Consider the following statements:
Statement 2 is correct.
The 'eye' is a distinct feature primarily observed in mature and intense tropical cyclones. Weaker or less organized tropical cyclones, as well as temperate cyclones, generally do not develop a well-defined eye. Thus, only some cyclones develop an eye.
Statement 1 is incorrect.
Jet streams are narrow bands of strong, high-altitude westerly winds that occur in both the Northern and Southern Hemispheres, not exclusively in the Northern Hemisphere.
Statement 3 is incorrect.
The eye of a tropical cyclone is typically characterized by warmer temperatures compared to the surrounding eyewall. This warmth is due to the adiabatic compression of subsiding air within the eye. Therefore, the temperature inside the eye is usually warmer, not cooler, than its surroundings.