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Based on observations over an alpine glacier, we investigate the turbulent flux dissimilarity between momentum and sensible heat transfer in a stably stratified katabatic flow. The flux correlation coefficient RF is employed as a measure of variable levels of the flux similarity, which are found to be modulated by the anisotropy of turbulence. In the katabatic wind regime over this glacier, heat is transported more efficiently than momentum. Based on quadrant analysis, the sweep–ejection differences in the flux fraction constitute turbulence characteristics in terms of the velocity aspect ratio, which unravel dissimilar transport of momentum and heat. Moreover, an innovative method is established for connecting quadrant analysis and cospectral analysis, whereby the hyperbolic quadrant hole size is coupled to the frequency underlying the fast Fourier transform. In extending applications of octant analysis, we introduce a hypothetical octant hole, whose size is solicited as a proxy for the amplitude scale of fluctuating fluxes. The contributions to R F can then be quantified for eddy structures that are associated with different amplitude scales. The katabatic flow structures identified from octant analysis differ in their behaviour so helping illuminate the outcome of flux dissimilarity. Exhibited as a statistical behaviour regardless of amplitude scale, along-wind rapid motions of heated air parcels can modify fractional contributions to the heat flux instead of the momentum flux, with reductions in R F related to decreasing heat-flux fractions. Besides, along-wind slow motions of cooled air parcels cannot modify the flux fractions for both momentum and heat. Thus, the flux dissimilarity due to low-speed low-temperature eddies cannot be explicable in terms of the flux fractions alone. These findings are an incipient step towards physical understanding of the turbulent flux dissimilarity for a stably stratified katabatic flow. [ABSTRACT FROM AUTHOR]