Cross Section of a Polar Trough
This is a West to East cross section along 50S. Notice that the trough originates at 1000 hPa near 50S 60W, and at 300 hPa it lies along 50S 73W. It is a positively tilted trough extending from east-to-west with height.
The potential temperatures (degrees Kelvin) clearly show a cold core trough below 300 hPa, as the horizontal temperatures gradually decrease as we approach the center of the trough.