The topic is Vector fields. Im working on homework and I just need help with thi

Question

The topic is Vector fields. Im working on homework and I just need help with this first question.
It's hard to visualize Vector fields, and also to figure out why it's important to know what one is. Fortunately, satellite imaging gives us one nice example which is easy to visualize, and is important, too: the wind system making up a hurricane. In this homework, I want you to figure out a Vector function to represent the winds of a hurricane. The picture shows hurricane Maria, which knocked out power and water to puerto rico last week. Storms like this will become more and more common as global warming affects the Earth's weather system.
Modeling the storm
We're only going to look at one small part of the science behind the storm system. In this homework, you are going to decide how to describe the winds generated by the storm system as a vector function of two spatial coordinates. We're not going to worry about how the winds change over time. However, as a part of the exercise, I want you to think about all of the things we're also leaving out - we'll come back to that part later on. This problem you may use web resources to look up information on hurricanes.
a) Look at the storm; imagine a 2D coordinate system (x and y axes) running through it, with the origin at the eye. You may as well choose the x axis to run East-West and the Y axis North-South. Based on the circulation of the storm, think about how the wind speed and the wind direction depends on the coordinates. Discuss the following two points qualitatively: How should the wind speed vary as the distance from the eye increases? How should the wind direction vary based on the angle which the point makes to the x-axis? Figure 1: Hurricane Maria

Explanation / Answer

First let us consider our origin at the center to the eye, x axis along east-west direction and y axis along north-south direction.

A) When we are plotting wind speed, the graph will rise steeply and then fall steadily. This is because the wind speed at the eye is 0 knots. At the eye the sky is clear. But as we move to the right according to our graph, we come across the eye wall where wind speed is the highest reaching almost 225 mph. Smaller the eye, stronger are the winds. Then as we move further east, away from the eye wall there is decrease in the wind speed.

B) When we study the wind direction, they are anticlockwise in the northern hemisphere and clockwise in the southern hemisphere. The direction is towards the eye wall and once they reaches the wall they move upwards.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.