# The Birth of the Earth System and the Convection Paradigm

Steven R Dickman

, Binghamton University

Author Profile### This activity has benefited from input from faculty educators beyond the author through a review and suggestion process.

This review took place as a part of a faculty professional development workshop where groups of faculty reviewed each others' activities and offered feedback and ideas for improvements. To learn more about the process On the Cutting Edge uses for activity review, see http://serc.carleton.edu/NAGTWorkshops/review.html.

This page first made public: Jul 5, 2007

#### Summary

Convection is a major process operating throughout the Earth System. This combination lecture sequence / problem set activity sets the stage for the appearance and importance of convection within the Earth System, then presents an advanced theoretical discussion (best introduced after my other contributed activity, on cooling times) of basic mathematical and physical aspects of convection. These 'basics' will allow students to subsequently move on to rigorous treatments of geophysical fluid dynamics in the context of Earth System Science.

## Context

#### Audience

The first portion of the lecture sequence (through section III.A. in the lecture outline—see file 1) is general and qualitative enough for the introductory geology / climatology course I teach (which is open with no pre-requisites to all students).

The second portion of the lecture sequence and the problem set are used in an advanced geophysics course that I teach, intended for upper-division undergrads or grad students in geophysics, physics, or mechanical engineering.

However, I note that if my upper-level survey course in geophysics (for geology seniors and grad students) was a month longer, it would include this entire activity. That is, geology seniors and grad students who have worked through my other contributed activity (on cooling times) have successfully completed this activity as well.

Designed for a geophysics course

Designed for an introductory geology course

The second portion of the lecture sequence and the problem set are used in an advanced geophysics course that I teach, intended for upper-division undergrads or grad students in geophysics, physics, or mechanical engineering.

However, I note that if my upper-level survey course in geophysics (for geology seniors and grad students) was a month longer, it would include this entire activity. That is, geology seniors and grad students who have worked through my other contributed activity (on cooling times) have successfully completed this activity as well.

Designed for a geophysics course

Designed for an introductory geology course

#### Skills and concepts that students must have mastered

No prior skills are required for the first portion of the lecture sequence.

Students *must* have been exposed to partial derivatives, Fourier's Law, and the diffusion equation (i.e., my other contributed activity, activity 1) prior to the second portion of the lecture sequence or the problem set.

Students *must* have been exposed to partial derivatives, Fourier's Law, and the diffusion equation (i.e., my other contributed activity, activity 1) prior to the second portion of the lecture sequence or the problem set.

#### How the activity is situated in the course

The first portion of the lecture sequence is part of the first "chapter" of my introductory geology course; it sets the stage for the rest of the course.

The second portion of the lecture sequence, and the problem set, are situated about 2/3 of the way through my advanced geophysics course—it makes sense to cover gravity and Earth's internal constitution before beginning heat flow.

The first portion of the lecture sequence requires only about one and a half hours of lecture. The entire sequence ideally (including peripheral topics and applications of heat flow) requires about 2 weeks of lecture time (= 6 hours of lecture).

The second portion of the lecture sequence, and the problem set, are situated about 2/3 of the way through my advanced geophysics course—it makes sense to cover gravity and Earth's internal constitution before beginning heat flow.

The first portion of the lecture sequence requires only about one and a half hours of lecture. The entire sequence ideally (including peripheral topics and applications of heat flow) requires about 2 weeks of lecture time (= 6 hours of lecture).

## Goals

#### Content/concepts goals for this activity

- understanding the nature of advection, and how to express it mathematically
- understanding how convection works in a fluid
- being able to quantify some of the forces acting within a fluid
- determining the relative importance of terms in a differential equation—the technique of scaling equations (necessary for dealing quantitatively with the complex Earth System)
- deriving and exploring applications of dimensionless numbers

#### Higher order thinking skills goals for this activity

- appreciating the pervasiveness of convection in the Earth System, and throughout the Universe
- appreciating the origin of the Earth System

#### Other skills goals for this activity

- -

## Description of the activity/assignment

This combination lecture sequence / problem set activity focuses on the process of convection, its importance throughout the Earth System and its physical & mathematical description. Though the first portion of the lecture sequence is suitable for presentation even in an intro' course for non-majors, the remainder of the lecture sequence and the problem set are intended for students who have seen partial derivatives and the diffusion equation. Concepts of advection, adiabatic temperature gradient, and buoyancy & drag forces are developed quantitatively; the technique of scaling equations to identify their dominant terms is introduced; and dimensionless ratios, including the Rayleigh Number, are constructed and applied to various terrestrial and planetary situations. These lectures, when combined with the problem set, will provide students with a foundation for understanding and studying convection in the various sub-disciplines of Earth System Science.

Uses geophysics to solve problems in other fields

Uses geophysics to solve problems in other fields

## Determining whether students have met the goals

Grading the problem set and the exam corresponding to those lectures should allow for an accurate assessment.

More information about assessment tools and techniques.## Download teaching materials and tips

- Activity Description/Assignment (Microsoft Word 47kB Jul5 07)
- Solution Set (Microsoft Word 50kB Jul5 07)

## Other Materials

## Supporting references/URLs

I found Tritton's text, Physical Fluid Dynamics (especially the first edition), to be very helpful.