This paper presents results from the first fully three-dimensional direct numerical simulations of initially turbulent wakes with net momentum in unstratified and density stratified fluids. The initial conditions contain a super-position of an initially axisymmetric mean streamwise velocity profile plus a spectrally specified fluctuation velocity field with initially incoherent phases to model initial turbulence. To provide evidence in favor of their validity, we compare results from these simulations with previous measurements behind towed bodies in wind tunnels and towing tanks, and also compare with theories of turbulent wakes. Comparisons with laboratory flow experiments provide agreement, both with statistical quantities and vortex structures and evolution. We subsequently investigate open questions by analysis of the fully three-dimensional flow. Coherent vortices in stratified wakes have their origins in the vortex geometry of the mean wake flow, and do not require stratification or coherent seeding in the initial velocity fluctuations. We conclude that the simulations provide a trustworthy and valuable complement to wake research, and that the vortex structures result from a combination of the necessity that vortices form loops and diffusion of vorticity to smooth the loops into rings.

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Instabilities and turbulence extending to the smallest dynamical scales play important roles in the deposition of energy and momentum by gravity waves throughout the atmosphere. However, these dynamics and their effects have been impossible to quantify to date due to lack of observational guidance. Serendipitous optical images of polar mesospheric clouds at ∼82 km obtained by star cameras aboard a cosmology experiment deployed on a stratospheric balloon provide a new observational tool, revealing instability and turbulence structures extending to spatial scales < 20 m. At 82 km, this resolution provides sensitivity extending to the smallest turbulence scale not strongly influenced by viscosity: the "inner scale" of turbulence, l0 ∼10(ν 3 / ) 1/4 . Such images represent a new window into small-scale dynamics that occur throughout the atmosphere but are impossible to observe in such detail at any other altitude. We present a sample of images revealing a range of dynamics features, and employ numerical simulations that resolve these dynamics to guide our interpretation of several observed events.

We present a formal solution to the initial value problem for small perturbations of a straight vortex tube with constant vorticity, and show that any initial perturbation to such a tube evolves exclusively as a collection of Kelvin vortex waves. We then study in detail the evolution of the following particular initial states of the vortex tube: (i) an axisymmetric pinch in the radius of the tube, (ii) a deflection in the location of the tube, and (iii) a flattening of the tube's cross-secton. All of these initial states are localized in the direction along the tube by weighting them with a Gaussian function. In each case, the initial perturbation is decomposed into packets of Kelvin vortex waves which then propagate outward along the vortex tube. We discuss the physical mechanisms responsible for the propagation of the wave packets, and study the consequences of wave dispersion for the solution.