Nearby Flows Research Articles

Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

We study the behavior of solutions to the incompressible 2d Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier–Stokes problems. We exhibit a large family of new, non-trivial stationary states that are arbitrarily close to the Kolmogorov flow on the square torus mathbb {T}^2 in analytic regularity. This situation contrasts strongly with the setting of some monotone shear flows, such as the Couette flow: there the linearized problem exhibits an “inviscid damping” mechanism that leads to relaxation of perturbations of the base flows back to nearby shear flows. Our results show that such a simple description of the long-time behavior is not possible for solutions near the Kolmogorov flow on mathbb {T}^2. Our construction of the new stationary states builds on a degeneracy in the global structure of the Kolmogorov flow on mathbb {T}^2, and we also show a lack of correspondence between the linearized description of the set of steady states and its true nonlinear structure. Both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel are very different. We show that the only stationary states near them must indeed be shears, even in relatively low regularity. In addition, we show that this behavior is mirrored closely in the related Navier–Stokes settings: the linearized problems near the Poiseuille and Kolmogorov flows both exhibit an enhanced rate of dissipation. Previous work by us and others shows that this effect survives in the full, nonlinear problem near the Poiseuille flow and near the Kolmogorov flow on rectangular tori, provided that the perturbations lie below a certain threshold. However, we show here that the corresponding result cannot hold near the Kolmogorov flow on {mathbb T}^2.

Traveling Waves Near Couette Flow for the 2D Euler Equation

In this paper we reveal the existence of a large family of new, nontrivial and smooth traveling waves for the 2D Euler equation at an arbitrarily small distance from the Couette flow in $$H^s$$ , with $$s<3/2$$ , at the level of the vorticity. The speed of these waves is of order 1 with respect to this distance. This result strongly contrasts with the setting of very high regularity in Gevrey spaces [see Bedrossian and Masmoudi (Publ Math Inst Hautes Etudes Sci 122:195–300, 2015)], where the problem exhibits an inviscid damping mechanism that leads to relaxation of perturbations back to nearby shear flows. It also complements the fact that there not exist nontrivial traveling waves in the $$H^{\frac{3}{2}+}$$ neighborhoods of Couette flow [see Lin and Zeng (Arch Ration Mech Anal 200:1075–1097, 2011)].

Computational Fluid Dynamics Approach for Oscillating and Interacting Convective Flows

The oscillation and collective behavior of convective flows is studied by a computational fluid dynamics approach. More specifically, the rising dynamics of heated fluid columns is simulated in gravitational field using a simplified 2D geometry. The numerical method uses the FEniCS package for solving the coupled Navier–Stokes and heat-diffusion equations. For the flow of a single heated fluid column, the effect of the inflow yield and the nozzle diameter is studied. In agreement with the experiments, for a constant nozzle diameter the oscillation frequency increases approximately linearly as a function of the the flow rate, while for a constant flow rate the frequency decreases as a power law with the increased nozzle diameter. For the collective behavior of two nearby flows, we find a counter-phase synchronization and a decreasing trend of the common oscillation frequency with the distance between the jets. These results are in agreement with the experiments, and our computational study also suggests that the phenomenon is present on largely different length-scales.

Integrated Surface Water and Groundwater Modeling in Arid Environment, Al-Lusub Watershed, Saudi Arabia

Coupling surface and groundwater for a better understanding of the hydrologic response in arid basins is essential for managing water resources. The study aims to integrate surface water (SW) and groundwater (GW) modeling in an arid environment and to identify groundwater sources at Hadat Ash-Sham farm station in the Al-Lusub watershed, located in the western part of Saudi Arabia. The curve number (CN) method for SW modeling is primarily used to estimate GW potential recharge based on a developed correlation equation between event-based rainfall and potential recharge, which is processed in the Hydrologic Engineering Center-Hydrologic Modeling System (HEC-HMS) software. Monthly potential recharge is utilized to compute GW modeling in MODFLOW. Van Mullem’s equation is used to calculate hydraulic conductivity (K) from CN. The calibration of steady-state GW modeling reveals that the K (from Van Mullem’s equation) is within the range of measured K in the field. The transient groundwater modeling phase concludes that the groundwater system in the Al-Lusub watershed can be interpreted based on two different scenarios. The first is that an extra recharge from a nearby watershed flows through the geological structure into a downstream area. The second scenario involves potential recharge from surface water flowing on the Al-Lusub watershed’s mainstream bed. Validation reveals a strong relationship between predicted and observed water tables. The root mean square error (RMSE) for Scenarios 1 and 2 are 0.6 m and 0.7 m, respectively. Further investigation is needed to determine the region’s most common scenario.

