3 added 294 characters in body
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Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.
The actual oceans are stirred by currents, so this equilibrium concentration difference isn't present in them. 

Basically they saying that it takes energy to separate a homogeneous solution into parts which are more or less concentrated (and hence more or less dense). Taking into account the gravitational energy, it follows that the least energy state of a column of water is saltier at the bottom.

Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.
The actual oceans are stirred by currents, so this equilibrium concentration difference isn't present in them.

Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.
The actual oceans are stirred by currents, so this equilibrium concentration difference isn't present in them. 

Basically they saying that it takes energy to separate a homogeneous solution into parts which are more or less concentrated (and hence more or less dense). Taking into account the gravitational energy, it follows that the least energy state of a column of water is saltier at the bottom.

2 Mention stirring.
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Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.
The actual oceans are stirred by currents, so this equilibrium concentration difference isn't present in them.

Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.

Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.
The actual oceans are stirred by currents, so this equilibrium concentration difference isn't present in them.

1
source | link

Saltier water has higher mass density, so the gravitational energy can be lowered that way. The concentration differences go up until the free-energy of creating that big a concentration difference balances the gravitational energy change.
Department of Physics, University of Illinois at Urbana-Champaign

Making some simplifying assumptions, they find:

the equilibrium concentration goes up exponentially with depth, by a factor of e for each 10 km or so.