I mean "follow in one’s father’s footsteps = do as he did … in the present case “shorty afterr” or “immediately after” “the first thing after” … “right after something/ somebody”
In the wake of World War I, Giannini bought up and expanded an Italian chain banking system, enthusiastically financing Mussolini’s enterprises. (V. Petro, “The Empire of High Finance”)
Mrs. McGillicuddy panted along the platform in the wake of the porter carrying her suitcase. (behind him - threat in someone’s step, follow in the in the steps, follow in someone’s footsteps.
Following directly on, as in ”In the wake of the procession, a number of small children came skipping down the aisle.” This usage alludes to the waves made behind a passing vessel. [c. 1800]
In the aftermath of, as a consequence of, as in Famine often comes in the wake of war. [Mid-1800s]
In my poor opinion repercusation, backlash, comscequence, echo, rebound, recoil, result, reverberation, and even side effect are at a very far remove from the truth.
Following directly on, as in In the wake of the procession, a number of small children came skipping down the aisle. This usage alludes to the waves made behind a passing vessel. [c. 1800] – exactly as Thredder indicated.
In the aftermath of, as a consequence of, as in Famine often comes in the wake of war. [Mid-1800s] – in other words, it is a repercussion of, a backlash of, a consequence of, a result of the prior event – just as Thredder said.