Conjugate and cut points in ideal fluid motion

Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be seen as a consequence of the (infinite dimensional) group of volume preserving diffeomorphisms having sufficiently strong positive curvatures which ‘pull’ nearby flows together. Physically, they indicate a form of (transient) stability in the configuration space of particle positions: a family of flows starting with the same configuration deviate initially and subsequently re-converge (resonate) with each other at some later moment in time. Here, we first establish existence of conjugate points in an infinite family of Kolmogorov flows—a class of stationary solutions of the Euler equations—on the rectangular flat torus of any aspect ratio. The analysis is facilitated by a general criterion for identifying conjugate points in the group of volume preserving diffeomorphisms. Next, we show non-existence of conjugate points along Arnold stable steady states on the annulus, disk and channel. Finally, we discuss cut points, their relation to non-injectivity of the exponential map (impossibility of determining a flow from a particle configuration at a given instant) and show that the closest cut point to the identity is either a conjugate point or the midpoint of a time periodic Lagrangian fluid flow.

BiFlowLISA: Measuring spatial association for bivariate flow data

Spatial flow data are often used to represent spatial interaction phenomena such as daily commuting trips, human or animal migrations, and the exchanges of commodities, capital, or even information between regions. With the increasingly available large volume of flow data in fine spatiotemporal resolution, exploratory spatial data analysis (ESDA) has become more important than ever to gain understanding of the data and the story behind it. A major group of flow-related ESDA methods focus on measuring spatial associations, which proves useful in improving the prediction power and interpretability of spatial interaction model (SIM), as well as in identifying local clusters and outliers of flow events. This paper introduces a new spatial statistical method called BiFlowLISA—a local indicator of spatial association of bivariate flow data. BiFlowLISA evaluates the association between two types of flows in close proximity, in other words, how the value of type-I flows associate with the value of nearby type-II flows. We develop BiFlowLISA by extending the local bivariate Moran's I to the flow context. We also put forth its global version to measure the global patterns, and another variant of BiFlowLISA to measure both spatial and in-situ correlations at the same time. Several flow-specific issues are discussed and solved, including flow neighbor definition, OD matrix sparsity, and conditional permutation. We experiment with synthetic datasets to verify its functionality and to summarize its characteristics. A case study of taxi and ride-hailing services in New York City demonstrates its usefulness in the comparative analysis of the spatial patterns of two types of travel flows. More applications of BiFlowLISA await to be explored in the future.

A persistent quiet-Sun small-scale tornado

Context. Recently, the appearance, characteristics, and dynamics of a persistent 1.7 h vortex flow, resembling a small-scale tornado, have been investigated with observations both from the ground and from space in a quiet-Sun region in several lines and channels and for the first time in the Hα line centre. The vortex flow showed significant substructure in the form of several intermittent chromospheric swirls. Aims. We investigate the oscillatory behaviour of various physical parameters in the vortex area in an attempt to better understand the physics of the reported vortex flow. This is the first analysis of this extent. Methods. We used the same data set of high spatial and temporal resolution CRisp Imaging SpectroPolarimeter (CRISP) observations in several wavelengths along the Hα and Ca II 8542 Å line profiles, as well as Doppler velocities and full-width at half-maximum (FWHM) derived from the Hα line profiles. The spectral analysis of oscillations is based on a two-dimensional wavelet analysis performed within the vortex flow area and in a quiet-Sun region (used for comparison), as well as along line and circular slices. Results. The vortex flow shows significant oscillatory power in the range of 3–5 min, peaking around 4 min. This power behaves differently than the reference quiet-Sun region. The derived oscillations reflect the cumulative action of different components such as swaying motions, rotation, and waves. The derived periods for swaying motions are in the range of 200–220 s, and the rotation periods are ∼270 s for Hα and ∼215 s for Ca II 8542 Å. Periods increase with atmospheric height and seem to decrease with radial distance from the vortex centre, suggesting a deviation from a rigid rotation. The behaviour of power within the vortex flow as a function of period and height implies the existence of evanescent waves. Moreover, considerable power is obtained even for periods as long as 10 min, not only at photospheric but also at chromospheric heights, while the formation of vortexes is related to turbulent convection or to twisting motions exercised in the magnetic field concentrations. These imply that different types of waves may be excited, such as magnetoacoustic (e.g. kink) or Alfvén waves. Conclusions. The vortex flow seems to be dominated by two motions: a transverse (swaying) motion, and a rotational motion. The obtained oscillations point to the propagation of waves within it. Nearby fibril-like flows could play an important role in the rotational modulation of the vortex flow. There also exists indirect evidence that the structure is magnetically supported, and one of the swirls, close to its centre, seems to be acting as a “central engine” to the vortex flow.

