The Vertical Velocity Skewness in the Atmospheric Boundary Layer without Buoyancy and Coriolis Effects

Background: One of the main statistical features of near-neutral atmospheric boundary layer (ABL) turbulence is the positive vertical velocity skewness (Sk_w) above the roughness sublayer (RSL) or the buffer region (in smooth-walls). It is the most elementary flow statistic quantifying asymmetry due to the presence of a boundary. The Sk_w variations are receiving renewed interest in many climate-related parameterizations of the ABL given their significance to cloud formation and to testing sub-grid schemes for Large Eddy Simulations (LES). While much attention has been traditionally devoted to Sk_w within the convective boundary layer (CBL), less attention has been paid to models of Sk_w in near-neutral conditions, the focus here. These near-neutral conditions are prevalent in many planetary flow situations such as air flow over ice sheets, large open water bodies, and in many occasions over land, and thus form a logical limit for ABL characterizations of asymmetry. They also form limiting states for modeling approaches now being implemented in climate centers such as the Cloud Layers Unified By Binormals (or CLUBB). In the absence of any thermal stratification or Coriolis effects, laboratory measurements of Sk_w over rough turbulent boundary layers (including k-type and d-type) suggest that Sk_w<0 in the RSL or in the buffer region of smooth walls but switches to Sk_w>0 in the inertial (i.e. log-layer) and outer-layers. This switch was shown to be linked to a switch in the type of eddy motion dominating momentum transport. Sweeping motion dominates within the roughness sublayer and ejective motion in the remaining layers of the boundary layer. A clear explanation as to why and how this switch occurs remains elusive and motivates the present work.

What will be accomplished: The vertical variations of Sk_w are explored here using high Reynolds number wind tunnel and flume experiments collected above smooth, rough, and permeable-walls in the absence of buoyancy and Coriolis effects. These laboratory experiments form a necessary starting point to explore the canonical structure of Sk_w as they deal with a key limiting case (i.e. near-neutral conditions) that has received much less attention compared to its convective counterpart in atmospheric studies. Diagnostic models based on cumulant expansions, realizability constraints, and the now-popular constant mass flux approach routinely employed in the convective boundary layer as well as prognostic models based on first, second, and third-order budgets are used to explain variations in Sk_w for the idealized laboratory conditions. The failure of flux-gradient relations to model Sk_w from gradients of the vertical velocity variance are explained and corrections based on models of energy transport offered. For the inertial sublayer where the log-law for the mean velocity profile is expected to hold, a bridge between Sk_w and Townsend's Attached Eddy Hypothesis is established. Novel links between the diagnostic and prognostic models are also featured, especially for the inertial term in the third order budget of the vertical velocity fluctuation. The co-spectral properties of w'/σ_w versus w'²/(σ_w²) are also presented for the first time to assess the dominant scales governing Sk_w, where w' is the fluctuating vertical velocity, and σ_w is the vertical velocity standard deviation. These assessments support the assumptions used to derive an algebraic expression for the vertical velocity skewness that can be imminently used in models such as CLUBB.

Study limitations and future outlook: While the results featured here do not address all aspects of ABL parameterizations needed in models such as CLUBB, they do offer bench-mark outcomes for the near-neutral limit. In this respect, they may be viewed as necessary but not sufficient to progress on turbulence parameterizations in climate models. Future effort will explore the extension of these approaches (prognostic and diagnostic) to stratified flows in the atmosphere (mainly surface layer and roughness sublayer including vegetated and urban) - where buoyancy, elevated Reynolds numbers, Coriolis forces, and enhanced roughness values are expected.