Generalizing Monin-Obukhov Similarity Theory (1954) for Complex Atmospheric Turbulence.

Monin-Obukhov similarity theory (MOST) forms the basis for parametrizations of turbulent exchange in virtually all numerical models of atmospheric flows. Yet, its limitations to flat and horizontally homogeneous terrain have plagued the theory since its inception. Here we present a first generalized extension of MOST based on the inclusion of turbulence anisotropy as an additional nondimensional term. This novel theory developed based on an unprecedented ensemble of complex atmospheric turbulence datasets covering flat to mountainous terrain, is shown to be valid in conditions in which MOST fails and thus paves the way to a better understanding of complex turbulence.

Universal Return to Isotropy of Inhomogeneous Atmospheric Boundary Layer Turbulence.

A recalcitrant problem in the physics of turbulence is the representation of the tendency of large-scale anisotropic eddies to redistribute their energy content with decreasing scales, a phenomenon referred to as return to isotropy. An unprecedented dataset of atmospheric turbulence measurements covering flat to mountainous terrain, stratification spanning convective to very stable conditions, surface roughness ranging over several orders of magnitude, and Reynolds numbers that far exceed the limits of direct numerical simulations and laboratory experiments was assembled for the first time and used to explore the scalewise return to isotropy. The multiple routes to energy equipartitioning among velocity components are shown to be universal once the initial anisotropy at large scales, linked to turbulence generation, is accounted for.

Validation of a simple diagnostic relationship for downslope flows.

A simple conceptual view of downslope flows allows a derivation of a diagnostic relationship between the maximum depth of the flow, its speed, the slope angle and the cooling flux. This relationship is obtained considering that the turbulence cooling causing the air to flow downslope is essentially compensated by the warming by compression as the flow reaches higher pressure levels. The obtained relationship is consistent with the bulk heat budget for the along-slope flows, and its agreement with existing prognostic layer-averaged models is checked. Finally, the depth of the flow obtained from the diagnostic relationship is compared against the observational estimations of katabatic flows from two experimental campaigns.

Anisotropy of Unstably Stratified Near-Surface Turbulence.

Classic Monin-Obukov similarity scaling states that in a stationary, horizontally homogeneous flow, in the absence of subsidence, turbulence is dictated by the balance between shear production and buoyancy production/destruction, whose ratio is characterized by a single universal scaling parameter. An evident breakdown in scaling is observed though, through large scatter in traditional scaling relations for the horizontal velocity variances under unstable stratification, or more generally in complex flow conditions. This breakdown suggests the existence of processes other than local shear and buoyancy that modulate near-surface turbulence. Recent studies on the role of anisotropy in similarity scaling have shown that anisotropy, even if calculated locally, may encode the information about these missing processes. We therefore examine the possible processes that govern the degree of anisotropy in convective conditions. We first use the reduced turbulence-kinetic-energy budget to show that anisotropy in convective conditions cannot be uniquely described by a balance of buoyancy and shear production and dissipation, but that other terms in the budget play an important role. Subsequently, we identify a ratio of local time scales that acts as a proxy for the anisotropic state of convective turbulence. This ratio can be used to formulate a new non-dimensional group. Results show that building on this approach the role of anisotropy in scaling relations over complex terrain can be placed into a more generalized framework.

On the turbulence structure of deep katabatic flows on a gentle mesoscale slope.

A comprehensive analysis of the turbulence structure of relatively deep midlatitude katabatic flows (with jet maxima between 20 and 50 m) developing over a gentle (1°) mesoscale slope with a long fetch upstream of the Meteor Crater in Arizona is presented. The turbulence structure of flow below the katabatic jet maximum shows many similarities with the turbulence structure of shallower katabatic flows, with decreasing turbulence fluxes with height and almost constant turbulent Prandtl number. Still stark differences occur above the jet maximum where turbulence is suppressed by strong stability, is anisotropic and there is a large sub-mesoscale contribution to the flux. Detecting the stable boundary-layer top depends on the method used (flux- vs. anisotropy-profiles) but both methods are highly correlated. The top of the stable boundary layer, however, mostly deviates from the jet maximum height or the top of the near-surface inversion. The flat-terrain formulations for the boundary-layer height correlate well with the detected top of the stable boundary layer if the near-surface and not the background stratification is used in their formulations; however, they mostly largely overestimate this boundary-layer height. The difference from flat-terrain boundary layers is also shown through the dependence of size of the dominant eddy with height. In katabatic flows the eddy size is semi-constant with height throughout the stable boundary-layer depth, whereas in flat terrain, eddy size varies significantly with height. Flux-gradient and flux-variance relationships show that turbulence data from different stable boundary-layer scaling regimes collapse on top of each other showing that the dominant dependence is not on the scaling regime but on the local stability.

