Accurate prediction of the global properties of wall-bounded turbulence holds significant importance for both fundamental research and engineering applications. In atmospheric boundary layers, the relationship between friction drag and geostrophic wind is described by the geostrophic drag law (GDL). We use carefully designed large-eddy simulations to study nocturnal stable atmospheric boundary layers (NSBLs), which are characterized by a negative potential temperature flux at the surface and neutral stratification higher up. Our simulations explore a wider range of the Kazanski–Monin parameter, $\mu = L_f / L_s = [16.7, 193.3]$, with $L_f$ the Ekman length scale and $L_s$ the surface Obukhov length. We show collapse of the GDL coefficients onto single curves as functions of $\mu$, thereby validating the GDL's applicability to NSBLs over a very wide $\mu$ range. We show that the boundary-layer height $h$ scales with $\sqrt {L_f L_s}$, while both the streamwise and spanwise wind gradients scale with $u_*^2 / (h^2 f)$, where $u_*$ represents the friction velocity and $f$ the Coriolis parameter. Leveraging these insights, we developed new analytical expressions for the GDL coefficients, significantly enhancing our understanding of the GDL for turbulent boundary layers. These formulations facilitate the analytical prediction of the geostrophic drag coefficient and cross-isobaric angle.

The existence of a maximum drag enhancement (MDE) asymptote at high rotation ($Ro$) and Weissenberg ($Wi$) numbers in turbulent viscoelastic spanwise-rotating plane Couette flow has been demonstrated. Specifically, it is shown that above a critical $Wi$, drag enhancement plateaus and the MDE asymptote is realized in a broad range of $Ro$. The mean velocity profiles at MDE appear to closely follow a log-law profile that has a nearly identical slope but different intercepts as a function of $Ro$. Much like the maximum drag reduction (MDR) asymptote, the logarithmic function in MDE is closely followed if the mean velocity is plotted using the traditional inner variable scaling; however, the logarithmic function is not well defined when examined by the indicator function. Hence, in this study, we have used the logarithmic fit as a visual guide for the mean velocity profile. Last and perhaps the most intriguing finding of this study is that MDE occurs in the elasto-inertial turbulence (EIT) flow state; hence, it is mainly sustained by elastic forces much like the MDR flow state. To that end, a universal picture of elastically induced drag modification asymptotes is emerging, namely these asymptotic states are an inherent property of the elastically sustained EIT flow state.

The wind energy industry relies on computationally efficient engineering-type models to design wind farms. Typically these models do not account for the effect of atmospheric stratification in either the boundary layer or the free atmosphere. This study proposes a new analytical model for fully developed wind-turbine arrays in conventionally neutral atmospheric boundary layers frequently encountered in nature. The model captures the effect of the free-atmosphere stratification, Coriolis force, wind farm layout and turbine operating condition on the wind farm performance. The model is developed based on the physical insight derived from large-eddy simulations. We demonstrate that the geostrophic drag law (GDL) for flow over flat terrain can be extended to flow over fully developed wind farm arrays. The presence of a vast wind farm significantly increases the wind farm friction velocity compared with flow over flat terrain, which is modelled by updated coefficients in the GDL. The developed model reliably captures the vertical wind speed profile inside the wind farm. Furthermore, the power production trends observed in simulations are reliably reproduced. The wind farm performance, normalized by the geostrophic wind speed, decreases as the free-atmosphere thermal stability increases or the Coriolis force decreases. In addition, we find that the optimal wind farm performance is obtained at a lower thrust coefficient than the Betz limit, which indicates that optimal operating conditions for turbines in a wind farm are different than for a single turbine.

Direct numerical simulation of spanwise-rotation-driven flow transitions in viscoelastic plane Couette flow from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow state followed by full relaminarization is reported for the first time. Specifically, this novel flow transition begins with a drag-reduced inertial turbulent flow state at a low rotation number $0\leqslant Ro \leqslant 0.1$, and then transitions to a rotation/polymer-additive-driven drag-enhanced inertial turbulent regime, $0.1\leqslant Ro \leqslant 0.3$. In turn, the flow transitions to a drag-enhanced elasto-inertial turbulent state, $0.3\leqslant Ro \leqslant 0.9$, and eventually relaminarizes at $Ro=1$. In addition, two novel rotation-dependent drag enhancement mechanisms are proposed and substantiated. (1) The formation of large-scale roll cells results in enhanced convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow between adjacent roll cells at $Ro\leqslant 0.2$. (2) Coriolis-force-generated turbulent vortices cause strong incoherent transport and homogenization of significant polymer stress in the bulk via their vortical circulations at $Ro=0.5 - 0.9$.

