Quasilinear gyrokinetic theory: a derivation of QuaLiKiz

In order to predict and analyse turbulent transport in tokamaks, it is important to model transport that arises from microinstabilities. For this task, quasilinear codes have been developed that seek to calculate particle, angular momentum and heat fluxes, both quickly and accurately. In this tutorial, we present a derivation of one such code known as QuaLiKiz, a quasilinear gyrokinetic transport code. The goal of this derivation is to provide a self-contained and complete description of the underlying physics and mathematics of QuaLiKiz from first principles. This work serves both as a comprehensive overview of QuaLiKiz specifically as well as an illustration for deriving quasilinear models in general.

A theory for surface-layer scaling of thermally-driven slope flows

<p>Sloping terrains of any inclination favour the development, under the daily cycle of day time surface heating and night time cooling, of thermally-driven organised flows, displaying peculiar boundary layer structures, and eventually triggering the development of atmospheric convection.</p><p>The ubiquitous occurrence over the Earth of variously tilted surfaces - from gently sloping plains to steep cliffs, or valley and basin sidewalls – makes the understanding of such flows of utmost importance in view of the appropriate forecasting of the associated boundary layer transport processes. Also, they display a highly conceptual relevance, as they represent a prototypal situations for many other thermally driven-flows over complex terrain.   </p><p>An appropriate surface-layer scaling for slope wind is derived extending the classical analysis for flat horizontal terrain situations to the cover inclines. In the former, momentum and heat fluxes at the surface are two independent quantities, and vertical profiles of velocity and temperature can only be connected to them by means  of similiarity relationships, as fluxes are nearly invariant with height.</p><p>Instead, equations governing slope winds show that the mean wind and temperature profiles are closely connected to the flux structure normal to the slope, as this is not constant. Also, surface values of momentum flux and sensible heat flux are shown to be proportional to each other.</p><p>Based on the above relationships, suitable expressions are derived for the slope-normal profiles of velocity and temperature, both in the viscous sublayer and in the fully turbulent surface layer, as well as for the appropriate scaling factors in the two regions.</p>

Oceanic eddy-induced modifications to air–sea heat and CO2 fluxes in the Brazil-Malvinas Confluence

Sea surface temperature (SST) anomalies caused by a warm core eddy (WCE) in the Southwestern Atlantic Ocean (SWA) rendered a crucial influence on modifying the marine atmospheric boundary layer (MABL). During the first cruise to support the Antarctic Modeling and Observation System (ATMOS) project, a WCE that was shed from the Brazil Current was sampled. Apart from traditional meteorological measurements, we used the Eddy Covariance method to directly measure the ocean–atmosphere sensible heat, latent heat, momentum, and carbon dioxide (CO2) fluxes. The mechanisms of pressure adjustment and vertical mixing that can make the MABL unstable were both identified. The WCE also acted to increase the surface winds and heat fluxes from the ocean to the atmosphere. Oceanic regions at middle and high latitudes are expected to absorb atmospheric CO2, and are thereby considered as sinks, due to their cold waters. Instead, the presence of this WCE in midlatitudes, surrounded by predominantly cold waters, caused the ocean to locally act as a CO2 source. The contribution to the atmosphere was estimated as 0.3 ± 0.04 mmol m−2 day−1, averaged over the sampling period. The CO2 transfer velocity coefficient (K) was determined using a quadratic fit and showed an adequate representation of ocean–atmosphere fluxes. The ocean–atmosphere CO2, momentum, and heat fluxes were each closely correlated with the SST. The increase of SST inside the WCE clearly resulted in larger magnitudes of all of the ocean–atmosphere fluxes studied here. This study adds to our understanding of how oceanic mesoscale structures, such as this WCE, affect the overlying atmosphere.

Observation of wave-driven air–water turbulent momentum exchange in a large but fetch-limited shallow lake

Wind-induced waves play a key role in air–sea momentum and heat exchange. Fetch-limited shallow lakes differ significantly from open ocean circumstances since the wave field is characterized by young and growing waves that (i) are steeper and can collapse by white-capping at lower wind speeds, and (ii) travel with lower phase velocity. Consequently, momentum (and heat) flux estimation methods arising from oceanographic observations cannot be directly applied; however, few attempts have been made to describe air–water turbulent exchange in case of large, but still fetch-limited shallow lakes. Within a Croatian-Hungarian measurement campaign, turbulent flux measurements were performed in Lake Balaton. Momentum and heat fluxes were measured with eddy-covariance technique at an offshore station, while waves were simultaneously recorded with underwater acoustic surface tracking. Momentum fluxes were also recorded at two further stations closer to the shore. In this study, we analyze the measured wind stress and surface waves to reveal surface drag in case of highly fetch-limited conditions. We compare our results with relevant model formulations that attempt to estimate momentum flux using different wave state parameterizations (i.e. wave age and wave slope modified Charnock formulations) and show that derived drag and roughness length parameterizations differ significantly from oceanographic formulas.

Quantifying the Annular Mode Dynamics in an Idealized Atmosphere

The linear response function (LRF) of an idealized GCM, the dry dynamical core with Held–Suarez physics, is used to accurately compute how eddy momentum and heat fluxes change in response to the zonal wind and temperature anomalies of the annular mode at the quasi-steady limit. Using these results and knowing the parameterizations of surface friction and thermal radiation in Held–Suarez physics, the contribution of each physical process (meridional and vertical eddy fluxes, surface friction, thermal radiation, and meridional advection) to the annular mode dynamics is quantified. Examining the quasigeostrophic potential vorticity balance, it is shown that the eddy feedback is positive and increases the persistence of the annular mode by a factor of more than 2. Furthermore, how eddy fluxes change in response to only the barotropic component of the annular mode, that is, vertically averaged zonal wind (and no temperature) anomaly, is also calculated similarly. The response of eddy fluxes to the barotropic-only component of the annular mode is found to be drastically different from the response to the full (i.e., barotropic + baroclinic) annular mode anomaly. In the former, the eddy generation is significantly suppressed, leading to a negative eddy feedback that decreases the persistence of the annular mode by nearly a factor of 3. These results suggest that the baroclinic component of the annular mode anomaly, that is, the increased low-level baroclinicity, is essential for the persistence of the annular mode, consistent with the baroclinic mechanism but not the barotropic mechanism proposed in the previous studies.

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

A Wall-Function Based Model for Multi-Perforated Walls

Effusion cooling is one of the most effective techniques to prevent combustor liner from being damaged. As effusion-cooled liners are comprised of a large number of sub-millimeters closely-spaced holes, full 3D numerical simulations of the combustion chamber are still unaffordable. Thus, aero-thermal models are needed to describe the main flow-liner interaction. The aim of this paper is to provide a homogeneous wall model for gas turbine combustor liners based on wall-function similarities. In order to develop such a model, a numerical database was built up covering a wide range of interest for gas turbine applications. The model proposed here consists of two modified wall-functions for both sides of a liner and an analytical model to take into account the heat exchange within the holes. As holes are not reproduced and coarse near-wall grids are sufficient, the computational cost of this methodology is very low. The performance and limitations of the model are discussed. The model has proved satisfactory in assessing the effect of a liner on the surrounding and vice-versa. Although discrepancies were observed for the first rows, momentum and heat fluxes between the flow and the impinged wall are reproduced with a good level of agreement. Overall effectiveness is predicted with a mean relative error of less than 5%.