Transition from a split to a forward kinetic energy cascade system is explored in the context of rotating turbulence using direct numerical simulations with a three-dimensional isotropic random force uncorrelated with the velocity field. Our parametric study covers confinement effects in large aspect ratio domains and a broad range of rotation rates. The data here presented add substantially to previous works, which, in contrast, focused on smaller and shallower domains. Results indicate that for fixed geometrical dimensions the Rossby number acts as a control parameter, whereas for a fixed Rossby number the product of the domain size along the rotation axis and forcing wavenumber governs the amount of energy that cascades inversely. The regime transition criterion hence depends on both control parameters.

Two aspects of homogeneous rotating turbulence are quantified through forced Direct Numerical Simulations in an elongated domain, which is in the direction of rotation about 340 times larger than the typical initial eddy size. First, by following the time evolution of the integral length-scale along the axis of rotation , the growth rate of the columnar eddies and its dependency on the Rossby number Ro ε is determined as γ = 4 exp(−17Ro ε ), where γ is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate ε ν is sought. Comparison with current available scaling laws shows that the relation proposed by Baqui & Davidson (2015), i.e., ε ν ∼ u 3 / , where u is the r.m.s. velocity, approximates well part of our data, more specifically the range 0.39 Ro ε 1.54. However, relations proposed in the literature fail to model the data for the second and most interesting range, i.e., 0.06 Ro ε 0.31, which is marked by the formation of columnar eddies. To find a similarity relation for the latter, we exploit the concept of a spectral transfer time introduced by Kraichnan (1965). Within this framework, the energy dissipation rate is considered to depend on both the nonlinear time-scale and the relaxation time-scale. Thus, by analyzing our data, expressions for these different time-scales are obtained that results in ε ν ∼ u 4 /( 2 ⊥ Ro 0.62 ε τ iso nl ), where ⊥ is the integral length-scale in the direction normal to the axis of rotation and τ iso nl is the non-liner time-scale of the initial homogeneous isotropic field. † Email address for correspondence: t.pestana@tudelft.nl arXiv:1907.10133v1 [physics.flu-dyn]

This work employs for the first time invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider horizontal plane Couette flow and focus on Nagata's upper-branch equilibrium solution (Nagata, 1990) at low Reynolds numbers where this solution is linearly stable. When adding a single heavy particle with a diameter equivalent to 2.5 wall units (one twelfth of the gap width), we observe that the solution remains stable and is essentially unchanged away from the particle. This result demonstrates that it is technically feasible to utilize exact coherent structures in conjunction with particle-resolved DNS. While translating in the streamwise direction, the particle migrates laterally under the action of the quasi-streamwise vortices until it reaches the region occupied by the low-speed streak, where it attains a periodic state of motion -independent of its initial position. As a result of the ensuing preferential particle location, the time-average streamwise particle velocity differs from the plane-average fluid-phase velocity at the same wall-distance as the particle center, as previously observed in experiments and in numerical data for fully turbulent wall-bounded flows. Additional constrained simulations where the particle is maintained at a fixed spanwise position while freely translating in the other two directions reveal the existence of two equilibria located in the low-speed and in the high-speed streak, respectively, the former being an unstable point. A parametric study with different particle to fluid density ratios is conducted which shows how inertia affects the spanwise fluctuations of the periodic particle motion. Finally, we discuss a number of potential future investigations of solid particle dynamics which can be conducted with the aid of invariant solutions (exact coherent structures) of the Navier-Stokes equations.

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 the buoyancy period. While the former was studied by Remmler et al. (2013), 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. (2014), 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.

Currently, hundreds of petroleum wells, mainly in the northeast region of Brazil, are equipped with Intermittent Gas-Lift systems (IGL), due to the high number of mature fields with low reservoir static pressure. Over the years, mathematical models based on integral analysis were developed to predict the behavior of the entire production system of IGL wells. Although these models have evolved, they do not include, in their current forms, models for some important parts and components of the well installation. This paper extends the IGL mathematical model, which was first laid out by T. Liao (1991) and later developed by Carvalho Filho (2004), including specific formulations for topics such as the throttling flow regime for the gas-lift valve, the two-phase flow on the production line, the behavior of the pressure upstream of the motor valve during the injection stage, the behavior of the flowing bottom-hole pressure while the standing valve is closed and evaluation of the gas velocity during the decompression stage. A mathematical model for the conventional IGL was built, based on Liao’s and Carvalho’s models, including the aforementioned new formulations. This new model was used as the core of a computer program, which was extended to simulate various other variants of the IGL commonly employed by the petroleum producers in Brazil: the Gas-Lift with Plunger, the Inverted Gas-Lift and the Gas-Lift with Chamber. An algorithm was written for each variant and simulations were carried out using hypothetical and real data to test the code and the models. A graphical user interface was also designed and built, making it easier for the users to input the well completion parameters and to read and display the results of the IGL simulations.