Question

why the Pacific Ocean and the Atlantic ocean water will not mix

Answer 1

They do but under the right conditions it can take quite a while for two different flows to mix thoroughly. During calm weather with few waves, or when there is a low flow rate (resulting in laminar flow) mixing can be very slow.

If the flows have different levels of salt, silt or algae you will see a boundary where the two flows meet.
Two flows with distinctly different temperatures can result in the colder heavier water diving below the warmer lighter water. It appears from above that the two different waters are stationary but the mixing is taking place deep below the surface.

Answer 2

It is due to difference in water density, temperature & salinity of the glacial melt water & off shore waters of Gulf of Alaska