Why are fluid properties continuous with respect to spatial variables?

Question

I get the intuition behind the continuum hypothesis in which we may treat a fluid as a continuous distribution of matter if we’re studying the fluid at a macroscopic scale. But the continuum hypothesis doesn’t provide any reasoning behind why fluid properties like density and temperature tend to be continuous in space — that is, fluid properties usually do not jump from one value to another as you go from one point to the next in the fluid continuum. With that said, why do fluid properties tend to be continuous in space?

Answer 1

That's because all the neighboring fluid parcels surrounding any point within that fluid are in communication with the fluid parcel occupying that point. This means that in any given fluid parcel, its temperature, pressure, and velocity are "felt" across the interfaces shared between that parcel and all its nearest neighbor parcels. This means that any initially discontinuous properties in one parcel are shared with the nearest neighbor parcels at a speed which is determined by the vibrational speed of movement of the molecules making up that parcel, which is fast enough to render the macroscopic properties of the fluid continuous on the time scales characteristic of (macroscopic) pressure, temperature, and velocity measurement devices. .