Background Flow Research Articles

Geometrical dependence of optimal bounds in Taylor–Couette flow

This paper is concerned with the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) obtained in the framework of the background method for the Taylor–Couette flow with a stationary outer cylinder. Along the way, we perform the energy stability analysis of the laminar flow, and demonstrate that below radius ratio $0.0556$ , the marginally stable perturbations are not the axisymmetric Taylor vortices but rather a fully three-dimensional flow. The main result of the paper is an analytical expression of the optimal bound as a function of the radius ratio. To obtain this bound, we begin by deriving a suboptimal analytical bound using analysis techniques. We use a definition of the background flow with two boundary layers, whose relative thicknesses are optimized to obtain the bound. In the limit of high Reynolds number, the dependence of this suboptimal bound on the radius ratio (the geometrical scaling) turns out to be the same as that of numerically computed optimal bounds in three different cases: (1) the perturbed flow only satisfies the homogeneous boundary conditions but need not be incompressible; (2) the perturbed flow is three-dimensional and incompressible; (3) the perturbed flow is two-dimensional and incompressible. We compare the geometrical scaling with the observations from the turbulent Taylor–Couette flow, and find that the analytical result indeed agrees well with the available direct numerical simulations data. In this paper, we also dismiss the applicability of the background method to certain flow problems and therefore establish the limitation of this method.

Characterizing temporal and spatial scales of radiatively driven convection in a deep, ice‐free lake

AbstractFrom May to July 2019, an array of moored equipment was deployed in Lake Superior to characterize the spatial and temporal scales of radiatively driven convection (RDC). Previous work suggested that convective plumes have horizontal scales on the order of tens of meters, posing a significant observational challenge. The centerpiece of the deployment was a large, two‐dimensional (2D) array of thermistors that provided resolution on the order of 10 meters in both the vertical and a single horizontal dimension. This was augmented by an acoustic Doppler current meter mooring and a meteorology buoy capable of estimating surface heat and momentum fluxes. Instantaneous temperature variability at a given location is dominated by a lateral background flow advecting strong horizontal temperature gradients. By combining velocity data with temperature data, this fact can be used to examine horizontal structure at centimeter scales, and can produce 2D images of instantaneous temperature distribution on a horizontal surface, revealing multiple patterns of temperature anomaly distribution. The walls of convective structures are very sharp, with horizontal gradients on the order of 1°C m−1; horizontal scales of convective structures themselves are on the order of many tens of meters. Finally, convection is shown to strongly control the vertical distribution of water quality parameters.

Implicit Motion-Compensated Network for Unsupervised Video Object Segmentation

Unsupervised video object segmentation (UVOS) aims at automatically separating the primary foreground object(s) from the background in a video sequence. Existing UVOS methods either lack robustness when there are visually similar surroundings (appearance-based) or suffer from deterioration in the quality of their predictions because of dynamic background and inaccurate flow (flow-based). To overcome the limitations, we propose an implicit motion-compensated network (IMCNet) combining complementary cues ($\textit{i.e.}$, appearance and motion) with aligned motion information from the adjacent frames to the current frame at the feature level without estimating optical flows. The proposed IMCNet consists of an affinity computing module (ACM), an attention propagation module (APM), and a motion compensation module (MCM). The light-weight ACM extracts commonality between neighboring input frames based on appearance features. The APM then transmits global correlation in a top-down manner. Through coarse-to-fine iterative inspiring, the APM will refine object regions from multiple resolutions so as to efficiently avoid losing details. Finally, the MCM aligns motion information from temporally adjacent frames to the current frame which achieves implicit motion compensation at the feature level. We perform extensive experiments on $\textit{DAVIS}_{\textit{16}}$ and $\textit{YouTube-Objects}$. Our network achieves favorable performance while running at a faster speed compared to the state-of-the-art methods.

