Honestly I don't even want to know, basics are enough.
I can't get into too much detail, but there are alternative methods to the normal electromagnetic or SONAR detection that is most common.
Tracking sea life moving away from the submarine has been shown possible, though the ocean isn't saturated and it's inconsistent at best as a form of detection. Think of this like John Warner here. While these dolphins are playing, there are methods, such as SONAR or various remote sensing capabilities (the exact methods are classified) to track the movement of sea life moving away from the submarine:
I know we had a discussion about reactor noise on AMF, but what we didn't have a discussion about is reactor leakage. Radiological contaminants. Nothing that would be harmful to the crew, but definitely noticeable enough to orbiting aircraft like the WC-135 Constant Phoenix that monitors deep underground North Korean nuclear tests:
The US also maintains a fleet of radiological contaminant detecting UAVs, for tracking radiological material smuggling, such as stolen medical waste or to patrol high value, high traffic areas such as G20 meetings or Olympics, where terrorism concerns are heightened.
The United States maintains a handful of maritime orient versions.
Water is great at diluting nuclear particles, but a near surface nuclear boat, or Boomer near surface to fire its weapons can be detected. The depth of detection, you guessed it, is classified.
Wave currents can also be detected. While streamlined, a moving body does create a current, typically in a V shape. Noise is also generated during this event and it's one of the main reasons we see submarine sails, dive plains and rudders being refined, such as the Virginia Class's storable dive plains and angled forward tower.
How these currents are detected is not something I can currently give out.
Finally, though they are a significant contributor to noise, cavitation, or bubbles as they are often known as, can leave a detectable trail. The prop designs are giving way to Pump Jets which produce less and less long-lasting bubble trails. While the bubbles themselves dissipate rather quickly, and generate detectable noise in the process, disturbed water lingers longer and can be detected.
Pump Jets help with this problem.
This is a but a few signatures that are alternatives to the electromagnetic and acoustic that most people highlight when discussing ASW warfare. They are not the only alternative methods.