Øyvind Andreassen

Gravity wave breaking in two and three dimensions: 2. Three‐dimensional evolution and instability structure

A companion paper by Andreassen et al. (this issue) introduced and used a nonlinear, compressible, spectral collocation code to address the relative evolutions of two-dimensional motions obtained in two- and three-dimensional simulations of gravity wave breaking. That study illustrated the effects of instability on the wave field and mean flow evolution and suggested that two-dimensional models are unable to fully describe the physics of the wave breaking process. The present paper examines in detail the structure, evolution, and energetics of the three-dimensional motions accounting for wave instability as well as their associated transports of momentum and heat. It is found that this instability comprises counterrotating vortices which evolve very rapidly within the convectively unstable region of a breaking wave. Instability scales are selected based on wave geometry and vortices are elongated in the streamwise direction (horizontal wavenumber in the spanwise direction) and result in the rapid collapse of superadiabatic regions within the wave field. The resulting spectra show clearly the transition from gravity wave forcing of harmonics of the incident wave to instability onset and evolution. Fluxes of momentum and heat by the instability reveal the manner in which the gravity wave amplitude is constrained and the influences of instability on the wave transports of these quantities. The breakdown of the instability structure and its evolution toward isotropic small-scale structure is the subject of the companion paper by Isler et al. (this issue).

Gravity wave breaking in two and three dimensions: 1. Model description and comparison of two-dimensional evolutions

A nonlinear, compressible, spectral collocation code is employed to examine gravity wave breaking in two and three spatial dimensions. Two-dimensional results exhibit a structure consistent with previous efforts and suggest wave instability occurs via convective rolls aligned normal to the gravity wave motion (uniform in the spanwise direction). Three-dimensional results demonstrate, in contrast, that the preferred mode of instability is a series of counterrotating vortices oriented along the gravity wave motion, elongated in the streamwise direction, and confined to the region of convective instability within the wave field. Comparison of the two-dimensional results (averaged spanwise) for both two- and three-dimensional simulations reveals that vortex generation contributes to much more rapid wave field evolution and decay, with rapid restoration of near-adiabatic lapse rates and stronger constraints on wave energy and momentum fluxes. These results also demonstrate that two-dimensional models are unable to describe properly the physics or the consequences of the wave breaking process, at least for the flow parameters examined in this study. The evolution and structure of the three-dimensional instability, its influences on the gravity wave field, and the subsequent transition to quasi-isotropic small-scale motions are the subjects of companion papers by Fritts et al. (this issue) and Isler et al. (this issue).

Wave breaking signatures in noctilucent clouds

Results of a recent modeling study of gravity wave breaking in three dimensions by Andreassen et al. and Fritts et al. showed wave saturation to occur via a three-dimensional instability oriented normal to the direction of wave propagation. The instability was found to occur at horizontal scales comparable to the depth of unstable regions within the wave field and to lead to substantial vertical displacements and tilting of isentropic surfaces. Because of strong similarities between the wave and instability structures in the simulation and the structure observed in noctilucent cloud layers near the summer mesopause, we have used these model results to compute the advective effects on cloud visibility and structure for a range of viewing angles and cloud layer widths. Our results show the gravity wave breaking signature to provide a plausible explanation of the observed structures and suggest that noctilucent cloud structures may be used in turn to infer qualitative properties of gravity wave scales, energy and momentum transports, and turbulence scales near the summer mesopause.

Evolution and Breakdown of Kelvin–Helmholtz Billows in Stratified Compressible Flows. Part I: Comparison of Two- and Three-Dimensional Flows

Abstract The authors use a nonlinear, compressible, spectral collocation code to examine the evolution and secondary instability of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. Two-dimensional results exhibit structure consistent with previous numerical studies and suggest dissipation via diffusive transports within the billow cores. Results obtained permitting three-dimensional structures show, in contrast, that secondary instability results in a series of counter-rotating vortices that occupy the outer portions of the billow structures, are oriented in the plane of two-dimensional motion, largely along the two-dimensional velocity field, and contribute substantially to mixing and homogenization of the billow cores at later times. Examination of the flow structure leading to secondary instability also suggests an alternative explanation of the nature of this instability in stratified flows to that offered previously. Comparison of the two-dimensional and spanwise-a...

Vorticity dynamics in a breaking internal gravity wave. Part 1. Initial instability evolution

A three-dimensional simulation of a breaking internal gravity wave in a stratied, compressible, sheared fluid is used to examine the vorticity dynamics accompanying the transition from laminar to turbulent flow. Our results show that baroclinic sources contribute preferentially to eddy vorticity generation during the initial convective instability of the wave eld; the resulting counter-rotating vortices are aligned with the external shear flow. These vortices enhance the spanwise vorticity of the shear flow via stretching and distort the spanwise vorticity via advective tilting. The resulting vortex sheets undergo a dynamical (Kelvin{Helmholtz) instability which rolls the vortex sheets into tubes. These vortex tubes link with the original streamwise convective rolls to produce a collection of intertwined vortex loops. A companion paper (Part 2) describes the subsequent interactions among and the perturbations to these vortices that drive the evolution toward turbulence and smaller scales of motion.

