I'm going to spend more time on Midway, because it's a cleaner answer than the Coral Sea (and I have better sources on hand for it). The Coral Sea was a bit of a mess all around. It was the first battle between aircraft carriers, so neither side was particularly adept. Land-based coast watchers in the Solomons also played a role in the reconnaissance and scouting during the Coral Sea. It also included a greater number of land-based Army aircraft, but the disjointed command structure of Coral Sea created problems with Army-Navy cooperation.

Some Army aircraft were used for reconnaissance at Coral Sea, but you asked specifically about doctrine. Generally speaking, pre/early war naval doctrine would not have accounted for Army Air Corps units participating in naval reconnaissance. It was seen as a naval mission best accomplished by naval personnel. Naval aviators received special training in navigating over the open ocean and in sighting/identifying ships that Army pilots generally did not have. The Army Air Corps also preferred to use its aircraft to attack strategic targets on land. Army aircraft were sometimes used for naval reconnaissance and naval strike missions, but it wasn't anyone's preference to be using Army aircraft for naval search missions. The Army did attempt to use horizontal bombers like the B-17 for strike missions at Coral Sea and Midway, but it quickly became clear that these aircraft just weren’t accurate enough to hit ships that were maneuvering.

Midway's reinforced air wing included about 31 PBY-5 Catalinas along with 17 B-17s and 7 B-26s from the Army. The Army aircraft here were placed under the command of a Navy captain responsible for all of Midway's air forces. The B-17s did undertake some patrols but the Catalinas did much of the heavy lifting. On the morning of June 3, 22 of the Catalinas lifted off at about 4:30 a.m. for their daily patrols which had been going on since mid-May. They covered a 180-degree arc on the compass from 200 degrees to 20 degrees. Each PBY would fly about 680 miles out, then turn either left or right (they would all turn the same direction) at the end of their arc, patrol about 100 miles around the perimeter of their range, then turn for home. This image illustrates a Japanese search pattern at Midway, but it’s the same general idea. You can imagine several aircraft flying in patterns that created something looking like pizza slices, or the construction of a ferris wheel.

One key doctrinal difference between the U.S. Navy and the Japanese navy of the time was that American carrier air wings included dedicated scout squadrons. In the early days of the war (such as Coral Sea and Midway), American carrier air wings generally included a fighter squadron, torpedo squadron, dive bomber squadron, and scouting squadron, designated as VF (followed by a hyphen and number, like VF-6), VT, VB, and VS. The scouting squadrons flew the Douglas SBD Dauntless dive bomber, same as the dive bomber squadron. The scouting squadrons would also participate in attacks when their scouting missions were completed. Japanese doctrine relied more on float planes aboard cruisers for scouting missions, though attack planes aboard carriers could be and were also used for scouting.

However, the Catalinas were the kings of long-range search. It was a Catalina that first spotted six Japanese ships on June 3 at about 9:30 a.m. Midway time, 700 miles out on the perimeter of its search pattern. The Catalina radioed “Sighted main body” back to base (in fact, this was the Midway occupation force and not the Japanese strike force). On the morning of June 4, another Catalina spotted the Japanese carrier strike force and reported its position.

Both of these were visual sightings. Radar played a larger role as the war progressed; it became more reliable and was even mounted on some variants of the F6F fighter aboard carriers in later years. But early in the war, naval reconnaissance relied on eyeballs and binoculars. Unsurprisingly, this led to plenty of errors. Thick cloud cover could impede aerial scouting, and it wasn’t uncommon for carrier groups to sail behind rainclouds to hide from “snoopers” that could dip out of the clouds to sight them and report their position. Ships were often misidentified, and reporting the position of sightings, along with the heading and speed, relied on good navigation skills. Miscommunication was also a factor; at Coral Sea, an SBD pilot named John Nielsen mistakenly sent a message that he had sighted “two enemy carriers,” when he meant to report “two enemy cruisers.” By the time the mistake was realized, the Americans had launched a full strike package. The American aircraft carriers then received another report from a B-17 that a Japanese carrier was sighted south of the position Nielsen reported. The already-airborne planes were redirected to this location, where they found and sunk the Japanese carrier Shoho… which was actually part of the group Nielsen had originally sighted.

