Events for 04/26/2023 from all calendars

Mathematics in Geosciences

Time: 11:00AM - 12:00PM

Location: BLOC 302

Speaker: Craig Epifanio, Department of Atmospheric Sciences, Texas A&M University

Title: Waves and Instability in Atmospheric Flows Past Mountains https://tamu.zoom.us/j/98780169614?pwd=cU91SHc3VUJ1L3NnZ1VUdnYreS9aUT09

Abstract: One of the primary sources of clear-air turbulence in the atmosphere is the breaking of internal gravity waves forced by flow past topography, otherwise known as mountain wave breaking. It has long been known that if the forcing for a mountain wave is sufficiently nonlinear (i.e., if the obstacle is sufficiently large), than the density surfaces in the wave will overturn and break, causing the flow to locally devolve into turbulence. However, recent work suggests that instability and breaking can also occur in flow past smaller obstacles, particularly if the wave field is susceptible to resonant wave-wave interactions. In the present study, the linear stability of nonlinear, steady-state mountain waves is explored, with an emphasis on obstacles smaller than the critical height for direct wave overturning. Steady, nonlinear wave solutions are obtained using a method based on a nonlinear Newton solver, as applied to a discretized, finite-difference problem in terrain-following coordinates. The Jacobian matrix for the method is then leveraged to form a discretized eigenvalue problem, which in turn yields the fastest growing disturbance modes. The results show that the classical, steady-state wave solutions found in the literature are often unstable, particularly for strongly nonhydrostatic flows. An analysis of the normal modes suggests that the instability stems from a pair of counter-propagating disturbance wave packets, which interact with the background, steady-state wave solution to form something resembling a resonant triad. Time dependent numerical simulations show that as the disturbance modes grow, the flow ultimately devolves into spatially and temporally intermittent turbulence, with characteristics broadly resembling those found in anecdotal turbulence reports.