How to wave texture distort the model of a basic plane? (and possibly animate?)

[b_t]

What I did so far was to create a wave texture that is a distorted and play with the distortion knob so that it becomes like moving oil (animation)

But I don’t want just the texture but the whole model of the subdivided plane.
Something like this :

[RSEhlers]

In EeVee use a Displace Modifier with a texture…Key Frame with the scale or distortion in the Texture

[LordoftheFleas]

With geometry nodes, you can use a 4D-noise tecture and use the frame number (I juts typed in #frame/100 in the W field) to control the 4th dimension.