What's the name of the effect that causes the aircraft to automatically pull out of a dive and buffet up due to aerodynamic lift produced at high speeds?
An aircraft with positive pitch stability (longitudinal stability) tends to maintain the trim1 angle-of-attack, regardless of airspeed. At any other angle-of-attack, the "teter-totter" balancing act between the wing and tail would be off-kilter, creating a pitch torque that would change the angle-of-attack.
At a given angle-of-attack, only one airspeed is compatible with level flight2. If the airspeed is too low, lift will be less than weight (or more precisely, less than the component of weight acting parallel to the lift vector, which is relevant when the flight path is aimed steeply upwards or downwards), and this will cause the flight path to curve downwards (in the aircraft's reference frame3). If the airspeed is too high, lift will be greater than weight (or more precisely, greater than the component of weight of acting parallel to the lift vector), and the flight path will curve upwards (in the aircraft's reference frame).
Since the angle-of-attack tends to remain constant, it follows that an upward curve of the flight path must be accompanied by a rise of the nose.
This whole dynamic is indeed one step in a "phugoid" oscillation. Other than that, there's no one specific name for it, (except perhaps "pitch stability", or perhaps simply "pitching upwards"!)
We've made one slight oversimplification here. In the second sentence we associated a pitch torque with a change in angle-of-attack. In fact, any change in the aircraft's pitch rotation rate requires a pitch torque. So some pitch torque is in fact being generated as the nose starts to rise. This implies that the angle-of-attack cannot be remaining exactly constant. To explain in more detail exactly what is going on here, is far beyond the scope of the original question. (Hint--the curving nature of the "relative wind" when the flight path is not linear plays a role in altering the apparent "decalage" between the wing and the tail.) The main thing to keep in mind is that the upward curve of the flight path is fundamentally being driven by a force imbalance, not a torque imbalance. There's too much speed, so there's too much lift, so the flight path must curve upwards. Meanwhile, the aircraft's pitch stability dynamics tend to maintain the trimmed angle-of-attack, keeping the nose aimed in the "right" direction in relation to the flight path, so when the flight path starts curving upwards, the nose must rise as well.
The concept of "trim" is not limited to what happens when the pilot lets go of the controls or exerts no force on the controls. It also could include what happens when the pilot holds the controls in a fixed position.
And to a first approximation, for shallow dive or climb angles, only one airspeed is compatible with linear flight, regardless of whether or not altitude is exactly constant.
Re "in the aircraft's reference frame"-- think about which way the flight path is curving in the instant during a loop when the flight path is aimed straight up or straight down.
That is part of what happens in a phugoid (the “downhill”).
A phugoid or fugoid is an aircraft motion in which the vehicle pitches up and climbs, and then pitches down and descends, accompanied by speeding up and slowing down as it goes "downhill" and "uphill".
What is the name of the effect that causes a plane in a dive to go up?
The best answer is simply "Lift". Lift exists, and exceeds weight (or strictly speaking, exceeds the component of the weight vector that acts parallel to the lift vector), so the flight path curves upward, and the nose rises.
Well, since airplanes trim to an AOA, if you force it into a dive by a down elevator input while trimmed for level flight, you're forced it to a lower AOA (higher speed) than it's trimmed for. If you let go, it will pull out because it's trying to "weathervane" (pitch stability is simply a weathervaning tendency in the vertical plane about a specific offset angle determined by trim forces) back to the AOA it is trimmed to.
So the forces causing it to pull out of the dive are trim forces, trim being an opposing force balance system of nose down and nose up pitching moments that achieve equilibrium, or trim, at some angle of the body to the airflow.
Any buffeting that occurs (like in the movies) in the real world will be due to shock waves causing flow separations and turbulence. But for that the dive has to get into the transsonic speed range. A highspeed dive that stays within the airplane's certified speed range shouldn't experience any buffeting.
If you push it over hand hold it in a dive, while trimmed for the original speed, once you let go, it'll smoothly pull up on its own, seeking to regain its trim AOA (it'll overshoot its trim AOA while doing that and hunt up and down in ever smaller deviations until it's fully regained its trim AOA - the Phugoid Oscillation).
It's called static stability.
A descending or diving aircraft has a gravity component pulling it forward, which increases its forward speed.
Increasing forward speed increases lift by the square of the velocity, causing the flight path to curve upwards.
As speed decreases, the process reverses, eventually settling at a velocity where flight remains linear. We then control climbing, descending, or level flight by adding or subtracting thrust with the throttle.
One must be aware, with a tiny tail and the weight too far forward, the wing torque on the center of gravity can overpower the the tail and continue to push the nose down
this is your lawn dart
This is especially true if the wing center of lift moves backwards as velocity increases and/or downwash from the wing helps stall the tail.
It's Called the "(Total) Aerodynamic Force"
The Aerodynamic Force is the net effect of the lift force produced by the aerofoil, and the drag force produced by the same. Because these are integrated, the aerodynamic force tends to be net-tilted back away from the vertical. This force acts on the center of lift (wing) rather than the center of mass of the aircraft as a whole. As such, under certain wing conditions, this force will impart rotation in the pitch axis.
As airspeed increases, both of these forces increase, and their integrated net effect increases. At some point it's enough to overwhelm the natural resistance from the tail and becomes the dominant effect.
Where and if this happens depends entirely on aircraft design. Some craft will NOT recover like this, they'll just lawn-dart without control input (because their wings produce lift in a slightly-forward direction. Some aircraft will do this very aggressively, as a function of deliberate design (it makes them naturally recover from stalls more quickly).
AIUI, This is also why, all things equal, your nose pops up when you add flaps.