A persistent quiet-Sun small-scale tornado

Context. Vortex flows have been extensively observed over a wide range of spatial and temporal scales in different spectral lines, and thus layers of the solar atmosphere, and have been widely found in numerical simulations. However, signatures of vortex flows have only recently been reported in the wings of the Hα, but never so far in the Hα line centre. Aims. We investigate the appearance, characteristics, substructure, and dynamics of a 1.7 h persistent vortex flow observed from the ground and from space in a quiet-Sun region in several lines/channels covering all atmospheric layers from the photosphere up to the low corona. Methods. We use high spatial and temporal resolution CRisp Imaging SpectroPolarimeter (CRISP) observations in several wavelengths along the Hα and Ca II 8542 Å line profiles, simultaneous Atmospheric Imaging Assembly (AIA) observations in several Ultraviolet (UV) and Extreme ultraviolet (EUV) channels and Helioseismic and Magnetic Imager (HMI) magnetograms to study a persistent vortex flow located at the south solar hemisphere. Doppler velocities were derived from the Hα line profiles. Our analysis involves visual inspection and comparison of all available simultaneous/near-simultaneous observations and detailed investigation of the vortex appearance, characteristics and dynamics using time slices along linear and circular slits. Results. The most important characteristic of the analysed clockwise rotating vortex flow is its long duration (at least 1.7 h) and its large radius (~3″). The vortex flow shows different behaviours in the different wavelengths along the Hα and Ca II 8542 Å profiles reflecting the different formation heights and mechanisms of the two lines. Ground-based observations combined with AIA observations reveal the existence of a funnel-like structure expanding with height, possibly rotating rigidly or quasi-rigidly. However, there is no clear evidence that the flow is magnetically driven as no associated magnetic bright points have been observed in the photosphere. Hα and Ca II 8542 Å observations also reveal significant substructure within the flow, manifested as several individual intermittent chromospheric swirls with typical sizes and durations. They also exhibit a wide range of morphological patterns, appearing as dark absorbing features, associated mostly with mean upwards velocities around 3 km s−1 and up to 8 km s−1, and occupying on average ~25% of the total vortex area. The radial expansion of the spiral flow occurs with a mean velocity of ~3 km s−1, while its dynamics can be related to the dynamics of a clockwise rigidly rotating logarithmic spiral with a swinging motion that is, however, highly perturbed by nearby flows associated with fibril-like structures. A first rough estimate of the rotational period of the vortex falls in the range of 200–300 s. Conclusions. The vortex flow resembles a small-scale tornado in contrast to previously reported short-lived swirls and in analogy to persistent giant tornadoes. It is unclear whether the observed substructure is indeed due to the physical presence of individual intermittent, recurring swirls or a manifestation of wave-related instabilities within a large vortex flow. Moreover, we cannot conclusively demonstrate that the long duration of the observed vortex is the result of a central swirl acting as an “engine” for the vortex flow, although there is significant supporting evidence inferred from its dynamics. It also cannot be excluded that this persistent vortex results from the combined action of several individual smaller swirls further assisted by nearby flows or that this is a new case in the literature of a hydrodynamically driven vortex flow.

