Fluid instability analysis has been developed for the growth or decay of large, longitudinal roller vortex perturbations imposed at the base of fluids of exponentially stratified viscosities. The analysis is tied to the origin of longitudinal grooving and fluting observed in a region of converging flow in Tiu Vallis, Mars. The analysis tests the propensity of various types of fluids (water, mudflow/debris flow, lava, glacier), defined by their effective viscosity profiles, to develop longitudinal roll patterns as part of their flow field. Fluids which allow growth of these patterns at the scale appropriate to the Mars features have the potential of creating the observed features. The details of the analysis are not presented here; rather, physical description of assumptions used and boundary conditions imposed are discussed, and the results are presented as they pertain to Tiu Vallis. It is found that the grooving pattern in Tiu Vallis has probably been formed by vortex motion in a mudflow or debris-laden slurry, but exact representation of sediment/debris concentration or sediment transport mechanism is not yet possible. The results show that longitudinal vortex motion of the type modelled in the analysis can develop in water, lava, or ice, but that the specific flow characteristics (depth or velocity) of these models which include the vortex motion are physically unreasonable for flow in Tiu Vallis.