Inertia-Gravity Waves in Geophysical Flows

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Smith DMS-1008396 The project aims to better understand the role of inertia-gravity waves in two highly relevant problems in geophysical fluid dynamics: (i) the origin of observed ocean wave spectra, and (ii) tropical cyclogenesis and the preconditioned state for the development of hurricanes. Both studies involve a similar dynamical core, namely, the rotating Boussinesq equations with strong stratification. Previous theoretical progress toward understanding ocean spectra has been made by considering exact three-wave resonances under the weak turbulence paradigm. Here the investigator studies new partial-differential equation models including all three-wave interactions, thus capturing more complete physics. Effects of rotation, stratification and hydrostatic balance are deduced analytically through explicitly derived, nonlinear coupling coefficients. Numerical simulations characterize energy spectra and generation of shear. Adding simplified cloud dynamics (condensation and evaporation of water) to the Boussinesq core allows for investigation of the hurricane embryo. The latter project involves numerical implementation and exploration of a minimal, active moisture model including fast waves, extending recent work using imposed heat sources to incorporate moist processes within the context of balanced models (excluding fast waves). Inertia-gravity waves result from the earth's rotation and density stratification of the atmosphere and oceans. The effects of inertia-gravity waves are varied, for example, waves can self-organize to form large-scale coherent structures widely observed in nature, such as cyclones and/or anticyclones, east-west jets, and horizontal shear layers. Yet there are critically important flows for which the dynamical role of inertia-gravity waves is yet to be described by a fully self-consistent mathematical theory. The project addresses two such fundamental application problems using a combination of analytical and numerical calculations: (i) the scale distribution of wave energy in the oceans, and (ii) tropical cyclogenesis (also known as the hurricane embryo problem). In the oceans, tidal and wind forcing generate internal gravity-wave breaking, ultimately establishing the balance between small-scale mixing and global circulation. For the problem of tropical cyclogenesis, previous mathematical models have filtered out the fast waves, and there is much to learn about the role of fast waves for the emergence and stability of low-altitude cyclonic vertical vorticity, leading ultimately to the formation of a hurricane. The topics involve ocean mixing and ocean-atmosphere interactions, which are important factors in climate.