5 research outputs found
Homogeneous Rotating Turbulence: Inverse Energy Cascade and the Dissipation Scaling Law
Using direct numerical simulations, this thesis studies primarily fundamental aspects of homogeneous rotating turbulence. Within this context, we first investigate the transition from a split to a forward kinetic energy cascade system with a parametric study covering large aspect ratio domains, which are in the direction of rotation up to 340 times larger than the initial eddy size, and a broad range of rotation rates. This unprecedented database shows that, for fixed geometrical dimensions, the Rossby number governs the amount of energy that cascades to large scales, whereas, for a fixed Rossby number, the control parameter is given by the product between domain size along the rotation axis and forcing wavenumber. Second, we quantify the growth rate of the columnar eddies typical of rotating flows and seek for a scaling law for the energy dissipation rate. Our results indicate that the growth rate of the columnar eddies varies exponentially with the Rossby number, while, for the dissipation scaling law, an analysis based on timescales yields to a power law dependence on the Rossby number. Additionally, we also examine an inertia-gravity wave breaking in the middle-upper mesosphere. We show that optimal perturbations lead to an almost instantaneous wave breaking and secondary bursts of turbulence, a process marked by the formation of fine flow structures around the wave's least stable point. Further, we find that during the breaking events the energy dissipation rate tends to be an isotropic tensor and the local energy transfer, which is predominantly from mean to fluctuating field, is in balance with the pseudo kinetic energy dissipation rate. The latter is relevant to atmospheric flows and a case where rotation and stratification effects coexist.Aerodynamic
A one equation explicit algebraic subgrid-scale stress model
Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic nature of the model is that the Subgrid-Scale (SGS) kinetic energy production and dissipation are in balance, i.e., P/ε = 1. In this work, we propose an improved EASSM design that does not involve this precalibration and retains the ratio P/ε as a space and time dependent variable. Our model is based on the partial differential evolution equation for the SGS kinetic energy ksgs and the assumption that the ratio P/ε evolves slower in time than ksgs. Computational results for simple cases of forced isotropic turbulence show that the new model is able to track the evolution of the SGS kinetic energy significantly better than the dynamic and non-dynamic EASSMs of Marstorp et al. (2009). Also the predicted kinetic energy spectra and resolved dissipation evolution are in excellent agreement with reference data from Direct Numerical Simulations (DNS).Aerodynamic
Inertia-gravity waves breaking in the middle atmosphere at high latitudes: Energy transfer and dissipation tensor anisotropy
We present direct numerical simulations of inertia-gravity waves breaking in the middle-upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case. The simulations are designed based on the study of Fruman et al., and are initialized by superimposing primary and secondary perturbations to the convectively unstable base wave. Transient growth leads to an almost instantaneous wave breaking and secondary bursts of turbulence. We show that this process is characterized by the formation of fine flow structures that are predominantly located in the vicinity of the wave's least stable point. During the wave breakdown, the energy dissipation rate tends to be an isotropic tensor, whereas it is strongly anisotropic in between the breaking events. We find that the vertical kinetic energy spectra exhibit a clear 5/3 scaling law at instants of intense energy dissipation rate and a cubic power law at calmer periods. The term-by-term energy budget reveals that the pressure term is the most important contributor to the global energy budget, as it couples the vertical and the horizontal kinetic energy. During the breaking events, the local energy transfer is predominantly from the mean to the fluctuating field and the kinetic energy production is in balance with the pseudo kinetic energy dissipation rate.Aerodynamic
A priori investigations into the construction and the performance of an explicit algebraic subgrid-scale stress model
We investigate the underlying assumptions of Explicit Algebraic Subgrid-Scale Models (EASSMs) for Large-Eddy Simulations (LESs) through an a priori analysis using data from Direct Numerical Simulations (DNSs) of homogeneous isotropic and homogeneous rotating turbulence. We focus on the performance of three models: the dynamic Smagorinsky (DSM) and the standard and dynamic explicit algebraic models as in Marstorp et al. (2009), here refereed to as SEA and DEA. By comparing correlation coefficients, we show that the subgrid scale (SGS) stress tensor is better captured by the EA models. Overall, the DEA leads to the best performance, which is evidenced by comparing how each model reproduces the probability density function (p.d.f.) of the SGS kinetic energy production. Next, we evaluate the approximations that are inherent to EA models such as the model for the pressure-strain correlation. We analyze the performance of three pressure-strain models commonly employed in the RANS framework: the LRR-QI, the LRR-IP, and the SSG models. Again, through correlation coefficients, and by splitting the pressure contributions into slow and rapid, we assess the relative performance of each model. Finally, we test the local equilibrium assumption of Marstorp et al. (2009), which considers a local balance between the SGS kinetic energy production and the dissipation. The probability density function shows that the ratio of SGS kinetic energy production to dissipation is distributed over a broad range of values and that the local equilibrium assumption can be only viewed as a mathematical simplification.Aerodynamic
Energy transfer and dissipation tensor anisotropy in atmospheric turbulence
Turbulence in the atmosphere is generally affected by rotation and stratification. The combination of these two effects endows the atmosphere with wavelike motions, which are particularly relevant for the mixing processes in the middle and upper atmosphere. Gravity-waves, for instance, can transfer energy over large distances, carrying energy from where they are created to regions thousands of kilometers away (Fritts and Alexander (2003)). Due to wave instabilities, they break and induce small scale turbulence in the overall large scale flow, thus contributing to the mixing process. In current general circulation models, however, small scale motion is not resolved and instead only parametrized. Hence, understanding the breaking process can potentially lead to improved parametrization models and predictions. Depending on their frequency, gravity-waves can be classified as high-frequency gravity-waves (HGWs) and low-frequency inertia-gravity waves (IGWs). The breaking behavior of IGWs differs fundamentally from HGWs and must be investigated separately (Dunkerton (1997), Achatz and Schmitz (2006), Fruman et al. (2014)). Given that the wave breaking event leads to small scale three-dimensional turbulence, computational investigations must resolve a very large range of dynamic scales of motions (Lelong and Dunkerton (1998) and Fritts et al. (1994)). For HGWs, three-dimensional high resolution Direct Numerical Simulations (DNS) have already been performed, for example, by Fritts et al. (2009) and Remmler et al. (2015). For IGWs, fully threedimensional investigations of a IGW breaking in the upper mesosphere were first presented by Remmler et al. (2012) and Fruman et al. (2014). The present work focuses on turbulence induced by the breaking events of IGWs. We extend the work of Remmler et al. (2012) and Fruman et al. (2014) by performing DNS of an IGW breaking at a lower altitude and correspondingly higher Reynolds number typical of the middle mesosphere. Additionally, we explain the turbulent energy transfer during breaking events and analyze the structure of the turbulence dissipation tensor. Finally, we perform Large-Eddy Simulations (LES) using different models. We compare LES results to our DNS and asses if these models can be used to qualitatively predict breaking events.Aerodynamic