Wave Breaking and Transition to Turbulence in Stratified Shear Flows

Abstract In a previous study the authors used a nonlinear, compressible, spectral collocation numerical model to examine the evolution of a breaking gravity wave in two and three dimensions. The present paper extends that effort to examine the implications of higher resolution and smaller dissipation for wave and instability evolutions, transports, and energetics in shear flows aligned with and having a component transverse to the direction of wave propagation. A component of mean shear transverse to the direction of wave propagation (denoted as a skew shear) results in the alignment of instability structures with the background shear flow rather than in the direction of wave propagation. This alignment leads to asymmetric instability structures and less rapid instability growth relative to the parallel shear flow. Slower instability evolution due to a skew shear has several implications for wave breakdown, including a delayed state of maximum instability, a larger wave amplitude prior to and throughout w...

Wave breaking signatures in sodium densities and OH nightglow. 2. Simulation of wave and instability structures

Measurements of atmospheric structure and dynamics near the mesopause were performed using a sodium lidar, an MF radar, and a night-glow CCD camera during the CORN campaign performed in central Illinois during September 1992. The major features of the observed structure on September 27/28 include a low-frequency, large-scale wave accounting for persistent overturning of the temperature and sodium density fields, superposed higher-frequency motions, small-scale transient ripples in the nightglow images suggestive of instability structures, and large-scale wind shear near the height of apparent instability. We describe four simulations of wave breaking with a three-dimensional model designed to assist in the interpretation of these observations. Two simulations address the instability of a low-frequency wave in a background shear flow with and without higher-frequency modulation. These show higher-frequency motions to be important in assigning the spatial and temporal scales of instability structures. Two other simulations examine the instabilities accompanying a convectively unstable inertia-gravity wave with and without higher-frequency modulation without mean shear. These show the instability structure to remain aligned in the direction of wave propagation, with only weak influences by the high-frequency motion. Our results suggest that instability due to a superposition of waves accounts best for the nightglow features observed during the CORN campaign and that streamwise convective instabilities observed due to wave breaking at higher intrinsic frequencies continue to dominate instability structure for internal waves for which inertial effects are important.

Evolution and Breakdown of Kelvin–Helmholtz Billows in Stratified Compressible Flows. Part II: Instability Structure, Evolution, and Energetics

Abstract A companion paper by Fritts et al. employed a nonlinear, compressible, spectral collocation code to examine the effects of secondary instability on the evolution of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. The purpose of this paper is to examine the structure, sources, evolution, and energetics of the secondary instability itself. It is found that this instability comprises counterrotating vortices aligned largely along the two-dimensional velocity field (with spanwise wavenumber), with initial instability occurring in the stably stratified braids between adjacent billows and thereafter in the billow cores as maximum KH amplitudes are achieved. The more energetic secondary instabilities are confined to the billows, where the major sources of instability energy are buoyancy and shear due to negative stratification and the solenoidal generation of negative spanwise vorticity within the billow cores. Strain also represents a significant source of streamwis...

Visualization of vector fields using seed LIC and volume rendering

Line integral convolution (LIC) is a powerful texture-based technique for visualizing vector fields. Due to the high computational expense of generating 3D textures and the difficulties of effectively displaying the result, LIC has most commonly been used to depict vector fields in 2D or over a surface in 3D. We propose new methods for more effective volume visualization of three-dimensional vector fields using LIC: 1) we present a fast method for computing volume LIC textures that exploits the sparsity of the input texture. 2) We propose the use of a shading technique, called limb darkening, to reveal the depth relations among the field lines. The shading effect is obtained simply by using appropriate transfer functions and, therefore, avoids using expensive shading techniques. 3) We demonstrate how two-field visualization techniques can be used to enhance the visual information describing a vector field. The volume LIC textures are rendered using texture-based rendering techniques, which allows interactive exploration of a vector field.

Gravity wave breaking in two and three dimensions: 3. Vortex breakdown and transition to isotropy

Companion papers by Andreassen et al. (this issue) and Fritts et al. (this issue) introduced a nonlinear, compressible, spectral collocation code and applied it to studies of gravity wave breaking in two and three dimensions. The former showed the two simulations to differ dramatically in the mode of instability and in its implications for the wave and mean flow evolutions. The latter considered in detail the structure and energetics of the instability and its influences via eddy transports of momentum and heat. This paper addresses the instability structure and evolution at late times, focusing specifically on secondary instability, vortex breakdown, and the transition to isotropic structure. These results exhibit several distinct behaviors, depending on the local environment. In the presence of weak environmental shears, vortex breakdown occurs through mutual interactions which cause a gradual nonlinear evolution toward smaller scales of motion. Where wave and mean shears are strong, vortex breakdown is accelerated by dynamical instability processes at small scales which modulate strongly the vortex structures due to wave instability. Spectral results suggest that our simulation has described the transition from two-dimensional laminar wave motions to three-dimensional isotropic small-scale structure.