of the transition zone at 660 km depth. The magnitude of viscosity is reflected in the Rayleigh number. Lower Rayleigh numbers describe a higher overall mantle viscosity whereas higher Rayleigh numbers describe a lower overall mantle viscosity. This is examined in the third part of the tutorial. Finally, mantle convection is a result of heat transport. Heat sources in the mantle include both that entering the mantle from the core and from the radioactive decay of uranium, thorium, and potassium. Radioactive decay is typically referred to as internal heating. We investigate this in the final portion of the tutorial.

To understand how these parameters affect mantle convection, we start with a control case. This is a case by which all else can be compared to.

The Control Case

Rayleigh number 107
Temperature-dependence of viscosity 1000 x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (9.7 MB) Snapshot Image

Investigating the temperature-dependence of rheology

Viscosity Contrast due to temperature = 0 x [All material has the same viscosity]

Rayleigh number 107
Temperature-dependence of viscosity 0x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (16.8 MB) Snapshot Image

Viscosity Contrast due to temperature = 10 x [Coldest material is 10x more viscous than hottest]

Rayleigh number 107
Temperature-dependence of viscosity 10x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (16.8 MB) Snapshot Image

Viscosity Contrast due to temperature = 100 x [Coldest material is 100x more viscous than hottest]

Rayleigh number 107
Temperature-dependence of viscosity 100x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE ( 13.4 MB) Snapshot Image

Viscosity Contrast due to temperature = 1000 x [Coldest material is 1000x more viscous than hottest]

(CONTROL CASE)

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (9.7 MB) Snapshot Image

Viscosity Contrast due to temperature = 10,000 x [Coldest material is 10,000x more viscous than hottest]

Rayleigh number 107
Temperature-dependence of viscosity 10,000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (8.0 MB) Snapshot Image

Viscosity Contrast due to temperature = 100,000 x [Coldest material is 100,000x more viscous than hottest]

Rayleigh number 107
Temperature-dependence of viscosity 100,000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (5.7 MB) Snapshot Image

Investigating the viscosity increase with depth at the 660km depth boundary

Viscosity increase across the bottom of the transition zone (660 km depth) = 0x

(CONTROL CASE)

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (9.7 MB) Snapshot Image

Viscosity increase across the bottom of the transition zone (660 km depth) = 2x

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 2x
Dimensionless Internal heating 0
MPEG MOVIE (9.2 MB) Snapshot Image

Viscosity increase across the bottom of the transition zone (660 km depth) = 50x

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 50x
Dimensionless Internal heating 0
MPEG MOVIE (9.3 MB) Snapshot Image

Viscosity increase across the bottom of the transition zone (660 km depth) = 100x

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 100x
Dimensionless Internal heating 0
MPEG MOVIE (8.1 MB) Snapshot Image

Investigating the effect of Rayleigh Number

Rayleigh Number = 105

Rayleigh number 105
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (9.4 MB) Snapshot Image

Rayleigh Number = 106

Rayleigh number 106
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (10.5 MB) Snapshot Image

Rayleigh Number = 107

(Control Case)

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (9.7 MB) Snapshot Image

Rayleigh Number = 108

Rayleigh number 108
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (13.2 MB) Snapshot Image

Investigating the effect of Internal Heating, determined by non-dimensional heating rate.

Internal heating = 0.0

(Control Case)

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 0
MPEG MOVIE (9.7 MB) Snapshot Image

Internal heating = 10.0

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 10
MPEG MOVIE (9.8 MB) Snapshot Image

Internal heating = 20.0

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 20
MPEG MOVIE (10.4 MB) Snapshot Image

Internal heating = 30.0

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 30
MPEG MOVIE (9.2 MB) Snapshot Image

Internal heating = 40.0

Rayleigh number 107
Temperature-dependence of viscosity 1000x contrast between hottest and coldest
Viscosity increase across the 660 km depth 0
Dimensionless Internal heating 40
MPEG MOVIE (9.2 MB) Snapshot Image
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