As ice flows across the lake, deep within the ice sheet, the internal layers diverge from the ice base in the south of the lake and converge to the ice base in the north. Thus,...

Our results indicate that ice melts in one place and freezes in another. It is a mechanism by which nutrients can be input to the lake.

This means that (glacial) ice melts, leaves the gas hydrates and sediment in the lake, and then freezes as H2O.

The density contrast between these waters will cause the circulation.

Now you have to accept that there will be communication between the lakes.