The formation of patterns of peaks on the free surface of a magnetic fluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied using a perturbative energy minimization procedure. Extending previous studies the finite depth of the fluid layer is taken into account. Moreover, adding the wave number modulus k to the set of variational parameters also the wave number selection problem is addressed. The results are compared with previous investigations and recent experimental findings.

• Received 1 February 2001

DOI:https://doi.org/10.1103/PhysRevE.64.021406