Froude number and wave speed

For shallow water, the Froude number is defined as object speed / wave speed
or V/c where c=sqrt(g d) and d is water depth and g is acceleration of gravity.

For a boat, Froude number is boat speed / sqrt(g L)
where L is the waterline length.

My question is: What is the physical meaning of sqrt(g L)?
Is this some kind of wave speed?

 

Yes it is related to wave speed (c) where c = sqrt ((g/k) * tanh (k*d)) and where k is wave number (2*pi/wave length) and d is water depth. It has to do with the mass spring of a wave of length L and is required to make the Fn dimensionless. Get out a copy of Oceanographical Engineering by Weigel or Principles of Naval Architecture for a full discussion of the development of Fn and how it is related to the different k's via water depth.