# Deriving Ekman Transport in the Southern Hemisphere

• A
• ATY
In summary, the conversation revolves around the derivation of the Ekman transport equation and how it differs in the northern and southern hemispheres. The speaker is confused about the lack of explanation for this difference in existing derivations and wonders if they are missing a key point. They also mention a possible sign change in the derivation and provide a suggested equation for the velocity components.
ATY
Hey guys, I got this problem:
We had the derivation of the ekman transport today in class. And what I wondered about is this:
Usually the equation for the ekman transport looks similar to this (depends on the author)
$$u = V_0 e^{az} cos(\frac{\pi}{4}+az)$$
$$v = V_0 e^{az} sin(\frac{\pi}{4}+az)$$
$$a= \sqrt{\frac{f}{2 A_z}}$$

This is fine for the northern part of the earth, but what happens when I go to the southern hemisphere ? the coriolis parameter f should become negative (since f is $$f = 2 \Omega sin(\phi)$$)
So I can not use the equations above. I am really confused because none of the derivations that I found talked about this. Or am I missing a really obvious point ?
best wishes
ATY

ATY said:
Hey guys, I got this problem:
<snip> I am really confused because none of the derivations that I found talked about this. Or am I missing a really obvious point ?

The derivation I have is in Pozrikidis ("Introduction to Theoretical and Computational Fluid Mechanics"), and there is no ambiguity- I wonder if you have a choice-of-coordinates sign change hidden somewhere in your derivation. The Coriolus force can written as -2Ω×u, where Ω is the rotation rate (Ωez) of the fluid and u=(ux(z),uy(z),0) is the "horizontal" velocity. In the end, the velocity components of u are found to be:

ux+iuy=(Ux+iUy)exp(-(1+i) |z|/δ)

where Ux and Uy are the horizontal velocity components on the fluid surface (taken to be z = 0) and δ is the Ekman layer thickness.

Does this help?

## 1. What is Ekman Transport and why is it important in the Southern Hemisphere?

Ekman Transport is the net motion of ocean surface waters caused by the combination of wind and the Earth's rotation. In the Southern Hemisphere, the Coriolis Effect causes the direction of Ekman Transport to be to the left of the wind direction, resulting in a clockwise circulation pattern. This is important in understanding ocean currents and the movement of nutrients and heat in the Southern Hemisphere.

## 2. How is Ekman Transport derived in the Southern Hemisphere?

To derive Ekman Transport in the Southern Hemisphere, the equations for the Coriolis Effect and the drag force of wind on the ocean surface are used to calculate the direction and magnitude of the resulting current. This can be done using mathematical models or by analyzing data from observational studies.

## 3. What factors can affect Ekman Transport in the Southern Hemisphere?

Ekman Transport in the Southern Hemisphere can be affected by various factors such as wind strength, wind direction, ocean depth, and the Earth's rotation. Changes in these factors can result in variations in the direction and strength of Ekman Transport, which can impact ocean circulation patterns and climate.

## 4. How does Ekman Transport in the Southern Hemisphere impact marine ecosystems?

The direction and strength of Ekman Transport in the Southern Hemisphere can influence the movement of nutrients, plankton, and other organisms in the ocean. This can have significant impacts on marine ecosystems, as it affects the distribution of food and the productivity of different regions.

## 5. What are the practical applications of understanding Ekman Transport in the Southern Hemisphere?

Understanding Ekman Transport in the Southern Hemisphere is important for various practical applications. It can help with predicting ocean currents, which is crucial for shipping and navigation. It also plays a role in weather forecasting and understanding the effects of climate change on ocean circulation. Additionally, understanding Ekman Transport can aid in the development of sustainable fishing practices and the management of marine resources.

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