Alice in Wonderland -- Alice and her boat

We all have been familiar with the traditional model of a man and a boat, as shown above -- which is a very good demonstration of the conservation of momentum, and properties of the center of mass. But what if we make some twists?

Alice spent the whole morning sitting in her wooden boat on a still river near the shore and reading her books, sometimes yawning. Initially, she was at the stern of the boat. Suddenly, she saw a fish coming from the bow of the boat, and tried jumping to the bow of the boat, but eventually she didn't catch the fish. Although she didn't manage to do it, she noticed that after some time, the boat is exactly the same distance from the shore as before , which is quite different from what she was told in physic class. She then guessed that there must be some kind of mechanism that caused the boat to stay at the same position.

She considered that there must be some kind of drag force between the boat and water, whose direction is opposite to the velocity of the boat.

Which kind of drag force will allow the boat to stay at exactly the same position regardless of the mass of Alice and her boat after a sufficient period of time ?

Note: $f$ is the magnitude of drag force, $k$ is a constant and $k>0$ , $v$ is the velocity of the boat, $F_N$ is the normal force between boat and water, $f=0$ means there is actually no drag force.

Ignore the air resistance and only consider the drag force between boat and water.