Asymptotics of unit Burger number rotating and stratified flows for small aspect ratio

Rotating and stably stratified Boussinesq flow is investigated for Burger number unity in domain aspect ratio (height/horizontal length) δ<1 and δ=1. To achieve Burger number unity, the non-dimensional rotation and stratification frequencies (Rossby and Froude numbers, respectively) are both set equal to a second small parameter ?<1. Non-dimensionalization of potential vorticity distinguishes contributions proportional to (?δ)⁻¹, δ⁻¹ and O(1). The (?δ)⁻¹ terms are the linear terms associated with the pseudo-potential vorticity of the quasi-geostrophic limit. For fixed δ=1/4 and a series of decreasing ?, numerical simulations are used to assess the importance of the δ⁻¹ contribution of potential vorticity to the potential enstrophy. The change in the energy spectral scalings is studied as ? is decreased. For intermediate values of ?, as the flow transitions to the (δ?)⁻¹ regime in potential vorticity, both the wave and vortical components of the energy spectrum undergo changes in their scaling behavior. For sufficiently small ?, the (δ?)⁻¹ contributions dominate the potential vorticity, and the vortical mode spectrum recovers k⁻³ quasi-geostrophic scaling. However, the wave mode spectrum shows scaling that is very different from the well-known k⁻¹ scaling observed for the same asymptotics at δ=1. Visualization of the wave component of the horizontal velocity at δ=1/4 reveals a tendency toward a layered structure while there is no evidence of layering in the δ=1 case. The investigation makes progress toward quantifying the effects of aspect ratio δ on the ?→0 asymptotics for the wave component of unit Burger number flows. At the lowest value of ?=0.002, it is shown that the horizontal kinetic energy spectral scalings are consistent with phenomenology that explains how linear potential vorticity constrains energy in the limit ?→0 for fixed δ.