Initial Eddy Research Articles

Detection of Decarburising Depth in Hadfield Steels Using a Multi-magnetic NDE Method

ABSTRACT This paper reports the capability of a range of electromagnetic non-destructive evaluation (NDE) methods to characterise the decarburising phenomena in Hadfield steels. Four Hadfield steel samples were austenitised at 1050 °C for 1, 2, 3 and, 4 hours in an air furnace followed by water quenching to produce various decarburising depths. The decarburisation depth was characterised using hardness profile measurements, optical and scanning electron microscopy, and X-ray diffraction analysis. The results confirmed the occurrence of decarburising and presence of a surface martensite layer of 35 to 110 µm depending on austenitisation time. The microstructural change at the surface affects the magnetic properties of the sample and enables electromagnetic NDE methods to detect the transformed layers quantitatively. In the non-destructive characterisation step, the relationships between the austenitising time and the outputs from magnetic flux leakage (MFL), initial magnetisation curve (BH) and eddy current (EC) methods are reported. Comparing the results obtained from the three magnetic NDE methods, it can be concluded that MFL and EC (phase angle output) have the potential to quantify the surface microstructural changes occurring as a result of the decarburising process in Hadfield steels.

The surface current of Ekman flows with time-dependent eddy viscosity

<p style='text-indent:20px;'>In this paper we investigate transients in the oceanic Ekman layer in the presence of time-varying winds and a constant-in-depth but time dependent eddy viscosity, where the initial state is taken to be the steady state corresponding to the initial wind and the initial eddy viscosity. For this specific situation, a formula for the evolution of the surface current can be derived explicitly. We show that, if the wind and the eddy viscosity converge toward constant values for large times, under mild assumptions on their convergence rate the solution converges toward the corresponding steady state. The time evolution of the surface current and the surface deflection angle is visualized with the aid of simple numerical plots for some specific examples.</p>

Dynamics and decay of a spherical region of turbulence in free space

Abstract

Rossby-number effects on columnar eddy formation and the energy dissipation law in homogeneous rotating turbulence

Two aspects of homogeneous rotating turbulence are quantified through forced direct numerical simulations in an elongated domain, which, in the direction of rotation, is approximately 340 times larger than the typical initial eddy size. First, by following the time evolution of the integral length scale along the axis of rotation , the growth rate of the columnar eddies and its dependence on the Rossby number is determined as for , where is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate is sought. Comparison with current available scaling laws shows that the relation proposed by Baqui & Davidson (Phys. Fluids, vol. 27(2), 2015, 025107), i.e. , where is the root-mean-square velocity, approximates well part of our data, more specifically the range . However, relations proposed in the literature fail to model the data for the second and most interesting range, i.e. , which is marked by the formation of columnar eddies. To find a similarity relation for the latter, we exploit the concept of a spectral transfer time introduced by Kraichnan (Phys. Fluids, vol. 8(7), 1965, p. 1385). Within this framework, the energy dissipation rate is considered to depend on both the nonlinear time scale and the relaxation time scale. Thus, by analysing our data, expressions for these different time scales are obtained that result in , where is the integral length scale in the direction normal to the axis of rotation and is the nonlinear time scale of the initial homogeneous isotropic field.

Multi-objective design optimization of a permanent magnet axial flux eddy current brake

The main aim of this study is to optimize an axial flux eddy current damper to be used in a specific aviation application. Eddy current dampers are more advantageous compared to conventional mechanical dampers as they are maintenance-free due to contactless structure and have higher reliability, which is very desirable in aerospace applications. An initial eddy current brake prototype is manufactured and the test results are used to verify the 3-D finite element simulations. The effect of temperature on the brake performance is investigated. Finally, a multiobjective genetic algorithm optimization is applied to find the optimum pole number and geometric dimensions of the eddy current brake in order to achieve the desired torque-speed characteristic while the total weight of the brake is minimized. It is found that the mass and volume of the initial prototype can be halved by implementing this optimization algorithm.

Onset criteria for freely decaying isotropic turbulence

From DNS of turbulence decaying from specified initial conditions for the range of initial Taylor-Reynolds numbers 2.58 < R{\lambda}(0) < 358.6, it was found that the shape of the iconic curve of dimensionless dissipation versus Reynolds number depended strongly on the choice of measurement time. For our preferred time, a composite based on peak values in the dissipation and inertial transfer curves, the result was virtually identical to the forced, stationary case. In the course of studying onset criteria, we found that the exponent for the power-law decay of the energy decreased with increasing Reynolds number and lay in the range 1.35 < n < 2.60. An additional run was performed, using the data from a stationary, forced simulation with R{\lambda} = 335 for the initial condition. The results of this suggested that the time taken for energy to pass through the cascade was about one half of an initial eddy turnover time.

