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It is of interest to investigate how a swimming animal performs in a density stratified fluid. This paper studies a simplified swimmer, a pitching NACA0015 airfoil, considering its locomotion in both homogeneous, or unstratified, and stratified fluid flows. A direct comparison is made between these two conditions, through two-dimensional numerical simulations. Our numerical results show that the stratification modifies the dynamics of the pitching foil in both its wake structures and the drag force, or thrust, as well as its propulsive performance. We suggest that the effects of stratification on the flapping performance or the propulsive efficiency can be categorized according to the Froude number, or the level of stratification. First, in the range of high Froude numbers, notable modification of the flow structure can be observed, which however does not affect much the propulsive performance. Second, at a very low Froude number, i.e., $Fr=1$, the propulsive efficiency drops markedly compared to its homogeneous counterpart, attributed to the pronounced internal waves induced by the strong stratification. Moreover, at a moderate Froude number $Fr=2$, we find an increase in the propulsive efficiency, which can be explained by the unique variation in the wake structure. At $A_D=2.50$, the propulsive efficiency peaks at $Fr=2$, with its efficiency $18.3\%$ higher than its homogeneous counterpart, exhibiting a favourable influence of the stratification on a swimmer.

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Using two-dimensional numerical simulations, we investigate a circular cylinder in a stratified flow with a pycnocline of a smooth density profile. We are particularly concerned about the difference between stratified flows and their homogeneous, or unstratified, counterparts in drag coefficients. It is well known that the characteristics of a stratified flow depend on the Reynolds number Re and the internal Froude number Fr. First, we change the incoming flow velocity, with the Reynolds number and the internal Froude number varying simultaneously, in the ranges of 76{less than or equal to}Re{less than or equal to}579 and 0.14{less than or equal to}Fr{less than or equal to}1.046, respectively. We find that the flow experiences a sequence of flow patterns, namely `multiple centreline structures', `isolated mixed regions', and `vortex shedding', as we increase this combination, agreeing well with the previous experiments in the low Re and Fr ranges. Meanwhile, the mean drag coefficient decreases, and drops below the value for a homogeneous state as an empirical stability parameter, k, drops below unity, indicating the transition from a lee-wave dominant wake to an unsteady, vortex shedding wake. This unique variation of drag coefficient is more clearly shown in another situation, when we fix the Reynolds number at Re=234 while varying the Froude number within 0.094{less than or equal to}Fr{less than or equal to} 4.192. In such a situation, we observe a stable `double eddy' pattern at Fr=1.87, around which a minimum of mean drag coefficient is reached. At this critical point, we understand that the stratification in the flow inhibits lee-side separation, while the internal waves have not yet played a significant role.

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