Direct numerical simulation of polymer-induced flow relaminarization of turbulent spanwise-rotating plane Couette flow (RPCF) is reported for the first time. Specifically, the reverse transition pathway from a Newtonian turbulent RPCF to a fully relaminarized drag enhanced viscoelastic flow has been elucidated. Evidently, this transition occurs gradually by weakening and eventual elimination of small-scale vortices as the Weissenberg number ($Wi$) is enhanced, paving the way for a two-dimensional laminar flow consisting of large-scale and highly organized roll cells. The influence of polymer additives on convective momentum exchange by large-scale roll cells and small-scale turbulent vortices, namely, the drag reduction (DR) realized by elimination of turbulent vortices and the significant drag enhancement (DE) that results from polymer roll cell interactions has been identified as the mechanism of DE. The observed vortical changes point to a universal mechanism for the coupling of polymer chains and turbulent vortices in wall-bounded viscoelastic DE and DR flows.

We present an analytical model of nonlinear evolution of two-dimensional single-mode Rayleigh–Taylor instability (RTI) in cylindrical geometry at arbitrary Atwood number for the first time. Our model covers a full scenario of bubble evolution from the earlier exponential growth to the nonlinear regime with the bubbles growing in time as $\frac {1}{2}a_{b}t^2$ for cylindrical RTI, other than as $V_{b}t$ for planar RTI, where $a_{b}$ and $V_{b}$ are the bubble acceleration and velocity, respectively. It is found that from this model the saturating acceleration $a_{b}$ is formulated as a simplified function of the external acceleration, Atwood number and number of perturbation waves. This model's predictions are in good agreement with data from direct numerical simulations.

Drag reduction (DR) in plane Couette flow (PCF) induced by the addition of flexible polymers has been studied via direct numerical simulation (DNS). The similarities and differences in the drag reduction features of PCF and plane Poiseuille flow (PPF) have been examined in detail, particularly in regard to the polymer-induced modification of large-scale structures (LSSs) in the near-wall turbulence. Specifically, it has been demonstrated that in the near-wall region, drag-reduced PCF has features similar to those of drag-reduced PPF; however, in the core region, intriguing differences are found between these two drag-reduced shear flows. Chief among these differences is the significant polymer stretch that arises from the enhanced exchanges between elastic potential energy and turbulent kinetic energy and the commensurate observation of peak values of the conformation tensor components $\unicode[STIX]{x1D60A}_{yy}$ and $\unicode[STIX]{x1D60A}_{zz}$ in this region. This finding is in stark contrast to that of drag-reduced PPF where the polymer stretch and the exchanges between elastic potential energy and turbulent kinetic energy in the core region are insignificant; to this end, in drag-reduced PPF, peak values of the conformation tensor components appear in the near-wall region. Therefore, this study paves the way for understanding the underlying flow physics in drag-reduced PCF, particularly in the context of elastic theory. Moreover, the longitudinal large-scale streaks at the channel centre of drag-reduced PCF are greatly strengthened due to the increased production/dissipation ratio; the LSS imprint effects on the near-wall flow of drag-reduced PCF monotonically increase as the Weissenberg number is enhanced.

Experimental and numerical investigations on the interaction of a planar shock wave with two-dimensional (2-D) and three-dimensional (3-D) light gas cylinders are performed. The effects of initial interface curvature on flow morphology, wave pattern, vorticity distribution and interface movement are emphasized. In experiments, a wire-restriction method based on the soap film technique is employed to generate N$_{2}$ cylinders surrounded by SF$_{6}$ with well-characterized shapes, including a convex cylinder, a concave cylinder with a minimum-surface feature and a 2-D cylinder. The high-speed schlieren pictures demonstrate that fewer disturbance waves exist in the flow field and the evolving interfaces develop in a more symmetrical way relative to previous studies. By combining the high-order weighted essentially non-oscillatory construction with the double-flux scheme, numerical simulation is conducted to explore the detailed 3-D flow structures. It is indicated that the shape and the size of 3-D gas cylinders in different planes along the vertical direction change gradually due to the existence of both horizontal and vertical velocities of the flow. At very early stages, pressure oscillations in the vicinity of evolving interfaces induced by complex waves contribute much to the deformation of the 3-D gas cylinders. As time proceeds, the development of the shocked volume would be dominated by the baroclinic vorticity deposited on the interface. In comparison with the 2-D case, the oppositely (or identically) signed principal curvatures of the concave (or convex) SF$_{6}$/N$_{2}$ boundary cause complex high pressure zones and additional vorticity deposition, and the upstream interface from the symmetric slice of the concave (or convex) N$_{2}$ cylinder moves with an inhibition (or a promotion). Finally, a generalized 3-D theoretical model is proposed for predicting the upstream interface movements of different gas cylinders and the present experimental and numerical findings are well predicted.