Investigation of anomalous very fast decay regimes in homogeneous isotropic turbulence

ABSTRACTThe emergence of anomalous fast decay regimes in homogeneous isotropic turbulence (HIT) decay is investigated via both theoretical analysis and eddy-damped quasi-normal Markovian simulations. The work provides new insight about a fundamental issue playing a role in HIT decay, namely the influence of non-standard shapes of the energy spectrum, in particular in the large energetic scale region. A detailed analysis of the kinetic energy spectrum E(k) and the non-linear energy transfer T(k) shows that anomalous decay regimes are associated with the relaxation of initial energy spectra which exhibit a bump at energetic scales. This feature induces an increase in the energy cascade rate, toward solutions with a smooth shape at the spectrum peak. Present results match observations reported in wind-tunnel experiments dealing with turbulence decay in the wake of grids and bluff bodies, including scaling laws for the dissipation parameter Cϵ. They also indicate that the ratio between the initial eddy turnover time and the advection time determines of how fast anomalous regimes relax toward classical turbulence free-decay. This parameter should be used for consistent data comparison and it opens perspectives for the control of multiscale effects in industrial applications.

A three-dimensional modeling study on eddy-mean flow interaction between a Gaussian-type anticyclonic eddy and Kuroshio

The Princeton ocean model is employed to study the energy balance of a fast-moving anticyclonic eddy (AE) during eddy-mean flow interaction. The AE is initialized with an axisymmetric Gaussian-type temperature profile and is placed to the east of the Philippine Islands. An energy analysis suggests that the advection term, pressure work and friction term play dominant roles in the initial eddy decay. During the strong interaction stage, barotropic instability (BTI) becomes the main force for the eddy kinetic energy (EKE) production, with the largest positive BTI in the interaction zone, which means that the eddy always obtains kinetic energy from the Kuroshio during this stage. Most of the EKE dissipation, the large conversion from the eddy available potential energy to the EKE and that from the mean kinetic energy to the EKE all occur at the upper layer during the strong interaction stage. When the AE interacts with the mean flow on the eastern side of the Kuroshio, whether the AE gains kinetic energy from the Kuroshio or loses kinetic energy to the Kuroshio is mainly determined by its shape in the interaction zone.

Erosion of a California Undercurrent eddy by bottom topography

AbstractSubsurface eddies are ubiquitous features in eastern boundary current systems. These phenomena tend to modulate the across‐shore distribution of heat and biogeochemical tracers. A California Undercurrent eddy was detected by shipboard observations in October 2009 off the northern Baja California continental slope. The spatiotemporal variation in the California Undercurrent eddy is investigated by using a mesoscale‐resolving hindcast ocean simulation. A poleward coastal current that is driven by an upwelling‐wind relaxation event and the coastline geometry instigated the separation of the California Undercurrent from the slope, forming a meander‐like structure, which evolved as a mesoscale eddy‐like structure. The latter structure evolved as a subsurface eddy with a warm anomaly core, a distinctive feature of eddies that form from the California Undercurrent. During the initial stage, the subsurface eddy presented a cone‐shape form, with the maximum amplitude of the relative vorticity in the upper section. The inviscid effect of the irregular bottom topography altered both the initial direction of propagation and the initial eddy shape: the propagation direction of the eddy changed from north‐south to southwest, and the shape changed from a cone shape to a subsurface lens shape. The strong eddy‐topography interactions triggered a sign change in the heat flux direction from the environment toward the eddy and vice versa through the horizontally divergent component of the velocity field, which accelerated the eddy's decay. This study shows the relevance of the synoptic wind stress events and the irregularity of the bottom topography on the mesoscale eddy activity in the southern portion of the California Current.

