The wind is a meteorological phenomena, resulting from air movements due to differences in pressure, or differences between earth and air temperatures. The wind flow shows a wide range of different behaviours, and it has great relevance in weather conditions, deeply influences the landscape, and even plays a role in the spread of infectious diseases, so it is of great importance to study and model its behaviour. The wind velocity is a vector field, so we consider in this work a multivariate spatial model that can be addressed through systems of Stochastic Partial Differential Equations (SPDEs). The main goal is to estimate the wind velocity, considering a system of SPDEs, and applying Bayesian inference, based on integrated nested Laplace approximation (INLA) methods, which are theoretically explored here for the particular multivariate case. The results are encouraging, and open new lines of investigation, such as applying statistical methods to study the velocity field of certain fluid flows, instead of solving strongly non-linear partial differential equations.