In underwater acoustics, shallow-water environments (depth < 200 m) act as modal dispersive waveguides for low frequency sources (f < 250 Hz). Then the signal can be described as a sum of few modal components, each mode propagating with its own wavenumber. A good estimation of those wavenumbers allows environment assessment or source localization. Considering a horizontal line array, a classical method to estimate wavenumber is the 2D Fourier transform, which requires however a long antenna to achieve good performance. In this study, we propose to take into account some physical priors to overcome those limitations. First, the small number of modal components motivates the use of a sparse representation. Different algorithms can be considered to recover the sparse model. Classically, they exploit a discretized wavenumber grid which can result in a lack of precision and be prejudicial for a fine characterization of the underlying physics. To remedy this defect, we propose then to insert a gradient-descent step in a greedy well-known procedure, that is the Orthogonal Matching Pursuit algorithm (OMP). Moreover, as a second physical prior, we also propose to integrate into the estimation procedure a general but robust dispersion relation that relates wavenumbers from one frequency to the next. The performance of the proposed method is validated using the Jaccard?s distance on simulated data, as well as real data acquired in the North Sea during a seismic campaign. It appears in particular more robust to noise or sensor number variations than other state-of-the-art algorithms such as the Bayesian approach proposed in previous work.