If this sounds messy and imprecise, it’s because it was. Sighting and reporting an enemy force was one thing, but tracking it long enough to bring in an attack was another thing entirely. Pilots could sometimes duck into cloud cover to hide while transmitting updated information. But for the most part, if your reconnaissance aircraft could see the enemy, they could also see you. Finding an enemy carrier group meant that you were likely to encounter enemy fighters nearby to shoot you down or drive you off.

Even if you could correctly report the location, composition, heading, and speed of an enemy task force, the ships could still change directions and sail away after you lost contact. In the span of just a few hours, a fleet sailing at 20+ knots could be nearly 100 miles away. This is what happened at Midway. On the morning of June 4, the USS Enterprise dive bombers (both VB-6 and VS-6) flew to the location of the Japanese carriers reported by Midway-based aircraft that had attacked earlier that morning. They found nothing but open ocean. Lt. Cmdr. Wade McClusky directed his bombers to start a search pattern in the area and eventually sighted the lone Japanese destroyer Arashi steaming alone at high speed. Arashi had been detached from the strike force to drop depth charges on the submarine USS Nautilus that had attacked earlier that morning. McClusky reasoned that Arashi was likely trying to catch up to the rest of the Japanese fleet, and vectored his aircraft to follow its course. His hunch proved correct, and the resulting attack sank the Japanese carriers Akagi and Kaga. Dive bombers from Yorktown also arrived and struck fatal blows against the carrier Soryu.

If you want more granular and technical details, Chapter 5 of this handbook, titled “Current Tactical Orders and Doctrine, U.S. Fleet Aircraft, Volume 1, Carrier Aircraft” lays out the process for carrier-based scouts but not land-based patrol aircraft. The section on scouting is pages 49-66.

Sources

“Battle of the Coral Sea Combat Narrative.” Naval History and Heritage Command. Office of Naval Intelligence. https://www.history.navy.mil/research/library/online-reading-room/title-list-alphabetically/b/battle-of-the-coral-sea-combat-narrative.html.

Craven, Wesley Frank, and James Lea Cate, eds. “Chapter 12: Drawing the Battle Line in the Pacific.” Essay. In The Army Air Forces in World War II: Plans and Early Operations, January 1939 to August 1942, 427–70. University of Chicago Press, 1948.

Crooms, Hubert. “An Unsinkable Carrier: The Midway-Based Forces and the Battle of Midway,” 2011. https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=1595&context=etd.

“Current Tactical Orders and Doctrine: U.S. Fleet Aircraft - Volume One, Carrier Aircraft.” http://www.admiraltytrilogy.com/read/USF-74_Tact%26Doct-Acft_V1-CV-Acft_194103.pdf.

Mundorff, George T. “The Catalina Patrol Bomber.” Aerospace Historian 23, no. 4 (1976): 217–21. http://www.jstor.org/stable/44523024.

Parshall, Jonathan, and Anthony Tully. Shattered Sword: The Untold Story of the Battle of Midway. Potomac Books, 2007.

Reilly, John. “Organization of Naval Aviation in World War II.” Naval Aviation News, 1991: 26-31. https://www.history.navy.mil/content/dam/nhhc/browse-by-topic/commemorations/commemorations-toolkits/wwii/articles-on-world-war-ii-naval-aviation/pdf/ww2-11.pdf.

Reynolds, George. “Flying, Floating and Fighting Angels.” Aerospace Historian 18, no. 4 (December 1971): 200–202. https://www.jstor.org/stable/44522556.

Vego, Milan. “The Port Moresby-Solomons Operation and the Allied Reaction, 27 April–11 May 1942.” Naval War College Review 65, no. 1 (2012): 93–151. http://www.jstor.org/stable/26397269.