Acoustic black hole analogy to analyze nonlinear acoustic wave dynamics in accelerating flow fields

We present a physical model and a numerical method based on a space- and time-dependent Galilean-type coordinate transformation to simulate acoustic waves in the presence of an accelerating background flow field with sonic transition. Kinematically, the coordinate transformation is designed so as to maintain the well-posedness of the transformed wave equation, which is solved in a fixed computational domain using standard finite differences. Considering an acoustic black hole analogy, we analyze the nonlinear dynamics of acoustic waves in a stationary but non-uniformly accelerating flow field under the assumption of spherical symmetry. The choice of the acoustic black hole analogy is motivated by the fact that the steady-state spherical sonic horizon allows us to parameterize the wave-flow configuration in terms of a Helmholtz number He=c2/(λagh), which is expressed as a function of the speed of sound c, the emitted wavelength λa, and the flow acceleration at the sonic horizon, that is, the acoustic surface gravity gh. The results of the numerical simulations show that He describes geometrically similar sets of wave characteristics for different combinations of gh and λa. However, we also observe nonlinear variations of the wave amplitude along the wave characteristics, which are attributed to nonlinear Doppler modulations. It appears that these amplitude modulations depend on the acceleration of the flow field and can, therefore, differ for geometrically similar characteristics.

Entrainment, diffusion and effective compressibility in a self-similar turbulent jet

An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle$ , is found to be essentially indistinguishable from the global mean velocity field of the jet, $\langle \boldsymbol {U} \rangle$ , for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which $\boldsymbol {\nabla }\boldsymbol {\cdot } \langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle \neq 0$ even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated with entrained fluid particles. By considering a classical advection–diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity $K_T$ ) and momentum (through the turbulent viscosity $\nu _T$ ) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $\nu _T$ (and hence of the turbulent Prandtl number $\sigma _T = \nu _T/K_T$ ) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets.

Short timescale variability in large-amplitude internal waves on the western Portuguese shelf

Timescales in the ocean can range from the transient turbulence to the long-term climate scales. Quantifying its changes involves establishing meaningful background states, but that can be challenging if an extensive array of wave phenomena is masking the ocean's variability. Internal Waves (IWs) are a fundamental part of these wave phenomena, which are now widely acknowledged as major contributors in ocean dynamics. In this study we use satellite imagery from Synthetic Aperture Radars (SAR) and moored temperature records to assess the variability scales and magnitudes of coastal IW systems propagating onshore off the western Portuguese shelf. The data shows significant variability in timescales of just a few days, and hence within the waves' typical propagation lifespan. A regional ocean circulation model is used together with linear theory to assess how mesoscale variability is contributing to the observed variability patterns observed in the IWs in the SAR and in situ data. According to linear theory, the IW variability is mostly owing to variable mesoscale currents, which off the Portuguese coast typically result from geostrophic flows, eddies and upwelling dynamics. IW variability owing to changes in stratification is found to amount to about half of that in background flows, but their effect can go unnoticed within the largest contributions from mesoscale currents. One extreme event is highlighted in which IWs from consecutive tidal cycles could possibly decouple from (i.e. not traceable back to) their originating tides in just a few days and hence within their typical lifespans.

On the Propagation and Translational Adjustment of Isolated Vortices in Large-Scale Shear Flows

Abstract This study explores the dynamics of intense coherent vortices in large-scale vertically sheared flows. We develop an analytical theory for vortex propagation and validate it by a series of numerical simulations. Simulations are conducted using both stable and baroclinically unstable zonal background flows. We find that vortices in stable westward currents tend to adjust to an equilibrium state characterized by quasi-uniform zonal propagation. These vortices persist for long periods, during which they propagate thousands of kilometers from their points of origin. The adjustment tendency is realized to a much lesser extent in eastward background flows. These findings may help to explain the longevity of the observed oceanic vortices embedded in predominantly westward flows. Finally, we examine the influence of background mesoscale variability induced by baroclinic instability of large-scale flows on the propagation and persistence of isolated vortices.

Incoherent signatures of internal tides in the Tokara Strait modulated by the Kuroshio

Internal tides are ubiquitously generated from disturbances between barotropic tides and bottom topography in stratified oceans. Incoherence is routinely considered as non-stationary phase discrepancy between internal and astronomical tides. Internal tides, especially incoherent constituents, contribute substantial energy to dissipation and turbulent mixing. Using ∼8-month near-full-depth moored current observations, we investigated internal tides in the Tokara Strait, where the Kuroshio exits the East China Sea. Semidiurnal internal tides, especially the M2 internal tides, dominate the diurnal internal tides by approximately one-order of magnitude. We decomposed the bandpass-filtered tidal currents into coherent and incoherent constituents, both of which presented a spring–neap cycle; however, the former was largely coupled with local barotropic tides, while the latter had an incoherent phase. The coherent semidiurnal internal tides were intensified and had larger variability near the bottom; nevertheless, the intensity and variability of incoherent internal tides decreased with depth. These results suggest that the incoherent internal tides are exogenous and are possibly affected by the background flow field during propagation. The mean incoherence (above 54 % for both semidiurnal and diurnal internal tides) was expectedly higher than the global mean (∼44 %), implying a robust effect of nonlinear Kuroshio-tide interactions. Moreover, the relationship between the variability of the incoherence and the north–south shift of the Kuroshio further revealed the impact of the background flow intensity variation on internal tides. A ray tracing model demonstrated different refraction indices during the propagation of internal tides, leading to converged (diverged) ray paths in the mooring when the Kuroshio was at the northern (southern) axis position, thus explaining the differential incoherence caused by the variability of the Kuroshio.

