A weakly nonlinear framework to study shock–vorticity interaction

Linear interaction analysis (LIA) is routinely used to study the shock–turbulence interaction in supersonic and hypersonic flows. It is based on the inviscid interaction of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, and hence it is limited to small-amplitude disturbances. In this work, we extend the LIA framework to study the fundamental interaction of a two-dimensional vorticity wave with a normal shock. The predictions from a weakly nonlinear framework are compared with high-order accurate numerical simulations over a range of wave amplitudes ( $\epsilon$ ), incidence angles ( $\alpha$ ) and shock-upstream Mach numbers ( $M_1$ ). It is found that the nonlinear generation of vorticity at the shock has a significant contribution from the intermodal interaction between vorticity and acoustic waves. Vorticity generation is also strongly influenced by the curvature of the normal shock wave, especially for high incidence angles. Further, the weakly nonlinear analysis is able to predict the correct scaling of the nonlinear effects observed in the numerical simulations. The analysis also predicts a Mach number dependent limit for the validity of LIA in terms of the maximum possible amplitude of the upstream vorticity wave.

Instability and turbulent relaxation in a stochastic magnetic field

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. The cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will ‘lock on’ to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale. Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed.

Gravitomagnetic vorticity generation in black hole accretion disks: a potential spatial constraint on plasma flow stability

We calculate the vorticity generation rate in the accretion disk near a slowly rotating black hole in the low velocity, weak-field limit of general relativity. Specifically, we find that the frame-dragging effect due to the black hole’s rotation – manifested through the gravitomagnetic field – can generate vorticity in a moving plasma in the accretion disk. The mechanism remains operational as long as the accretion disk has non-negligible vertical height and is independent of the exact thermodynamical profile of the disk. The enstrophy density generation rate, as a measure of turbulence and dissipation, is presented, which indicates that the frame-dragging effect can disrupt the stability of the disk away from the z = 0 plane.

Role of surfactant-induced Marangoni stresses in drop-interface coalescence

We study the effect of surfactants on the dynamics of a drop-interface coalescence using full three-dimensional direct numerical simulations. We employ a hybrid interface-tracking/level-set method, which takes into account Marangoni stresses that arise from surface-tension gradients, interfacial and bulk diffusion and sorption kinetic effects. We validate our predictions against the experimental data of Blanchette and Bigioni (Nat. Phys., vol. 2, issue 4, 2006, pp. 254–257) and perform a parametric study that demonstrates the delicate interplay between the flow fields and those associated with the surfactant bulk and interfacial concentrations. The results of this work unravel the crucial role of the Marangoni stresses in the flow physics of coalescence, with particular attention paid to their influence on the neck reopening dynamics in terms of stagnation-point inhibition, and near-neck vorticity generation. We demonstrate that surfactant-laden cases feature a rigidifying effect on the interface compared with the surfactant-free case, a mechanism that underpins the observed surfactant-induced phenomena.

Diagnostic study of diabatic heating and potential vorticity during a case of cyclogenesis

On 16-17 November, 2015, north and middle regions of Saudi Arabia were hit by a case of cyclogenesisassociated with heavy rainfall. This work presents a diagnostic study of this heavy rainfallcase based on the analysis of diabatic heating and potential vorticity. The synoptic analysis investigate that the important dynamical factors that causes this case are the northward extension of Red Sea Trough, anticyclone over the Arabian Peninsula, a travailing midlatitude upper trough, moisture transport pathways and strong upward motion arising from tropospheric instability. The calculation of diabatic heating by the thermodynamic equation illustrate that the contribution of vertical temperature advection and the adiabatic term are opposite to each other during the period of study. The largest contribution of the horizontal cold advection occurs during the first two days while the largest contribution of the horizontal warm advection occurs during the maximum development days. The dynamics of the studied case are also investigated in terms of isobaric Potential Vorticity. It is found that the location of the low-level Potential Vorticity anomaly and the Potential Vorticity generation estimates coincides with the heating region, which implies that condensation supports a large enough source to explain the existence of the low-level Potential Vorticity anomaly.

