  In this work we introduce a certified Reduced Basis VMS-Smagorinsky
turbulence model with local projection stabilisation (LPS) on the pressure. We
prove its stability for Taylor-Hood discretisations of velocity-pressure. We
construct an \textit{a posteriori} error estimator for the snapshot selection
through a Greedy algorithm, based on the Brezzi-Rappaz-Raviart theory of
approximation of non-singular branches of non-linear PDEs. The Empirical
Interpolation Method (EIM) is used for the approximation of the non-linear
terms. We present some numerical tests in which we show an improved speedup on
the computation of the reduced basis problem with the LPS pressure
stabilisation, with respect to the method of using pressure supremizers.