Dynamical analog spacetimes in nonrelativistic flows

Analogue gravity models describe linear fluctuations of fluids as a massless scalar field propagating on stationary acoustic spacetimes constructed from the background flow. In this paper, we establish that this paradigm generalizes to arbitrary order nonlinear perturbations propagating on dynamical analogue spacetimes. Our results hold for all inviscid, spherically symmetric and barotropic non-relativistic flows in the presence of an external conservative force. We demonstrate that such fluids always admit a dynamical description governed by a coupled pair of wave and continuity equations. We provide an iterative approach to solve these equations about any known stationary solution to all orders in perturbation. In the process, we reveal that there exists a dynamical acoustic spacetime on which fluctuations of the mass accretion rate propagate. The dynamical acoustic spacetime is shown to have a well defined causal structure and curvature. In addition, we find a classical fluctuation relation for the acoustic horizon of the spacetime that admit scenarios wherein the horizon can grow as well as recede, with the latter being a result with no known analogue in black holes. As an example, we numerically investigate the Bondi flow accreting solution subject to exponentially damped time dependent perturbations. We find that second and higher order classical perturbations possess an acoustic horizon that oscillates and changes to a new stable size at late times. In particular, the case of a receding acoustic horizon is realized through `low frequency' perturbations. We discuss our results in the context of more general analogue models and its potential implications on astrophysical accretion flows.

Вклад мезомасштабных вихрей Лофотенской котловины в ее энергетику

A comparative assessment of the contribution of eddies and other dynamic structures to the energy of the Lofoten Basin is carried out. The basis of the study is the data of global ocean reanalysis GLORYS12V1 for 1993–2019. We estimate the total kinetic and potential energy as well as the corresponding contribution of eddy energy for a region bounded by an isobath of 3000 m. We use the method of automatic identification of vortices for the analysis which allows us to calculate the eddy kinetic and potential energy in the automatically selected areas of the eddies. We establish that the potential energy of both cyclones and anticyclones is on average 2–3 times higher than the kinetic
 energy values, and the energy values of kinetic and potential for anticyclones dominate relative to the energy of cyclones. We also consider the interannual variability and seasonal course of eddy kinetic and potential energy. The seasonal course revealed an increase in both types of energy in the winter months. It is established that the contribution of eddies to the total energy of the basin is small. The contribution of eddy kinetic energy to the total energy of the basin is 7.3%, and the contribution of eddy potential energy is 8.4%. This means that the main contribution to the energy of the basin is made not by mesoscale eddies, but by other dynamic structures i.e. filaments and background flow.

Anisotropic stresslet and rheology of stick–slip Janus spheres

A Janus sphere with a stick–slip pattern can behave quite differently in its hydrodynamics compared with a no-slip or uniform-slip sphere. Here, using the Lorentz reciprocal theorem in conjunction with surface harmonic expansion, we rigorously derive the extended Faxén formula for the stresslet of a weakly stick–slip Janus sphere, capable of describing the anisotropic nature of the stresslet with an arbitrary axisymmetric stick–slip pattern in an arbitrary background flow. We find that slip anisotropy not only causes a variety of additional contributions to the stresslet, but also naturally renders a stresslet–rotation coupling that may turn a suspension of couple-free stick–slip Janus spheres into a dipolar one under the actions of an external couple. Moreover, to correctly account for the impacts of slip anisotropy on the stresslet, it is necessary to include at least the first four surface harmonic contributions. As a result, the anisotropies of both the stresslet and torque on the sphere in a linear flow field are purely reflected by a symmetric quadrupole and hexadecapole. These hydrodynamic quantities can be further mediated by an antisymmetric dipole and octupole due to the gradients of the imposed strain field. The average bulk stress and effective viscosity for a suspension of stick–slip spheres are also determined, showing characteristics quite distinct from those of a suspension of near spheres. If the spheres possess permanent dipole moments, in particular, additional stresslets and couplets can be generated by an applied external couple on each sphere and added into the bulk stress, accompanied by non-Jeffery orientational orbits of such dipolar stick–slip spheres. In addition to the above, the extended Faxén stresslet and torque relations found in this work will also provide the formulae needed for tackling problems involving hydrodynamically interacting stick–slip spheres on which small slip anisotropy may have profound impacts.

