The amplitude of nonstationary trapped waves

Prior studies of trapped lee waves have typically focused on simplified 2D cases that can mask more complex 3D behavior that waves may experience in nature (such as untrapping by gradients in the mean flow). Steady simulations of trapped waves have shown that such waves are weaker in the 3D case than in 2D due to the increase in flow around the mountain, and the lateral dispersion of wave energy. 3D simulations of both vertically propagating and trapped waves in steady flows show that the drag generated by 3D waves is weaker than in 2D – tending towards an upper limit at large aspect ratio.

Results from our numerical simulation of 3D trapped waves in a time-varying, horizontally uniform flow show 3D nonstationary lee waves may be stronger than their 2D nonstationary equivalent. The intensification in 3D is the result of nonlinear perturbations in the flow around the mountain, acting to strengthen waves in the lee through interactions with waves in a mean flow different to that which forced the perturbation. Amplification of the waves in 3D appears strongest as waves interact with perturbations that were generated around the time of peak flow. Strengthening is strongest in the immediate lee, but persists downstream despite increased lateral dispersion in 3D. There is an optimal horizontal aspect ratio for the greatest strengthening to occur, and 3D waves tend towards the 2D limit from above at large aspect ratios. In contrast, pressure drag caused by the non-steady waves shows no amplification in 3D, and there is no optimal aspect ratio for the drag. Instead, non-steady wave drag tends towards an upper limit at large aspect-ratio - in a similar manner to the behavior of steady waves.

Additionally, simulations of trapped waves with a stratosphere aloft show wave amplitude varies in response to the stability in the stratosphere. Waves are stronger at the surface with a stratosphere due to constructive reflections of wave energy from each stability interface – a process that can be well explained using previous theories. It has long been thought that leakage of wave energy into the stratosphere is a mechanism through which trapped waves decay over time in nature – a process that occurs in our steady, 2D simulations. However, the downstream decay of lee waves is slower with a stratosphere aloft than in the no-stratosphere case for waves in our 3D spatially-varying, time-evolving flow and we discuss the wave mechanisms that lead to this result.