Boundary layer-mediated vorticity generation in currents over sloping bathymetry

Current-topography interactions in the ocean give rise to eddies spanning a wide range of spatial and temporal scales. Latest modeling efforts indicate that coastal and underwater topography are important generation sites for submesoscale coherent vortices (SCVs), characterized by horizontal scales of (0.1 – 10) km. Using idealized, submesoscale and BBL-resolving simulations and adopting an integrated vorticity balance formulation, we quantify precisely the role of bottom boundary layers (BBLs) in the vorticity generation process. In particular, we show that vorticity generation on topographic slopes is attributable primarily to the torque exerted by the vertical divergence of stress at the bottom. We refer to this as the Bottom Stress Divergence Torque (BSDT). BSDT is a fundamentally nonconservative torque that appears as a source term in the integrated vorticity budget and is to be distinguished from the more familiar Bottom Stress Curl (BSC). It is closely connected to the bottom pressure torque (BPT) via the horizontal momentum balance at the bottom and is in fact shown to be the dominant component of BPT in solutions with a well-resolved BBL. This suggests an interpretation of BPT as the sum of a viscous, vorticity generating component (BSDT) and an inviscid, ‘flow-turning ’ component. Companion simulations without bottom drag illustrate that although vorticity generation can still occur through the inviscid mechanisms of vortex stretching and tilting, the wake eddies tend to have weaker circulation, be substantially less energetic, and have smaller spatial scales.

Pressure drag for shallow cumulus clouds: from thermals to the cloud ensemble

<p>This study takes the first step to bridge the gap between the pressure drag of a shallow cloud ensemble and that of an individual cloud composed of rising thermals. It is found that the pressure drag for a cloud ensemble is primarily controlled by the dynamical component. The dominance of dynamical pressure drag and its increased magnitude with height are independent of cloud lifetime and are common features of individual clouds except that the total drag of a single cloud over life cycle presents vertical oscillations. These oscillations are associated with successive rising thermals but are further complicated by the evaporation-driven downdrafts outside the cloud. The horizontal vorticity associated with the vortical structure is amplified as the thermals rise to higher altitudes due to continuous baroclinic vorticity generation. This leads to the increased magnitude of local minima of dynamical pressure perturbation with height and consequently to increased dynamical pressure drag.</p>

Numerical Investigation of Unsteady Cavitation Flow around E779A Propeller in a Nonuniform Wake with an Insight on How Cavitation Influences Vortex

In the current study, the turbulent cavitation flow around a marine propeller in a nonuniform wake is simulated with the shear stress transport (k−ω SST) turbulence model combining Zwart–Gerber–Belamri (ZGB) cavitation model. The predicted cavity evolution shows a fairly well agreement with the available experimental results. Important mechanisms of propeller cavitation flow, including side-entrant jet and cavitation-vortex interaction, are analyzed in this paper. Vorticity is found to be mainly located in cavitation regions and the propeller wake during propeller rotating. The unsteady behavior of cavitation and side-entrant jet can both promote local vorticity generation and flow unsteadiness. In addition, it is indicated with the relative vorticity transport equation that the stretching term plays a major role in vorticity transportation, while baroclinic torque and Coriolis force term mainly influence the vorticity distribution along the liquid-vapor interface.

Cold Pool Characteristics of Tornadic Quasi-Linear Convective Systems and Other Convective Modes Observed During VORTEX-SE

Many numerical studies have focused on the importance of baroclinically generated vorticity at the edge of cold pools in supercellular tornadogenesis, and observational work has consistently found that strongly tornadic supercells have less dense, more buoyant cold pools than weakly or nontornadic supercells. However, there is a lack of observational studies that consider potential relationships between cold pool characteristics (e.g., density) and tornado production within linear systems, such as MCS or QLCS events. This study presents two tornadic QLCS events that were observed during the Verification of the Origins of Rotation in Tornadoes Experiment – Southeast (VORTEX-SE) field project in 2016 and 2017. Supercell and hybrid modes were also observed and compared to the observations from the linear systems. No obvious differences in the thermodynamic deficits of the tornadic and nontornadic samples were found, likely due to the weakness of the produced tornadoes (≤EF1) and the small tornadic sample size (five cold pools). Comparison across storm mode did find some differences, with QLCS cold pools producing larger θv and θe deficits than those observed in supercells. More importantly, our findings suggest that, in a QLCS, the magnitude of density gradients along the leading edge of the cold pool may be related to tornadogenesis by virtue of the implied baroclinic vorticity generation.