I'm not going to touch on surface ships with this write-up considering this is a submarine thread. Just wakes as they pertain to subs.
Wake Homing - What is wake homing?
Wake homing is a pretty simple concept. A moving ship, whether at sea or moored in port, makes a wake that can be used to detect, track or engage a submarine. Pretty simple right?
Turns out wakes are a bit more complicated.
Wake Homing - Wake formation and properties.
Wakes aren't simply bubbles and noise, as they are often thought of. Effects influencing the formation, duration and detection of wakes vary greatly and include several types of thermal and non-thermal energy, in additional to topographical and macro-influences like water salinity, depth, terrain, vector and the influence of gravity. Let's look more deeply at the more obscure factors that play a very large part in non-acoustic detection systems used by wake homers.
The first type of wake property is essentially thermal energy. Essentially thermal energy is the actual heat change produced due to the influence of the submarine that the wake is acted upon by. This includes the heat transfer from the submarine to the surrounding water, the generation of heat as turbulence from the submarine's motion degrades, and water from neighboring thermal grades being pulled into the wake by turbulence and vortex formation from a submarine's prop. Finally the inability of the ocean's surface to cool via evaporation due to inhibition from surface films (hydrocarbons, sea life, ocean traffic, humidity) influences a wake's thermal energy by trapping additional heat within the wake from the surrounding ocean thermal grade. Conversely if a surface film is typically present in an ocean area and a submarine disturbs it this may actually cool the wake and produce a noticeably colder patch in the ocean behind the submarine.
non-essentially thermal energy is any change in the water's properties that are detectable, that need not be directly related to a submarine's activity, and can even produce no noticeable temperature changes. Physical changes would be the breaking of the water by rising bubbles, surface turbulence and chemical changes such as a submarine's snorkel leaking oil lubricants that form a film or anti-corrosive runoff - zinc being a common material used on submarines. Oils can dampen capillary waves, producing a smoother ocean surface as well. All of this has the effect of contributing to a wake's heat by altering the surrounding water's properties.
Akula class submarine with its SOKS system deployed. SOKS - System Obnarujenia Kilvaternovo Sleda - detects radioactive decay runoff from a hostile submarine's reactor that is diluted with the submarine's wake. SOKS could also measure zinc runoff.
The last influence sytem is non-thermal energy which would include optical changes including changes in water's reflectivity, index of refraction and absorptivity, governing its rate and suseptability to changes in its thermal grade by light. mechanical changes like cavitation or turbulence propagated by passing ships or heavy winds or sea life effect surface tension and electrical changes such as differences in conductivity, temperature gradient potential, electrolyte concentration, unequal ion diffusion rate and frictional electricity, contribute as well. As do magentic changes that are largely related to water being an electrical conductor. Chemical changes to non-thermal energy could be influenced by a submarine as "wake seeding" is actually a thing that can detect the chemical makeup of a wake by injecting the water around with various chemicals. An example could be using ca0 to detect Co2, which when introduced produces a white chalk known as CaCo3 - calcium carbonate.
Rounding out the influences of non-thermal energy are biological influences such as barnacle waste, the attraction of or presence of sea life within the wake and waste from the submarine's crew and nuclear runoff in the form of phosphoresence (heat and light produced without combustion, as is common with radioactive decay), the Cherenkov Effect, producing a noticeable glow from the presence of a charged particle moving faster then the speed of light in a given medium, and radionuclide runoff, which is what the Russian SOKS system detects, along with chemical runoff.
Still with me? Good

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Wake formation isn't less complicated. But in simple terms a wake is formed when a body moves over a medium that itself moves over a medium with a different density. The above factors influence the properties of the wake and influence non-acoustic detection of an underwater body.
Wake Homing - Wake detection and tracking.
So now that we know the properties of a wake, what can we do with that info? Turns out there are a lot of really cool ways to detect and track wakes. Synthetic aperture radars on satellites and aircraft are some of the most capable wake hunters around today.
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Of course radar doesn't work well underwater, but how about detecting thermal changes? Much better. On MPAs like the P-3 and P-8A, but not P-8I, thermal radiometers are used to track down changes in thermal grade, chemical runoff and radionuclides. One early example found on the P2V-5 was a Barnes radiometer, which was used in japan to track both thermal energy and radionuclides near Mount Fuji and in both surface and ground water during the post-war cleanup of Japan. These track radioactive decay and the thermal energy produced from the process.
During ASW trials the system could rapidly detect hydrocarbons from conventional submarines and radiological contaminants, along with thermal energy at different thermal grades across varying ocean depths and conditions. Since then detection systems long the lines of the Barnes radiometer have only gotten better.
For detecting heat, MAD is used to detect the hull, not wake. Welds and rivets, when heated, produce a magnetic field that's noticeable. Infrared detection of submarines is largely considered non-viable due to heat's rapid dissipation in water.
Systems for detecting biological runoff or influences, such as tracking maritime wildlife in relation to a submarine's vector, have been explored, but ultimately deemed insufficient. LIDAR, green laser specifically, has been promising for tracking thermal changes and ultimately has been introduced as an operational capability for mine-hunting.
LIDAR imaging has been used to map the sea-floor, including during salvage operations, such as in finding USS S-28, which sunk of Hawaii.
China is believed to be developing high-powered LIDAR system for satellite surveillance of underseas objects.
Mentioned previously, SOKS-type systems, like this on a Royal Navy Trafalgar class submarine, track wake properties such as the presence of radionuclides and zinc-runoff from anti-corrosive measures. they could just as easily be tuned against hydrocarbons off-boarded by AIP designs that use fuel cells or batteries, and even oxygen scrubbers.
Wake homing torpedoes are far simpler and use active acoustic homing to track cavitation and turbulence. Acoustic homing is itself an interesting concept. Passive acoustic homing simply listens to background noise and orients itself to match where the single is loudest. Active acoustic homing, or sonar, emits an acoustic pulse when reflects of an object as an echo.
Wake Homing - Countermeasures?
¯\_(ツ)_/¯
This is one area I simply can't speak on without having to censor my writing. Sorry. Yes there are countermreasures to wake formation and properties, but as someone who made systems to track and engage submarines for a living I'm not really at liberty to say what they are.
What I can say publicly is that some hull designs and propulsion systems do cut down on surface and near-surface wake formation and cavitation. There's a reason that navies are investing in counter-torpedo torpedoes though.