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Pattern formation due to oscillating reactions represents variable naturaland engineering systems, but previous studies employed only simple flowconditions such as uniform flow and Poiseuille flow. We studied the oscillatingreaction in porous media, where dispersion enhanced the spreading of diffusingcomponents by merging and splitting flow channels. We considered the saddleflow, where the stretching rate is constant everywhere. We generated patternswith the Brusselator system and classified them by instability conditions andP\'eclet number (Pe), which was defined by the stretching rate. The resultsshowed that each pattern formation was controlled by the stagnation point andstable and unstable manifolds of the flow field due to the heterogeneous flowfields and the resulting heterogeneous dispersion fields. The characteristicsof the patterns, such as the position of stationary waves parallel to theunstable manifold and the size of local stationary patterns around thestagnation point, were also controlled by Pe.

Oscillating reaction in porous media under saddle flow