Sensitivity of Tropical Cyclone Track to the Vertical Structure of a Nearby Monsoon Gyre

Abstract The impact of different vertical structures of a nearby monsoon gyre (MG) on a tropical cyclone (TC) track is investigated using idealized numerical simulations. In the experiment with a relatively deeper MG, the TC experiences a sharp northward turn at a critical point when its zonal westward-moving speed slows down to zero. At the same time, the total vorticity tendency for the TC wavenumber-1 component nearly vanishes as the vorticity advection by the MG cancels the vorticity advection by the TC. At this point, the TC motion is dominated by the beta effect, as in a no-mean-flow environment, and takes a sharp northward turn. In contrast, the TC does not exhibit a sharp northward turn with a shallower MG nearby. In the case with a deeper MG, a greater relative vorticity gradient of the MG promotes a quicker attraction between the TC and MG through the vorticity segregation process. In addition, a larger outer size of the TC also favors a faster westward propagation from its initial position, thus having more potential to collocate with the MG. Once the coalescence is in place, the Rossby wave energy dispersion associated with the TC and MG together is enhanced and rapidly strengthens the southwesterly flow on the eastern flank of both systems. The steering flow from both the beta gyre and the Rossby wave dispersion leads the TC to take a sharp northward track when the total vorticity tendency is at its minimum. This study indicates the importance of good representations of the TC structure and its nearby environmental flows in order to accurately predict TC motions.

Feeder and post Deccan Trap dyke activities in the northern slope of the Satpura Mountain: Evidence from new 40Ar-39Ar ages

We present new 40Ar-39Ar plagioclase crystallization ages from the dykes exposed at the northern slope of the Satpura Mountain range near Betul-Jabalpur-Pachmarhi area, ∼800 km NE of the Western Ghats escarpment. Among the two plateau ages, the first age of 66.56 ± 0.42 Ma from a dyke near Mohpani village represents its crystallization age which is either slightly older or contemporaneous with the nearby Mandla lava flows (63–65 Ma). We suggest that the Mohpani dyke might be one of the feeders for the surrounding lava flows as these lavas are significantly younger than the majority of the main Deccan lavas of the Western Ghats (66.38–65.54 Ma). The second age of 56.95 ± 1.08 Ma comes from a younger dyke near Olini village which cuts across the lava flows of the area. The age correlates well with the Mandla lavas which are chemically similar to the uppermost Poladpur, Ambenali and Mahabaleshwar Formation lavas of SW Deccan. Our study shows that the dyke activities occurred in two phases, with the second one representing the terminal stage.

Chronology of tectonic, geomorphic, and volcanic interactions and the tempo of fault slip near Little Lake, California

Research Article| July 01, 2013 Chronology of tectonic, geomorphic, and volcanic interactions and the tempo of fault slip near Little Lake, California Colin B. Amos; Colin B. Amos † 1Geology Department, Western Washington University, Bellingham, Washington 98225, USA †E-mail:Colin.Amos@wwu.edu Search for other works by this author on: GSW Google Scholar Sarah J. Brownlee; Sarah J. Brownlee 2Department of Geology, Wayne State University, Detroit, Michigan 48202, USA Search for other works by this author on: GSW Google Scholar Dylan H. Rood; Dylan H. Rood 3Accelerator Mass Spectrometry Laboratory, Scottish Universities Environmental Research Centre (SUERC), East Kilbride G75 0QF, UK4Earth Research Institute, University of California, Santa Barbara, California 93106, USA Search for other works by this author on: GSW Google Scholar G. Burch Fisher; G. Burch Fisher 5Department of Earth Science, University of California, Santa Barbara, California 93106, USA Search for other works by this author on: GSW Google Scholar Roland Bürgmann; Roland Bürgmann 6Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA Search for other works by this author on: GSW Google Scholar Paul R. Renne; Paul R. Renne 7Berkeley Geochronology Center, Berkeley, California 94709, USA Search for other works by this author on: GSW Google Scholar Angela S. Jayko Angela S. Jayko 8U.S. Geological Survey, U.C. White Mountain Research Station, Bishop, California 93514, USA Search for other works by this author on: GSW Google Scholar GSA Bulletin (2013) 125 (7-8): 1187–1202. https://doi.org/10.1130/B30803.1 Article history received: 06 Oct 2012 rev-recd: 05 Mar 2013 accepted: 30 Mar 2013 first online: 08 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Colin B. Amos, Sarah J. Brownlee, Dylan H. Rood, G. Burch Fisher, Roland Bürgmann, Paul R. Renne, Angela S. Jayko; Chronology of tectonic, geomorphic, and volcanic interactions and the tempo of fault slip near Little Lake, California. GSA Bulletin 2013;; 125 (7-8): 1187–1202. doi: https://doi.org/10.1130/B30803.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract New geochronologic and geomorphic constraints on the Little Lake fault in the Eastern California shear zone reveal steady, modest rates of dextral slip during and since the mid-to-late Pleistocene. We focus on a suite of offset fluvial landforms in the Pleistocene Owens River channel that formed in response to periodic interaction with nearby basalt flows, thereby recording displacement over multiple time intervals. Overlap between 40Ar/39Ar ages for the youngest intracanyon basalt flow and 10Be surface exposure dating of downstream terrace surfaces suggests widespread channel incision during a prominent outburst flood through the Little Lake channel at ca. 64 ka. Older basalt flows flanking the upper and lower canyon margins indicate localization of the Owens River in its current position between 212 ± 14 and 197 ± 11 ka. Coupled with terrestrial light detection and ranging (lidar) and digital topographic measurements of dextral offset, the revised Little Lake chronology indicates average dextral slip rates of at least ∼0.6–0.7 mm/yr and <1.3 mm/yr over intervals ranging from ∼104 to 105 yr. Despite previous geodetic observations of relatively rapid interseismic strain along the Little Lake fault, we find no evidence for sustained temporal fluctuations in slip rates over multiple earthquake cycles. Instead, our results indicate that accelerated fault loading may be transient over much shorter periods (∼101 yr) and perhaps indicative of time-dependent seismic hazard associated with Eastern California shear zone faults. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Dark energy in six nearby galaxy flows: Synthetic phase diagrams and self-similarity

