How Do You Sketch a Geopotential Field at Different Altitudes?

[Mary_089]

Homework Statement

Hello, I need
a) to Sketch φ which is the geopotential field, dependent on four variables (x,y,z,t)
b) to Sketch the geopotential at 2.5 and 7.5 km altitude

Homework Equations

φ(x,y,z,t) = φ₀(z) + c * f₀ ( -y ( cos(π * (H-z)/H ) + 1 ) + 1/k * sink(x-ct))

The Attempt at a Solution

Well ... i know that c is a speed, k is the zonal wave number, but there are no numbers given - and I really have no clue how to start.

Thanks for help!

 

[nate808]

Hi there,

I can help you with this problem. Let's start by understanding what the geopotential field (φ) represents. It is a scalar field that describes the gravitational potential energy per unit mass of a fluid element in a rotating reference frame. In simpler terms, it is a measure of the strength of the Earth's gravitational pull at a specific location.

Now, let's break down the given equation for the geopotential field:

φ(x,y,z,t) = φ0(z) + c * f0 ( -y ( cos(π * (H-z)/H ) + 1 ) + 1/k * sink(x-ct))

The first term, φ0(z), represents the geopotential at a reference level (z=0). The second term, c * f0 ( -y ( cos(π * (H-z)/H ) + 1 ), represents the contribution of the zonal wind to the geopotential field. The third term, 1/k * sink(x-ct), represents the contribution of the meridional wind to the geopotential field.

To sketch the geopotential field, you can plot φ as a function of x, y, and z. Since t is not given, you can choose a specific value for it and plot the geopotential at that time. Alternatively, you can also plot the geopotential as a function of altitude (z) for a fixed value of x and y.

For part b), you are asked to sketch the geopotential at 2.5 and 7.5 km altitude. This means that you need to plot φ as a function of x and y for z=2.5 km and z=7.5 km. You can choose any value for t to plot the geopotential at those altitudes.

I hope this helps you get started. If you need further assistance, please let me know. Good luck!