Miscible and immiscible viscous fingering in porous media are undesirable for many engineering applications such as chemical enhanced oil recovery, contaminant transport, and liquid chromatography. For chemical enhanced oil recovery, polymer is injected to prevent immiscible viscous fingering between aqueous and oil phases. Polymer solution weakens the growth of immiscible viscous fingers but it may actuate miscible viscous fingering behind the polymer bank when polymer flooding is followed by water flooding. Due to the adsorption of polymer and presence of connate water, two saturation shocks are most commonly formed during polymer flooding. Therefore during typical polymer flooding two immiscible viscous fingering can occur around two saturation shocks. We have performed a Fourier analysis of the saturation and polymer concentration contours at water-oil interface and concentration front after the onset of viscous fingering to obtain the amplitude spectra for different instabilities. We also have calculated root mean square (RMS) of fingers and its variation with time. The Fourier analysis and calculation of RMS at different times are very useful to quantify the evolution of growth rate spectrum for immiscible and miscible instabilities. We have shown that due to adsorption the width of polymer bank decrease very fast for low injection concentration. In this case polymer bank disappear and polymer flooding becomes ineffective. But for high injection concentration the miscible viscous fingers grow very fast and reach the oil bank. This can affect the efficiency of oil displacement. © 2017 Elsevier Ltd