There are two mechanisms for mixing at a liquid-liquid interface, firstly diffusion and secondly physical agitation.
Diffusion is negligably slow in liquids, it takes days for solutes to travel a few centimetres, so the mixing is dominated by physical agitation e.g. wave action, convention currents, wind mixing etc.
In this particular case it's hard to judge what effect waves and wind have. The sea looks very calm, so I'd guess that waves and wind have little effect and it's not that surprising that mixing is slow. I bet that line wouldn't be as well defined the morning after a storm.
This sort of divison isn't that unusual. I grew up in Khartoum where the White Nile and the Blue Nile meet, and the division between them remains sharp for miles. Although I don't have any snaps from that era (I was five :-) the following picture found with google images shows the division nicely.