Vector field (VF) is a special kind of multidimensional data. In each pixel, VF contains information about the direction and the magnitude of the measured quantity. To detect the patterns of interest in the field, special matching methods must be developed. We propose a method for the description and matching of VF patterns under an unknown affine transformation of the field. Unlike digital images, transformations of VFs act not only on the spatial coordinates but also on the field values, which makes the detection different. To measure the similarity between the template and the field patch, we propose original invariants with respect to affine transformation designed from moments. Their performance is demonstrated by experiments on real data from fluid mechanics.