Introduction

Today many works are still devoted to RR Lyrae stars (see Barnes III 1997 or the last conference held in Los Alamos in June 1997). The recent massive photometric surveys (MACHO, EROS, OGLE, ...) have provided powerful databases to study some basic physical problems such as the existence of the second overtone (Kovács 1998a) or the dependence of absolute magnitude on metallicity (Bono et al. 1997 or Kovács 1998b). Moreover, detailed comparisons between observations and nonlinear pulsating models shows that serious discrepancies exist (Kovács & Kanbur 1998). Buchler (1998) gives a general review of the recent advances in nonlinear pulsation theory. In particular, the effect of the convection has been well investigated (Bono & Marconi 1998; Feuchtinger & Dorfi 1998). Nevertheless, hydrodynamical models of the pulsation of the atmosphere including shock waves together with the calculation of line profiles and their comparison with high resolution observations are still exceptional (e.g. Fokin & Gillet 1997).

Recently Gillet et al. (1998a) suggested that the microturbulent velocity variation in the atmosphere of the $\delta$ Cephei star has two physical origins. The first one is the slow global density variation due to pulsation, and the second one is associated with the shock waves propagating in the atmosphere. In the $\delta$ Cephei atmosphere the effect of the global pulsation prevails, causing the v_turb to vary from 2.2 to 7.5km/s at maximum compression. Shocks lead to a smaller turbulence amplification, by about 1.5 to 3km/s depending of the shock intensity.

An inspection of different theoretical models reveals that the shock waves generation in classical Cepheid, BL Herculis, W Virginis or RR Lyrae stars have many in common (Fokin & Gillet 1994; Fokin et al. 1996 or FGB hereafter; Fokin & Gillet 1997). In particular, three main shock waves are produced at each pulsation period due to similar physical mechanisms. However, their amplitudes strongly differ from one star to another. For instance, in $\delta$ Cephei the strongest shock amplitude does not exceed 20-25km/s , while in RR Lyrae the total cumulative shock reaches as high as 140-170km/s .

A simplified theoretical study of the turbulence amplification by a shock wave in $\delta$ Cephei has recently been given by Gillet et al. (1998b). It appears that the best turbulence amplification models, which are based on the adiabatic assumption (weak shocks), predict a too large amplification when the shock Mach number M exceeds 1.5. Unfortunately, an accurate quantitative comparison was not possible in this paper because of numerical problems were present at the phase of the strongest atmospheric shock in $\delta$ Cephei (M=2.4). On the contrary, RR Lyrae is known (Fokin & Gillet 1997) to exhibit quite strong shocks up to $M\approx\,25$ in the highest part of its atmosphere (log$\rho$=-13$g/cm³). Thus, RR Lyrae provides a good opportunity to check if the theoretical amplification rate of the turbulence is relevant for nonadiabatic shocks. It would be also interesting to know the real amplification rate which is overestimated by the adiabatic approach.

In Section2 we describe the method used for the reconstruction of the FeII line profiles. The determination of the turbulent velocity is presented in Sect.3, and the results are discussed in Sect.4. We also compare our results with those obtained earlier for $\delta$ Cephei. Finally, some concluding remarks are given in Sect.5.