The stability, structure and dynamics of gas giants’ intense east-west winds (so-called "zonal jets") are still poorly understood, especially in terms of coupling with the deep molecular interior of the planet. Here, we built an analogous experimental setup based on three key ingredients of zonal jets formation. First, we fill a 1.6 m high cylindrical tank with 800 L of water, and make it rotate at more than 1 round per second to reproduce the planet's fast rotation. Then, the paraboloidal free-surface due to rotation allows us to have a varying height of fluid which reproduces the varying height of the jets as a function of latitude. Finally, we reproduce the small storms and convective motions inside the planets by generating small eddies at the base of the tank using submersible pumps. A top view of this experiment is similar to a view of the planet from the pole. With those three ingredients, we indeed observe the self-development of zonal jets, going successively in clockwise and anticlockwise directions. Additionally, their strength is indicative of a regime relevant to gas giants, which has hardly ever been reached before experimentally.