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# Atmospheric Kinematics

## General

AHS

275

Undergraduate

### College/School

College of Science and Engineering

### Description

Kinematics of atmospheric flows using vector concepts and operations including vector functions, dot products, cross products, gradients, divergence, deformation, and vorticity. Spherical coordinates. Approximation techniques. Applications from atmospheric fluid dynamics.

2

2

No

No

No

## Learning Outcomes

### Outcome

Apply the chain rule to meteorological functions of more than one variable.

### Outcome

Apply dot products and gradients to compute advection of meteorological variables.

### Outcome

Apply cross products and gradients to compute the geostrophic wind.

### Outcome

Apply the curl operator to compute vorticity.

### Outcome

Apply divergence to mass conservation.

### Outcome

Identify translation, divergence, vorticity, and deformation in Taylor series expansion of the horizontal wind.

### Outcome

Identify the Laplacian operator as divergence of a gradient vector field.

### Outcome

Describe atmospheric forces and flows using spherical coordinates.

### Outcome

Construct Fourier series modeling 500 mb heights in a latitude zone.

### Outcome

Apply basic numerical techniques of integration to estimate energy values on a thermodynamic chart.

## Course Outline

### Course Outline

Representations, particularly contours, of functions of several variables. 10% Rectangular and spherical coordinate systems in three dimensions. 10% Basic numerical integration methods applied to thermodynamic charts. 5% Vector arithmetic and meteorological applications including wind shear, pressure gradient force, advection, geostrophic wind, and Coriolis force. 15% Partial differentiation, gradients, and the Laplacian. 15% Chain Rule for multivariate functions. 5% Vector fields and the concepts of measuring circulation and flux. 10% Divergence, vorticity, and deformation of air parcels. 15% Series expansion of wind in one and two variables. 5% Decomposition of Rossby waves using horizontal Fourier series. 10%

## Dependencies

### Courses

AHS275 is a prerequisite for:

### Programs

AHS275 is a completion requirement for:

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