Numerical algorithms for water waves with background flow over obstacles and topography

We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Diffraction of shock waves through a non-quiescent medium

An investigation of shock diffraction through a non-quiescent background medium is presented using both experimental and numerical techniques. Unlike diffracting shocks in quiescent media, a spatial distortion of the shock front occurs, producing a region of constant shock angle. An example of this process arises in the exhaust from a pulse-detonation combustor. As the background velocity is increased, such as through the inclusion of a converging nozzle at the exhaust, the spatial distortion becomes more apparent. Numerical simulations using a compressible Euler solver demonstrate that the distortion is not due to the geometrical influence of the nozzle, but rather is a function of the magnitude of the background flow velocity. The distortion is studied using a modified geometrical shock dynamics formulation which includes the background flow and is validated against experiments. A simple model is presented to predict the shock distortion angle in the weak-shock limit. Finally, the axial decay behaviour of the shock is investigated and it is shown that the advection of the shock by the background flow delays the arrival of the head and tail of the expansion characteristic at the centreline. This leads to an increase in the rate of decay of the shock Mach number as the background flow velocity is increased.

Effect of Advection by Upper-Tropospheric Background Zonal Wind on MJO Phase Speed

Abstract A robust linear regression algorithm is applied to estimate 95% confidence intervals on the background wind associated with Madden–Julian oscillation (MJO) upper-tropospheric atmospheric circulation signals characterized by different phase speeds. Data reconstructed from the ERA5 to represent advection by the upper-tropospheric background flow and MJO-associated zonal wind anomalies, together with satellite outgoing longwave radiation anomalies, all in the equatorial plane, are regressed against advection data filtered for zonal wavenumber 2 and phase speeds of 3, 4, 5, and 7 m s−1. The regressed advection by the background flow is then divided by the negative of the zonal gradient of regressed zonal wind across the central Indian Ocean base longitude at 80°E to estimate the associated background wind that leads to the given advection. The median estimates of background wind associated with these phase speeds are 13.4, 11.2, 10.5, and 10.3 m s−1 easterly. The differences between estimated values at neighboring speeds suggests that advection acts most strongly in slow MJO events, indicating that the slowest events happen to be slow because they experience stronger easterly advection by the upper-tropospheric background wind. Significance Statement The Madden–Julian oscillation (MJO) is the dominant subseasonal rainfall signal of the tropical atmosphere. This project shows that the background wind of the tropical atmosphere most especially slows down the slowest MJO events. Understanding what controls its speed might help scientists better predict events.

Urban street canyon flows under combined wind forcing and thermal buoyancy

In this work, we investigate buoyancy-driven flows within urban street canyon cavities of three aspect ratios under simultaneous inertial wind forcing. The main aim of this work is to enhance the understanding of induced urban airflow patterns under non-isothermal conditions through experimental investigation, which to date are relatively scarce. The experimental results can be used for corresponding computational fluid dynamics simulations. Scaled-down models of typical street-canyon cavity geometries were deployed inside a water channel, where different ambient atmospheric conditions were simulated using dimensional analysis and similarity criteria. Three model street-canyon cavities were examined with height-to-width (aspect) ratios of 2/3, 1, and 2. The thermal buoyancy forcing was applied by means of differential heating between the two canyon side antagonistic walls for a given background flow velocity well-above the canyon height. The non-dimensional parameter B was used to quantify the influences of buoyancy and inertial forcing on the urban-canyon flow, as well as factoring in the geometrical aspect of the street canyon. The particle image velocimetry technique was used to acquire velocity vector fields across the middle vertical planar cross section of the urban street canyon. The results showed that the canyon aspect ratio affects the resulting flow field; however, a main vortical structure is present in all the visualized flow patterns with flow direction always being consistent with that of an uprising flow along the canyon heated wall.

