Chantal Staquet

The mixing layer and its coherence examined from the point of view of two-dimensional turbulence

A two-dimensional numerical large-eddy simulation of a temporal mixing layer submitted to a white-noise perturbation is performed. It is shown that the first pairing of vortices having the same sign is responsible for the formation of a continuous spatial longitudinal energy spectrum of slope between k −4 and k −3 . After two successive pairings this spectral range extends to more than 1 decade. The vorticity thickness, averaged over several calculations differing by the initial white-noise realization, is shown to grow linearly, and eventually saturates. This saturation is associated with the finite size of the computational domain. We then examine the predictability of the mixing layer, considering the growth of decorrelation between pairs of flows differing slightly at the first roll-up. The inverse cascade of error through the kinetic energy spectrum is displayed. The error rate is shown to grow exponentially, and saturates together with the levelling-off of the vorticity thickness growth. Extrapolation of these results leads to the conclusion that, in an infinite domain, the two fields would become completely decorrelated. It turns out that the two-dimensional mixing layer is an example of flow that is unpredictable and possesses a broadband kinetic energy spectrum, though composed mainly of spatially coherent structures. It is finally shown how this two-dimensional predictability analysis can be associated with the growth of a particular spanwise perturbation developing on a Kelvin-Helmholtz billow: this is done in the framework of a one-mode spectral truncation in the spanwise direction. Within this analogy, the loss of two-dimensional predictability would correspond to a return to three-dimensionality and a loss of coherence. We indicate also how a new coherent structure could then be recreated, using an eddy-viscosity assumption and the linear instability of the mean inflexional shear.

Review of wave‐turbulence interactions in the stable atmospheric boundary layer

Flow in a stably stratified environment is characterized by anisotropic and intermittent turbulence and wavelike motions of varying amplitudes and periods. Understanding turbulence intermittency and wave-turbulence interactions in a stably stratified flow remains a challenging issue in geosciences including planetary atmospheres and oceans. The stable atmospheric boundary layer (SABL) commonly occurs when the ground surface is cooled by longwave radiation emission such as at night over land surfaces, or even daytime over snow and ice surfaces, and when warm air is advected over cold surfaces. Intermittent turbulence intensification in the SABL impacts human activities and weather variability, yet it cannot be generated in state-of-the-art numerical forecast models. This failure is mainly due to a lack of understanding of the physical mechanisms for seemingly random turbulence generation in a stably stratified flow, in which wave-turbulence interaction is a potential mechanism for turbulence intermittency. A workshop on wave-turbulence interactions in the SABL addressed the current understanding and challenges of wave-turbulence interactions and the role of wavelike motions in contributing to anisotropic and intermittent turbulence from the perspectives of theory, observations, and numerical parameterization. There have been a number of reviews on waves, and a few on turbulence in stably stratified flows, but not much on wave-turbulence interactions. This review focuses on the nocturnal SABL; however, the discussions here on intermittent turbulence and wave-turbulence interactions in stably stratified flows underscore important issues in stably stratified geophysical dynamics in general.

Instability mechanisms of a two-dimensional progressive internal gravity wave

We present a detailed investigation of the parametric subharmonic resonance mechanism that leads a plane, monochromatic, small-amplitude internal gravity wave, also referred to as the primary wave, to instability. Resonant wave interaction theory is used to derive a simple kinematic model for the parametrically forced perturbation, and direct numerical simulations of the Boussinesq equations in a vertical plane permit the nonlinear simulation of the internal gravity wave field. The processes that eventually drive the wave field to breaking are also addressed. We show that parametric instability may be viewed as an optimized scenario for drawing energy from the primary wave, that is, from a periodic flow with both oscillating shear and density gradient. Optimal energy exchange maximizing perturbation growth is realized when the perturbation has a definite spatio-temporal structure: its energy is phase-locked with the vorticity of the primary wave. This organization allows the perturbation energy to alternate between kinetic form when locally the primary wave shear is negative, then maximizing kinetic energy extraction from the primary wave, and potential form when the primary wave shear is positive, then minimizing the reverse transfer to that wave. The perturbation potential energy increases through the primary wave density gradient whether the latter is positive, that is when the medium is of reduced static stability, or negative (increased static stability). When the primary wave amplitude is small, all energy transfer terms are predicted well by the kinematic model. One important result is that the rate of potential energy transfer from the primary wave to the perturbation is always larger than the rate of kinetic energy transfer, whatever the primary wave. As the perturbation amplifies, overturned isopycnals first appear in reduced static stability regions, implying that the total field should become unstable through a buoyancy induced (or Rayleigh–Taylor) instability. Hence, a two-dimensional model is no longer valid for studying the subsequent flow development.

Numerical simulation of a two-dimensional internal wave attractor

Internal (gravity) wave attractors may form in closed containers with boundaries non-parallel and non-normal to the gravity vector. Such attractors have been studied from a theoretical point of view, in laboratory experiments and using linear numerical computations. In the present paper two-dimensional numerical simulations of an internal wave attractor are reported, based upon the nonlinear and non-hydrostatic MIT-gcm numerical code. We first reproduce the laboratory experiment of a wave attractor performed by Hazewinkel et al. (J. Fluid Mech. Vol. 598, 2008 p. 373) and obtain very good agreement with the experimental data. We next propose simple ideas to model the thickness of the attractor. The model predicts that the thickness should scale as the 1/3 power of the non-dimensional parameter measuring the ratio of viscous to buoyancy effects. When the attractor is strongly focusing, the thickness should also scale as the 1/3 power of the spatial coordinate along the attractor. Analysis of the numerical data for two different attractors yields values of the exponent close to 1/3, within 30 %. Finally, we study nonlinear effects induced by the attractor.

Valley heat deficit as a bulk measure of wintertime particulate air pollution in the Arve River Valley

Urbanized valleys are particularly vulnerable to particulate air pollution during the winter, when groundbased stable layers or cold-air pools persist over the valley floor. We examine whether the temporal variability of PM10 concentration in the section of the Arve River Valley between Cluses and Servoz in the French Alps can be explained by the temporal variability of the valley heat deficit, a bulk measure of atmospheric stability within the valley. We do this on the basis of temperature profile and ground-based PM10 concentration data collected during wintertime with a temporal resolution of 1 h or finer, as part of the Passy-2015 field campaign conducted around Passy in this section of valley. The valley heat deficit was highly correlated with PM10 concentration on a daily time scale. The hourly variability of PM10 concentrations was more complex and cannot be explained solely by the hourly variability of the valley heat deficit. The interplay of the diurnal cycles of emissions and local dynamics is demonstrated and a drainage mechanism for observed nocturnal dilution of near-surface PM10 concentrations is proposed.

Characterization of Oscillatory Motions in the Stable Atmosphere of a Deep Valley

In a valley sheltered from strong synoptic effects, the dynamics of the valley atmosphere at night is dominated by katabatic winds. In a stably stratified atmosphere, these winds undergo temporal oscillations, whose frequency is given by

Turbulent mixing in a katabatic wind under stable conditions

N \sin {\alpha }

The Atmospheric Boundary Layer during Wintertime Persistent Inversions in the Grenoble Valleys

Nsinα for an infinitely long slope of constant slope angle