During the Ice Ages, the level of the oceans was 100m lower than today. At this time the island of Kefalonia was part of the European continent. The area was karstified and a cave system, draining the whole area to the Mediterranean sea, was formed. Later the cave system was cut off by a forming valley and it became dry.
About 10.000 years ago, at the end of the Ice Age, the sea level started to rise. The water of the melting glaciers filled the sea and caused a rise in sea level between 80 and 100 meters. Many cave systems, which were less than 100m above sea level, became filled with sea water. A strong proof for this theory are speleothemes found in such caves at 30m below sea level.
The cave system unter the mountain which forms the island of Kefalonia today, was filled with sea water too. The entrances of this system are located at the northern tip of the Argostoli peninsula and all over the main island. The system ends at Sami on the other side of the island. In the system the sweet water of the mediterranean winter rains, which seeps into the rock all over the island mixes with the salt water.
After the Law of Communicating Vessels, the water level in connected tubes has the same level, regardless of their shape and diameter, or the number of tubes. You may remember the equlibrium glas tubes and the coloured water from the school experiment. But this is only the simple version of the law.
Pascal's Law says, that the pressure of liquids is directly proportional to their depth and density. But Leonardo da Vinci (1452-1519) much earlier presented the law of the equilibrium of two liquids of different density in communicating tubes.
Salt water is heavier than sweet water, brackish water in between. If you fill a U-tube with salt water on one side and sweet water on the other side, the level of the salt water will be deeper than the level of the sweet water, although the system is in an equilibrium. And of course, the level of brackish water will be in between.
And a last detail we must understand: if we remove some water from the tubes, both water levels will go down, no matter where we remove the water.
This was the experiment, now to reality. The cave system contains salt water at the Argosotoli end and brackish water at the Sami end, so the water level is below sea level at Argostoli and above sea level at Sami. The difference is about one metre on both sides.
As the water at Argostoli flows into the system, it would fill the whole system until the salt water side reached sea level. This does not happen, as the Sami side forms a spring. When the water level in the system rises, the water level of the spring rises, and brackish water flows into the sea, removing water from the system. As the water level at Sami can not rise above the level of the spring, the water level at Argosotoli will also stay below sea level.
At last we try to understand what happens over years, when above processes goes on and on. Most important is the fact, that brackish water is continually removed from the system at Karavomilos, and it is replaced with salt water at Argostoli.
So all in all we need a third element in our system, the source of the sweet water, which are the rains falling on the karstified center of the island. As long as we feed sweet water into the cave system, the different height of water level on both sides remains and water will flow into the Kathavothres and out of the springs. If there are some dry years with less rain, the water on the brackish side will become less brackish and the difference between water levels will decrease. As the sea water continues to flow, both water levels will rise and the water will still flow, but much slower. Without sweet water the process will come to an end.
And still there is another important detail. If there is a W-shaped tube filled with salt water, water level will be lower in both outer tubes, if we fill sweet water into the center tube. Or in other words: why does the water flow from Argostoli to Sami and not vice versa? The reason is the geography: Argostoli is an peninsula, divided from the main island by the harbour of Argostoli. The clay, which covers the sea floor seems to be more or less water tight, as the cave system is not filled with sea water in the area of the harbour. And also no rain water has a possibility to reach this part of the cave system. This part is always filled with pure salt water, while the rest of the system is filled with brackish water.