Outward flows of galaxies are observed around groups of galaxies on spatial scales of about 1 Mpc, and around galaxy clusters on scales of 10 Mpc. Using recent data from the Hubble Space Telescope (HST), we have constructed two synthetic velocity-distance phase diagrams: one for four flows on galaxy-group scales and the other for two flows on cluster scales. It has been shown that, in both cases, the antigravity produced by the cosmic dark-energy background is stronger than the gravity produced by the matter in the outflow volume. The antigravity accelerates the flows and introduces a phase attractor that is common to all scales, corresponding to a linear velocity-distance relation (the local Hubble law). As a result, the bundle of outflow trajectories mostly follow the trajectory of the attractor. A comparison of the two diagrams reveals the universal self-similar nature of the outflows: their gross phase structure in dimensionless variables is essentially independent of their physical spatial scales, which differ by approximately a factor of 10 in the two diagrams.

Treatment of industrial waste water from copper production process in RTB Bor

The biggest polluters of water resources are industrial waste water produced after various production technological processes. Within the industrial complex RTB Bor, the waste water are generated during the copper production process with negative impact on the environment, reflected in long-term contamination of soil with which they come into contact and accumulation of heavy metal ions in it, in inflow into surface water and mixing with ground water and their pollution. Directly, the most vulnerable are the Bor River and Krivelj River belonging to the catchment area of the River Timok that still flows into the Danube and therefore presents wider environmental problem of international character. The aim of this work is a characterization of industrial waste water generated in RTB Bor and their impact on the pollution of nearby water flows. The waste water samples were analyzed from the production process of sulfuric acid, production of copper sulfate, electrolytic copper refining and treatment plant of anode slime. Detailed qualitative and quantitative analysis of waste water samples was carried out from these production processes and high content of heavy metal ions (Cu, Fe, Mn, Zn, Pb, Ni, Bi, Cd, etc.) was established, that highly exceeds the limit values defined in the legal regulations of the Republic of Serbia. Neutralization of the waste industrial water was performed and after chemical characterization of purified water, it was found that they belong to the IV water category, according to the legislation of the Republic of Serbia. Based on chemical composition, a proposal for treatment with valorization of present copper was given.

First‐ and second‐order sensitivity equation methods for value and shape parameters

AbstractThis paper presents formulations of the sensitivity equation method (SEM) and applications to transient flow problems. Solutions are shown for both value and shape parameters using a three‐dimensional solution algorithm. Sensitivities are used for fast evaluation of the flow at nearby values of the parameters: the solution is approximated by a Taylor series in parameter space involving the flow sensitivities. The accuracy of nearby flows is much improved when second‐order sensitivities are used. We show how the sensitivity of the Strouhal number can be obtained from the flow sensitivities. Results are in agreement with the experimental correlation. The methodology is also applied to the flow past a cylinder in ground proximity. The proposed method is verified on a steady‐state problem by comparing the computed sensitivity with the actual change in the solution when a small perturbation is imposed on the shape parameter. We then investigate the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. The approach properly reproduces the damping or amplification of the vortex shedding with a reduction or increase of the gap size. Copyright © 2008 Crown in the right of Canada. Published by John Wiley &amp; Sons, Ltd.

