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Motivated by recent Parker Solar Probe (PSP) observations of "switchbacks"(abrupt, large-amplitude reversals in the radial magnetic field, which exhibitAlfv\'enic correlations) we examine the dynamics of large-amplitude Alfv\'enwaves in the expanding solar wind. We develop an analytic model which makesseveral predictions: switchbacks should preferentially occur in regions wherethe solar wind plasma has undergone a greater expansion, the switchbackfraction at radii comparable to PSP should be an increasing function of radius,and switchbacks should have their gradients preferentially perpendicular to themean magnetic field direction. The expansion of the plasma generates smallcompressive components as part of the wave's nonlinear evolution: these aremaximized when the normalized fluctuation amplitude is comparable to$\sin\theta$, where $\theta$ is the angle between the propagation direction andthe mean magnetic field. These compressive components steepen the primaryAlfv\'enic waveform, keeping the solution in a state of nearly constantmagnetic field strength as its normalized amplitude $\delta B/B$ grows due toexpansion. The small fluctuations in the magnetic-field-strength are minimizedat a particular $\theta$-dependent value of $\beta$, usually of order unity,and the density and magnetic-field-strength fluctuations can be correlated oranticorrelated depending on $\beta$ and $\theta$. Example solutions of ourdynamical equation are presented; some do indeed form magnetic-field reversals.Our predictions appear to match some previously unexplained phenomena inobservations and numerical simulations, providing evidence that the observedswitchbacks result from the nonlinear evolution of the initiallysmall-amplitude Alfv\'en waves already known to be present at the coronal base.

Evolution of large-amplitude Alfv\'en waves and generation of switchbacks in the expanding solar wind