Observations and Parametrization of the Turbulent Energy Dissipation Beneath Non-Breaking Waves

Here, for non-breaking short surface waves, we have experimentally determined the value of the turbulent eddy viscosity νT or its ratio νT*≡νT/ν, where ν is the water kinematic viscosity. The non-breaking wave-generated turbulent eddy viscosity νT was found to depend on the ratio of the wave period, T, to the microscale Kolmogorov time scale, τη. Our observations were consistent with νT*=1.46·(T/τη)−2.6 when (T/τη)<0.9. That implied that the νT*∝ϵ−1.3, where ϵ is the background turbulent energy dissipation rate. The near-surface turbulent flow associated with non-breaking waves was characterized by a short inertial subrange. The background turbulence appears to modulate the amount of energy the non-breaking waves dissipate locally and, consequently, the wave’s decay rate. Our results imply that the background turbulent flow acts as a lubricant, permitting waves to propagate further when traveling over a more energetic turbulent background flow. Our results have implications for the modeling of oceanic wave propagation or the air–sea exchange processes.

Retreatment of previously flow diverted intracranial aneurysms with the pipeline embolization device.

Flow diversion of intracranial aneurysms with the Pipeline Embolization Device (PED) is frequently performed, but the outcomes of retreatment for aneurysms that failed to occlude after prior treatment with PED have not been well studied. Here, we report the safety and efficacy of PED retreatment after initial failure to occlude. Clinical and angiographic data from eligible patients were retrospectively assessed for demographics, aneurysm occlusion status, and clinical outcomes. Patients were included in this study if they underwent PED retreatment to treat an aneurysm that had previously been treated with PED. Retreatment of previously flow-diverted aneurysms with PED was performed in 42 cases. At final angiographic follow-up, angiographic improvement was observed after 45% (19/42) of retreatments and complete aneurysm occlusion was observed following 26% (11/42). Significant clinical complications occurred in 10% (4/42) of PED retreatments. Retreatment of intracranial aneurysms with PED following initial failure to achieve aneurysm occlusion has a low rate of subsequent complete aneurysm occlusion.

Analytical Solution of the Ray Equations of Hamilton for Rossby Waves on Stationary Shear Flows

The asymptotic behavior of Rossby waves in the ocean interacting with a shear stationary flow is considered. It is shown that there is a qualitative difference between the problems for the zonal and non-zonal background flow. Whereas only one critical layer arises for a zonal flow, then several critical layers can exist for a non-zonal flow. It is established that the integrated ray equations of Hamilton are equivalent to the asymptotic behavior of the Cauchy problem solution. Explicit analytical solutions are obtained for the tracks of Rossby waves as a function of time and initial parameters of the wave disturbance, as well as the magnitude of the shear and angle of inclination of the flow to the zonal direction. The ray equations of Hamilton are analytically integrated for Rossby waves on a shear flow. The obtained explicit expressions make it possible to calculate in real-time the Rossby wave tracks for any initial wave direction and any shear current inclination angle. It is shown qualitatively that these tracks for a non-zonal flow are strongly anisotropic.

Dynamical processes controlling the evolution of early-summer cut-off lows in Northeast Asia

Cut-off lows are crucial extratropical circulation systems that can bring weather extremes over large areas, but the mechanism responsible for the life cycle of cut-off lows remains elusive. From a perspective of regional eddy-mean flow interaction, this study investigates the dynamical processes controlling the evolution of early-summer cut-off lows over Northeast Asia using the 6-hourly reanalysis data. Through the diagnostic of local wave activity (LWA) budget, we show that the cut-off low is initialized by a Rossby wave train originated from the subpolar North Atlantic, and then reinforced rapidly by zonal LWA flux convergence and local baroclinic eddy generation, and eventually decayed through energy dispersion by zonal wave activity advection. Furthermore, we show that the evolutions of the above dynamical processes are strongly modulated by the changes of background flow. In early summer, Northeast Asia is located at the eastern exit of the midlatitude jet to the north of the subtropical jet and exhibits a weak meridional gradient of potential vorticity, which favors frequent formation of cyclonic anomaly and energy accumulation. Prior to the onset of cut-off lows by several days, a Rossby wave train propagates along the Eurasian midlatitude jet, which initializes a cyclonic anomaly over Northeast Asia. With the aid of mean flow advection of anomalous zonal momentum, the zonal winds are then decelerated at the midlatitude jet exit and accelerated at the subtropical jet center. The former obstructs the wave packet proceeding downstream and the latter favors stronger baroclinic eddy generation below the subtropical jet. The two processes together maintain and strengthen the cyclonic anomaly in Northeast Asia rapidly.

Hydrodynamic model of fish orientation in a channel flow.

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.