Despite the streamlined appearance of submarines, it is actually difficult/expensive for them to travel at high speeds. Much of this cost comes from the drag that is induced by the speed itself. Consider this formula to calculate power needed to overcome drag:
$P = \frac 12 CADv^3$
- C: drag coefficient
- A: front facing area
- D: fluid density
- v: velocity/speed
My world assumes there is a strategic need for an extremely fast submarine. However, given the above equation, the power needed is a function of the speed cubed. To put it mildly, this exponential cost is not ideal for a defense department seeking to deploy supersonic submarines. For years, the war generals cycled through countless boxes of cigars and scientists had filled many a trash can with blueprints until...
artist's rendering: supercavitation. Wikipedia
Supercavitation was achieved by a scientist from my world. With a gas bubble enclosing the submarine, drag is reduced to a much more manageable level. There are a still a few kinks to work out regarding turbulence, but nothing the team isn't feeling confident about solving -- except for one glaring thing: navigation.
When at periscope depth, radar can be used as normal. However the majority of the time the supercavitation submarine will be at depths where sonar would normally be used -- which begs the question, what is going to replace sonar now that we have supersonic(in water) velocities? Such a fast vessel would have noise issues that might make sonar ineffective outright, but I'm still open to work-arounds if you truly think sonar is still viable.