In this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.

Numerical investigation of the underexpanded sonic coaxial jets is carried out using large eddy simulation for three typical inner nozzle lip-thicknesses. Various fundamental mechanisms dictating the flow phenomena including shock structure, shear layer evolution and sound production are investigated. It is found that the inner nozzle lip induces a recirculation zone between inner and outer jets, which significantly influences the behaviors of shock structures and shear layers. The sound properties of the coaxial jets are further analyzed in detail. As the inner lip-thickness increases, the helical screech mode switches to an axisymmetric one and high-frequency screech also occurs with an oscillation frequency of recirculation zone. Based on the temporal Fourier transform and correlation analysis, the primary sources of low- and high-frequency screeches are associated with the downstream shock cells in the jet column and the secondary shock structures in the outer annular jet, respectively. The proper orthogonal decomposition analysis reveals that the dominant structures constructed by the most energetic modes shift from the downstream shock cells region to the upstream secondary shock region as the lip-thickness increases. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the coherent structures and sound properties in sonic coaxial jets.

The motion and rotation of an ellipsoidal particle inside square tubes and rectangular tubes with the confinement ratio R/a∈(1.0,4.0) are studied by the lattice Boltzmann method (LBM), where R and a are the radius of the tube and the semi-major axis length of the ellipsoid, respectively. The Reynolds numbers (Re) up to 50 are considered. For the prolate ellipsoid inside square and rectangular tubes, three typical stable motion modes which depend on R/a are identified, namely, the kayaking mode, the tumbling mode, and the log-rolling mode are identified for the prolate spheroid. The diagonal plane strongly attracts the particle in square tubes with 1.2≤R/a<3.0. To explore the mechanism, some constrained cases are simulated. It is found that the tumbling mode in the diagonal plane is stable because the fluid force acting on the particle tends to diminish the small displacement and will bring it back to the plane. Inside rectangular tubes the particle will migrate to a middle plane between short walls instead of the diagonal plane. Through the comparisons between the initial unstable equilibrium motion state and terminal stable mode, it is seems that the particle tend to adopt the mode with smaller kinetic energy.

Interaction of vortex rings with solid is an important research topic of hydrodynamic. In this study, a multiple-relaxation time (MRT) lattice Boltzmann method (LBM) is used to investigate the flow of a vortex ring impacting spheroidal particles. The MRT-LBM is validated through the cases of vortex ring impacting a flat wall. The vortex evolution due to particle size, the aspect ratio of a prolate particle, as well as Reynolds (Re) number are discussed in detail. When the vortex ring impacting a stationary sphere, the primary and secondary vortex rings wrap around each other, which is different from the situation of the vortex ring impacting a plate. For the vortex ring impacting with a prolate spheroid, the secondary vortex ring stretches mainly along the long axis of the ellipsoid particle. However, it is found that after the vortex wrapping stage, the primary vortex recovers along the short axis of the particle faster than that in the long axis, i.e., the primary vortex ring stretches mainly along the short axis of the particle. That has never been address in the literature.

Turbulent swirling flows injected into a coaxial dump chamber at different swirl numbers were studied using large-eddy simulations. The Favre-filtered conservation equations of mass, momentum, and energy in three dimensions were solved numerically by means of a finite-volume approach. Results have been validated against experimental data in terms of mean flow velocity and turbulence properties. The work provides insight into several salient features of swirling flows, including vortex breakdown, shear-layer instability, and vortico-acoustic interactions. The dominant acoustic mode in the chamber was found to be sensitive to unsteady vorticity evolution, which in turn strongly depends on the swirl number. Low-frequency acoustic oscillations may arise from large-scale coherent motions in the central toroidal recirculation zone at high swirl numbers. In contrast, the shear-layer instability downstream of the backward-facing step results in high-frequency acoustic waves at low swirl numbers.