The eigenvalue problem of Kuo governing the linear stability of a parallel zonal flow of an inviscid incompressible fluid on a β-plane is treated in this paper. First, a synthesis of the known properties of the normal modes is presented, as a short summary. The rest of the paper is a study of the properties of one of the classes of stable modes, namely Rossby waves modified by the basic shear. These modes are found as the solution of the inverse of a regular Sturm–Liouville problem. Several asymptotic results for small and for increasing values of the basic shear (i.e. equivalently for large and decreasing values of β) are found for quite general velocity profiles. These are illustrated by some numerical calculations of the wave characteristics for a few particular basic velocity profiles.

Optical thresholds, that correspond to a level located at 1 eV above the valence band, are observed by photocapacitance techniques in n-type Mg-doped GaN. In undoped GaN, this level has been previously related to the yellow emission detected by photoluminescence. In Mg-doped GaN, this yellow luminescence is only observed for excitation energies below the Mg-related band (2.9 - 3 eV). This result evidences that Mg-doping may reduce but not avoid the formation of the yellow band related defects in n-type and semiinsulating Mg-doped samples. The fact that the yellow luminescence is not observed for excitation energies above the bandgap may be justified by a higher efficiency of the Mg-related recombination path.

Undoped layers of GaN grown by MOVPE on sapphire substrates have been characterized by photoluminescence, photocapacitance and photoinduced current transient spectroscopy (PICTS). Photocapacitance reveals in all samples two specific signatures at photon energies of 1 eV and 2.5 eV. The photocapacitance decrease observed at 1 eV seems to be due to an electron capture process from the valence band, whereas the capacitance increase at 2.5 eV is related to an electron emission process. The fact that the capacitance step at 1 eV is only seen after photoionization at energies above 2.5 eV, and the observed correlation between its amplitude and the photoluminescence intensity of the “yellow band”, lead us to conclude that both transitions are linked to the same trap, which is also suggested to be responsible for the yellow band. The position of this trap, at 2.5 eV below the conduction band, is confirmed by PICTS measurements, that show a hole thermal emission activation energy of 0.9 eV at 350 K.