Skin-friction drag reduction in turbulent channel flow based on streamwise shear control

It is known that stretching and intensification of a hairpin vortex by mean shear play an important role to create a hairpin vortex packet, which generates the large Reynolds shear stress associated with skin-friction drag in wall-bounded turbulent flows. In order to suppress the mean shear at the wall for high efficient drag reduction (DR), in the present study, we explore an active flow control concept using streamwise shear control (SSC) at the wall. The longitudinal control surface is periodically spanwise-arranged with no-control surface while varying the structural spacing, and an amplitude parameter for imposing the strength of the actuating streamwise velocity at the wall is introduced to further enhance the skin-friction DR. Significant DR is observed with an increase in the two parameters with an accompanying reduction of the Reynolds stresses and vorticity fluctuations, although a further increase in the parameters amplifies the turbulence activity in the near-wall region. In order to study the direct relationship between turbulent vortical structures and DR under the SSC, temporal evolution with initial eddies extracted by conditional averages for Reynolds-stress-maximizing Q2 events are examined. It is shown that the generation of new vortices is dramatically inhibited with an increase in the parameters throughout the flow, causing fewer vortices to be generated under the control. However, when the structural spacing is sufficiently large, the generation of new vortex is not suppressed over the no-control surface in the near-wall region, resulting in an increase of the second- and fourth-quadrant Reynolds shear stresses. Although strong actuating velocity intensifies the near-wall turbulence, the increase in the turbulence activity is attributed to the generation of counter-clockwise near-wall vortices by the increased vortex transport.

Auto-generation in wall turbulence by the interaction of weak eddies

For channel flow, we explore how commonly found weak eddies can still auto-generate and produce new eddies. Before, only strong eddies (above a threshold strength) were considered to auto-generate. Such strong eddies are rarely observed in actual turbulent flows however. Here, the evolution of two weak conditional eddies with different initial strengths, initial sizes, and initial stream-wise spacing between them is studied. The numerical procedure followed is similar to Zhou et al. [“Mechanisms for generating coherent packets of hairpin vortices in channel flow,” J. Fluid Mech. 387, 353 (1999)]. The two eddies are found to merge into a single stronger eddy when the initial upstream eddy is taller than the downstream eddy, which further auto-generates when the initial stream-wise separation is small (&amp;lt;120 wall units). However, it is observed that non-merging cases with small initial stream-wise separation also auto-generated. In the initial condition, the two conditional eddies are placed near to each other so their velocity fields (low-speed streaks and ejection events) get superimposed and amplified as a function of stream-wise spacing. To examine this effect, a divergence free low-speed streak is superimposed on an eddy. It is found that these low-speed streak simulations do not auto-generate. On the other hand, a rapid lift-up of an eddy by ejection events plays a role in the onset of auto-generation, which also leads to a modified interpretation of auto-generation mechanism. It differed from the existing auto-generation mechanism at the later stages of auto-generation where blockage of mean flow and shear layer deformation is considered instead of vortex dynamics.

Segmentation and tracking of anticyclonic eddies during a submarine volcanic eruption using ocean colour imagery.

The eruptive phase of a submarine volcano located 2 km away from the southern coast of El Hierro Island started on October 2011. This extraordinary event provoked a dramatic perturbation of the water column. In order to understand and quantify the environmental impacts caused, a regular multidisciplinary monitoring was carried out using remote sensing sensors. In this context, we performed the systematic processing of every MODIS and MERIS and selected high resolution Worldview-2 imagery to provide information on the concentration of a number of biological, physical and chemical parameters. On the other hand, the eruption provided an exceptional source of tracer that allowed the study a variety of oceanographic structures. Specifically, the Canary Islands belong to a very active zone of long-lived eddies. Such structures are usually monitored using sea level anomaly fields. However these products have coarse spatial resolution and they are not suitable to perform submesoscale studies. Thanks to the volcanic tracer, detailed studies were undertaken with ocean colour imagery allowing, using the diffuse attenuation coefficient, to monitor the process of filamentation and axisymmetrization predicted by theoretical studies and numerical modelling. In our work, a novel 2-step segmentation methodology has been developed. The approach incorporates different segmentation algorithms and region growing techniques. In particular, the first step obtains an initial eddy segmentation using thresholding or clustering methods and, next, the fine detail is achieved by the iterative identification of the points to grow and the subsequent application of watershed or thresholding strategies. The methodology has demonstrated an excellent performance and robustness and it has proven to properly capture the eddy and its filaments.

Spatiotemporal evolution of hairpin eddies, Reynolds stress, and polymer torque in polymer drag-reduced turbulent channel flows

