Inertia–Gravity Wave Generation by Balanced Motion: Revisiting the Lorenz–Krishnamurthy Model

The spontaneous generation of inertia-gravity waves by balanced motion at low Rossby number is examined using Lorenz's ve-component model. The mostly numerical analysis by Lorenz & Krishnamurthy of a particular (homoclinic) balanced solution is complemented here by an asymptotic analysis. An exponential-asymptotic technique provides an estimate for the amplitude of the fast inertia-gravity oscillations which are generated spontaneously, through what is shown to be a Stokes phenomenon. This estimate is given by 22 exp[=(2)], where 1 is proportional to the Rossby number and the prefactor is determined from recurrence relations. The nonlinear dependence of on the O(1) rotational Froude number indicates that the feedback of the inertia-gravity waves on the balanced motion directly aects their amplitude. Numerical experiments conrm the analytic results. Optimally truncated slaving relations are used to separate the exponentially small inertia-gravity oscillations from the (much larger) slow contribution to the dependent variables. This makes it possible to examine the switching-on of the oscillations in detail; it is shown to be described by an error function of t=1=2 as predicted theoretically. The results derived for the homoclinic solution of Lorenz & Krishnamurthy are extended to more general, periodic, solutions. 2 1