Application of a sensitivity equation method to the k–ε model of turbulence

In this paper, we present some examples of sensitivity analysis for flows modeled by the standard k–e model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adaptive finite element method. Our examples emphasize a number of applications of sensitivity analysis: identification of the most significant parameters, analysis of the flow model, assessing the influence of closure coefficients, calculation of nearby flows, and uncertainty analysis. The sensitivity parameters considered are closure coefficients of the turbulence model and constants appearing in the wall functions.

A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows

AbstractThis paper presents a general formulation of the continuous sensitivity equation method (SEM) for computing first‐ and second‐order sensitivities of time‐dependent, incompressible laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The SEM formulation is verified on a problem with a closed‐form solution. Systematic grid convergence studies confirm the theoretical rates of convergence in both space and time. The methodology is then applied to uniform flow around a circular cylinder. The flow starts with a symmetrical solution and transitions to the traditional Von Karman street (alternate vortex shedding). Sensitivities are used to demonstrate fast evaluation of nearby flows. The accuracy of nearby flows is much improved when second‐order sensitivities are used. The sensitivity of the Strouhal number with respect to the Reynolds number agrees well with the computed and experimental St–Re relationship. Copyright © 2007 John Wiley &amp; Sons, Ltd.

The newest twists in protostellar outflows: triggered star formation

AbstractWinds and outflows powered by the release of gravitational potential energy of infalling matter have been invoked as the triggering agent for further star-formation on scales from dwarf galaxies to individual, low-mass stars. This brief review will touch upon the circumstances under which outflows can serve as star-formation triggers, from specific observations of present-day, nearby protostellar flows.

A sensitivity equation method for fast evaluation of nearby flows and uncertainty analysis for shape parameters†

This paper presents the application of the continuous sensitivity equation method (CSEM) to fast evaluation of nearby flows and to uncertainty analysis for shape parameters. The flow and sensitivity fields are solved using an adaptive finite-element method. A new approach is presented to extract accurate flow derivatives at the boundary, which are needed in the shape sensitivity boundary conditions. Boundary derivatives are evaluated via high order Taylor series expansions used in a constrained least-squares procedure. The proposed method is first applied to fast evaluation of nearby flows: the baseline flow and sensitivity fields around a NACA 0012 airfoil are used to predict the flow around airfoils with nearby shapes obtained by modifications of the thickness (NACA 0015), the angle of attack and the camber (NACA 4512). The method is then applied to evaluate the influence of geometrical uncertainties on the flow around a NACA 0012 airfoil.

A continuous sensitivity equation method for time-dependent incompressible laminar flows

This paper presents a general sensitivity equation method (SEM) for time dependent incompressible laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The SEM formulation is verified on a problem with a closed form solution. Systematic grid convergence studies confirm the theoretical rates of convergence in both space and time. The methodology is then applied to pulsed flow around a square cylinder. The flow starts with symmetrical vortex shedding then transitions to the traditional Von Karman street (alternate vortex shedding). Simulations indicate that the transition phase manifests itself earlier in the sensitivity fields than in the flow field itself. Sensitivities are then demonstrated for fast evaluation of nearby flows and uncertainty analysis. Copyright © 2005 John Wiley & Sons, Ltd.

Application of a sensitivity equation method to turbulent flows with heat transfer

This paper presents a continuous sensitivity equation method (SEM) for incompressible turbulent heat transfer. The k– ɛ model of turbulence with wall functions is used to model turbulence. Heat transfer is handled using an eddy conductivity. The SEM formulation accounts for complex parameter dependence and is suitable for a wide range of problems. It is applied to turbulent flow over a heated backward facing step and to turbulent flow over a heated flat plate. Several uses of the SEM are demonstrated: fast computation of nearby flows, identification of key parameters controlling the flow, and uncertainty analysis. Sensitivities are used to cascade input data uncertainties through the CFD code to yield uncertainty estimates of the skin friction and Stanton number. The SEM also provides detailed information about the contribution of each parameter to the global uncertainty.