Fluids cannot withstand shear forces or "water seeks it's own level"
in the less than quantitative common expression.
In real life fluids exert and receive shear forces. Viscosity is in
fact a measure of shear force /unit area. Water just isn't going to
flow fast on a gradient of, say, 0.00000002, the 2.5" sea level drop
from Norfolk to NY.

To keep things simple and easy first set up this problem without taking into account curvature of the earth. Viscosity is const. and only the density varies with temp.

The initial condition is the warmer "packet" of water is a single uniform warmer temperature and cylindrical extending from the floor to the surface inside of a larger radius cylindrical reservoir. There are no independent currents or other issues.

How fast will the center of the warm water rise?

Bret Cahill

To keep things simple and easy first set up this problem without taking into account curvature of the earth. Viscosity is const. and only the density varies with temp.

The initial condition is the warmer "packet" of water is a single uniform warmer temperature and cylindrical extending from the floor to the surface inside of a larger radius cylindrical reservoir. There are no independent currents or other issues.

How fast will the center of the warm water rise?

Bret Cahill