Born in Christiania (later renamed Oslo), Bjerknes enjoyed an early exposure to fluid dynamics, as assistant to his father, Carl Anton Bjerknes, who had discovered by mathematical analysis the apparent actions at a distance between pulsating and oscillating bodies in a fluid, and their analogy with the electric and magnetic actions at a distance.

[7] Apparently no attempt had been made to demonstrate experimentally the theories arrived at by the older professor until Vilhelm Bjerknes, then about 17 or 18 years of age, turned his mathematical knowledge and mechanical abilities to the devising of a series of instruments by which all the well-known phenomena of electricity and magnetism were illustrated and reproduced by spheres and discs and membranes set into rhythmic vibration in a bath containing a viscous fluid such as syrup.

These demonstrations formed the most important exhibit in the department of physics at the Exposition Internationale d'Électricité held in Paris in 1881, and aroused greatest interest in the scientific world.

He succeeded in giving the explanation of the phenomenon called "multiple resonance," discovered by Sarasin and De la Rive.

[8] It was this work that inspired both V. Walfrid Ekman and Carl-Gustav Arvid Rossby to apply it to large-scale motions in the oceans and atmosphere and to make modern weather forecasting feasible.

[9] In his Vorlesungen über Hydrodynamische Fernkräfte nach C. A. Bjerknes Theorie (1900–1902) he gave the first complete mathematical and experimental exposition of the discoveries of his father, whose age and excessive self-criticism had prevented him from finishing his work himself.