Scaling, Anisotropy, and Complexity in Near-Surface Atmospheric Turbulence.

The development of a unified similarity scaling has so far failed over complex surfaces, as scaling studies show large deviations from the empirical formulations developed over flat and horizontally homogeneous terrain as well as large deviations between the different complex terrain data sets. However, a recent study of turbulence anisotropy for flat and horizontally homogeneous terrain has shown that separating the data according to the limiting states of anisotropy (isotropic, two-component axisymmetric and one-component turbulence) improves near-surface scaling. In this paper we explore whether this finding can be extended to turbulence over inclined and horizontally heterogeneous surfaces by examining near-surface scaling for 12 different data sets obtained over terrain ranging from flat to mountainous. Although these data sets show large deviations in scaling when all anisotropy types are examined together, the separation according to the limiting states of anisotropy significantly improves the collapse of data onto common scaling relations, indicating the possibility of a unified framework for turbulence scaling. A measure of turbulence complexity is developed, and the causes for the breakdown of scaling and the physical mechanisms behind the turbulence complexity encountered over complex terrain are identified and shown to be related to the distance to the isotropic state, prevalence of directional shear with height in mountainous terrain, and the deviations from isotropy in the inertial subrange.

Dependence of near-surface similarity scaling on the anisotropy of atmospheric turbulence.

Turbulence data from the CASES-99 field experiment, over comparatively horizontally homogeneous and flat terrain, are separated based on the anisotropy of the Reynolds stress tensor (into isotropic, two-component axisymmetric and one-component turbulence) and flux-variance similarity scaling relations are tested. Results illustrate that different states of anisotropy correspond to different similarity relations, especially under unstable stratification. Experimental data with close to isotropic turbulence match similarity relationships well. On the other hand, very anisotropic turbulence deviates significantly from the traditional scaling relations. We examine in detail the characteristics of these states of anisotropy, identify conditions in which they occur and connect them with different governing parameters. The governing parameters of turbulence anisotropy are shown to be different for stable and unstable stratification, but are able to delineate clearly the conditions in which each of the anisotropy states occurs.

Scalar-Flux Similarity in the Layer Near the Surface Over Mountainous Terrain.

The scaled standard deviations of temperature and humidity are investigated in complex terrain. The study area is a steep Alpine valley, with six measurement sites of different slope, orientation and roughness (i-Box experimental site, Inn Valley, Austria). Examined here are several assumptions forming the basis of Monin-Obukhov similarity theory (MOST), including constant turbulence fluxes with height and the degree of self-correlation between the involved turbulence variables. Since the basic assumptions for the applicability of the MOST approach-horizontally homogeneous and flat conditions-are violated, the analysis is performed based on a local similarity hypothesis. The scaled standard deviations as a function of local stability are compared with previous studies from horizontally homogeneous and flat terrain, horizontally inhomogeneous and flat terrain, weakly inhomogeneous and flat terrain, as well as complex terrain. As a reference, similarity relations for unstable and stable conditions are evaluated using turbulence data from the weakly inhomogeneous and flat terrain of the Cabauw experimental site in the Netherlands, and assessed with the same post-processing method as the i-Box data. Significant differences from the reference curve and also among the i-Box sites are noted, especially for data derived from the i-Box sites with steep slopes. These differences concern the slope and the magnitude of the best-fit curves, illustrating the site dependence of any similarity theory.

The Impact of Three-Dimensional Effects on the Simulation of Turbulence Kinetic Energy in a Major Alpine Valley.

The correct simulation of the atmospheric boundary layer (ABL) is crucial for reliable weather forecasts in truly complex terrain. However, common assumptions for model parametrizations are only valid for horizontally homogeneous and flat terrain. Here, we evaluate the turbulence parametrization of the numerical weather prediction model COSMO with a horizontal grid spacing of Δ x = 1.1 km for the Inn Valley, Austria. The long-term, high-resolution turbulence measurements of the i-Box measurement sites provide a useful data pool of the ABL structure in the valley and on slopes. We focus on days and nights when ABL processes dominate and a thermally-driven circulation is present. Simulations are performed for case studies with both a one-dimensional turbulence parametrization, which only considers the vertical turbulent exchange, and a hybrid turbulence parametrization, also including horizontal shear production and advection in the budget of turbulence kinetic energy (TKE). We find a general underestimation of TKE by the model with the one-dimensional turbulence parametrization. In the simulations with the hybrid turbulence parametrization, the modelled TKE has a more realistic structure, especially in situations when the TKE production is dominated by shear related to the afternoon up-valley flow, and during nights, when a stable ABL is present. The model performance also improves for stations on the slopes. An estimation of the horizontal shear production from the observation network suggests that three-dimensional effects are a relevant part of TKE production in the valley.