On the two-dimensional extension of one-dimensional algebraically growing waves at neutral stability

This work considers two linear operators which yield wave modes that are classified as neutrally stable, yet have responses grow or decay in time. Previously, King et al. (2016) and Huber (2020) examined the one-dimensional (1D) propagation governed by these operators. Here, we extend to spatial dimensions (2D) examine resulting solutions. We find increase of dimension leads long-time behaviour where magnitude is reduced a factor t−12 from 1D Thus, regions solution grew algebraically t12 now neutral 2D, whereas (algebraically exponentially) more quickly 2D. Additionally, admit solutions functions same similarity variable contracts space