Gentlemen; first off, what you see depicted above is NOT Damascus, although it is often referred to by that term. What that knife is made of is pattern welded steel. Rods of differing carbon content are heated while in a bundle, and then welded together by pounding with a hammer. The twisting of the rods produces a pleasant pattern.
Actually, the patterns seen today are primitive compared to the shotgun bbls. produced by pattern welding in the mid to late 1800's. Even after the introduction of the stronger fluid steel bbls., pattern welded 'Damascus' bbls. continued to command a premium price.
'Damascus' steel today has only one purpose: decoration. There was a day (starting about AD 800, ending around 1700 or so) when Damascus, or 'Wootz' steel offered advantages to knife and sword blades. Japanese blades, Nihonto, are made from Wootz steel. The layers are parallel to the surface, along the length of the blade. Contrast this with present day pattern welded steel, where the blade is fashioned by cutting across the cross sections of the welded, twisted rods.
I am unaware of any galvanic activity ever reported in Damascus or pattern welded steel. One consideration has been raised concerning the migration of carbon from the high carbon steel layers to the low carbon steel layers. This seems more to be fantasy than fact. Nohonto exist from before AD800, but one Nihonto, 'The Little Crow,' which dates from about 800, still clearly shows lamination marks, which argues against carbon migration to any significant degree.
Damascus, or pattern welded steel; I love it. For decoration and extremely light use only. Frankly, to use one of these knives for general use is a lot like letting your 4 yo son use your Ti golf clubs for knocking rocks around the yard.
Hope this helps. Walt