Do orographic gravity waves break in flows with uniform wind direction turning with height?

The properties and behaviour of orographically generated gravity waves which have a vertical component of propagation are examined by analysing the structure of stationary, hydrostatic waves embedded in a basic state wind field, U, whose direction and magnitude may vary linearly with height, z. From a ray‐tracing analysis it is evident that the wave energy density decays to zero approaching a three‐dimensional (3‐D) critical level in such an ambient flow field where U. k = 0 for the particular horizontal wave vector k = (k, l, 0). This decay of the wave energy density would appear to imply that wave breaking does not naturally occur in 3‐D flows where the wind turns uniformly with height (excepting that wave vectors which do not experience a 3‐D critical level can break due to the decrease of density with height). However, as a linear theory analysis of convective overturning demonstrates, the criterion for wave breaking relaxes as a 3‐D critical level is approached. the gravity wave amplitude is only required to exceed the inverse of the vertical wave number (which is proportional to U. k and decays to zero at the critical level) for overturning to occur. Consequently a linear estimate of whether convective instability will occur depends on the asymptotic limit of the ratio of the wave energy density to the square of the amplitude. It can be shown from the ray‐tracing analysis that for 3‐D flow fields with a mean wind which turns uniformly with height this ratio diverges, implying that the criterion for convective breaking of gravity waves will always be exceeded on approaching such a 3‐D critical level.