Carl Erik Wasberg

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).

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.

Variational multiscale turbulence modelling in a high order spectral element method

In the variational multiscale (VMS) approach to large eddy simulation (LES), the governing equations are projected onto an a priori scale partitioning of the solution space. This gives an alternative framework for designing and analyzing turbulence models. We describe the implementation of the VMS LES methodology in a high order spectral element method with a nodal basis, and discuss the properties of the proposed scale partitioning. The spectral element code is first validated by doing a direct numerical simulation of fully developed plane channel flow. The performance of the turbulence model is then assessed by several coarse grid simulations of channel flow at different Reynolds numbers.

Pseudospectral methods with open boundary conditions for the study of atmospheric wave phenomena

Abstract We consider Chebyshev pseudospectral methods for the study of atmospheric wave phenomena. The governing equations are the two-dimensional Euler equations for gas dynamics with gravity included, where accurate numerical approximation of the nonlinear behaviour is important. The methods are efficiently implemented on a Cray X-MP, and run at nearly optimal speed on one processor. In this case, space derivatives are calculated more efficiently with matrix multiplication than by the Fast Fourier Transform. The boundaries are artificial and we simulate open boundaries by using the characteristic variables of the equations. Different choices of such boundary conditions and their effects on the solutions are discussed. Numerical calculation of an example where the solution may be analytically verified is presented, and the pseudospectral method is seen to be well suited for these computations.

Post-Processing of Marginally Resolved Spectral Element Data

When derivatives of a spectral element solution are used in a different context, such as visualization or in calculations with a different numerical method, the discontinuity of the derivatives at the element interfaces is a potential problem. Asymptotically, the jumps in the derivatives decay spectrally fast, but it is not always possible or efficient use of computational resources to repeat the spectral element calculations with increased resolution. The usual way of treating the discontinuities is discussed here, however it is not always satisfactory. New methods based on polynomial interpolation across element interfaces and polynomial filtering are suggested, and illustrated by examples.

The formation of a thin horizontal layer by the interaction of a gravity wave with a wind shear as investigated by numerical methods

Abstract An internal gravity wave critical layer problem in a stably stratified isothermal atmosphere is treated numerically by the Chebyshev spectral collocation method. The processes involved give rise to nearly horizontal layers similar to those observed in the real atmosphere. Observation of the temporal behavior of the vertical component of the wind field carried out with the EISCAT VHF radar is compared with the simulations and there is qualitatively a striking similarity between the observed data and the results of the simulations. The evolution of the wind, temperature and Richardson number R i fields are considered.