To study the influence of dynamic interactions between turbulent vortical structures and polymer stress on turbulent friction drag reduction, a series of simulations of channel flow is performed. We obtain self-consistent evolution of an initial eddy in the presence of polymer stresses by utilizing the finitely extensible nonlinear elastic-Peterlin (FENE-P) model. The initial eddy is extracted by the conditional averages for the second quadrant event from fully turbulent Newtonian flow, and the initial polymer conformation fields are given by the solutions of the FENE-P model equations corresponding to the mean shear flow in the Newtonian case. At a relatively low Weissenberg number We(τ) (=50), defined as the ratio of the polymer relaxation time to the wall time scale, the generation of new vortices is inhibited by polymer-induced countertorques. Thus fewer vortices are generated in the buffer layer. However, the head of the primary hairpin is unaffected by the polymer stress. At larger We(τ) values (≥100), the hairpin head becomes weaker and vortex autogeneration and Reynolds stress growth are almost entirely suppressed. The temporal evolution of the vortex strength and polymer torque magnitude reveals that polymer extension by the vortical motion results in a polymer torque that increases in magnitude with time until a maximum value is reached over a time scale comparable to the polymer relaxation time. The polymer torque retards the vortical motion and Reynolds stress production, which in turn weakens flow-induced chain extension and torque itself. An analysis of the vortex time scales reveals that with increasing We(τ), vortical motions associated with a broader range of time scales are affected by the polymer stress. This is qualitatively consistent with Lumley's time criterion for the onset of drag reduction.

Application of the Boltzmann kinetic equation to the eddy problems

The main purpose of this work is to investigate the feasibility of applying a kinetic approach to the problem of modeling turbulent and unstable flows. First, initial value problems with the Taylor–Green (TG) type and isotropic velocity conditions for compressible flow in two-dimensional (2D) and three-dimensional (3D) periodic domains are considered. Further, 3D direct numerical simulation of decaying isotropic turbulence is performed. Macroscopic flow quantities of interest are examined. The simulation is based on the direct numerical solution of the Boltzmann kinetic equation using an explicit–implicit scheme for the relaxation stage. Comparison with the solution of the Bhatnagar–Gross–Krook (BGK) model equation obtained by using an implicit scheme is carried out for the decaying isotropic turbulence problem and demonstrates a small difference. For the TG initial condition results show a fragmentation of the large initial eddies and subsequently the full damping of the system. Numerical data are close to the analytic solution of TG problem. A dependence of the kinetic energy on the wave number is obtained by means of the Fourier expansion of velocity components. A power-law exponent for the kinetic energy spectrum tends to the theoretical value “−3” for 2D turbulence in 2D case and to the famous Kolmogorov value “−5/3” in 3D case.

Multiscale Interactions in the Life Cycle of a Tropical Cyclone Simulated in a Global Cloud-System-Resolving Model. Part I: Large-Scale and Storm-Scale Evolutions*

Abstract The Nonhydrostatic Icosahedral Atmospheric Model (NICAM), a global cloud-system-resolving model, successfully simulated the life cycle of Tropical Storm Isobel that formed over the Timor Sea in the austral summer of 2006. The multiscale interactions in the life cycle of the simulated storm were analyzed in this study. The large-scale aspects that affected Isobel’s life cycle are documented in this paper and the corresponding mesoscale processes are documented in a companion paper. The life cycle of Isobel was largely controlled by a Madden–Julian oscillation (MJO) event and the associated westerly wind burst (WWB). The MJO was found to have both positive and negative effects on the tropical cyclone intensity depending on the location of the storm relative to the WWB center associated with the MJO. The large-scale low-level convergence and high convective available potential energy (CAPE) downwind of the WWB center provided a favorable region to the cyclogenesis and intensification, whereas the strong large-scale stretching deformation field upwind of the WWB center may weaken the storm by exciting wavenumber-2 asymmetries in the eyewall and leading to the eyewall breakdown. Five stages are identified for the life cycle of the simulated Isobel: the initial eddy, intensifying, temporary weakening, reintensifying, and decaying stages. The initial eddy stage was featured by small-scale/mesoscale convective cyclonic vortices developed in the zonally elongated rainband organized in the preconditioned environment characterized by the WWB over the Java Sea associated with the onset of an MJO event over the East Indian Ocean. As the MJO propagated eastward and the cyclonic eddies moved southward into an environment with weak vertical shear and strong low-level cyclonic vorticity, a typical tropical cyclone structure developed over the Java Sea, namely the genesis of Isobel. Isobel experienced an eyewall breakdown and a temporary weakening when it was located upwind of the WWB center as the MJO propagated southeastward and reintensified as its eyewall reformed as a result of the axisymmetrization of an inward spiraling outer rainband that originally formed downwind of the WWB center. Finally Isobel decayed as it approached the northwest coast of Australia.

Intrinsic and forced interannual variability of the Gulf of Alaska mesoscale circulation

The response of the Gulf of Alaska (GOA) circulation to large-scale North Pacific climate variability is explored using three high resolution (15 km) regional ocean model ensembles over the period 1950–2004. On interannual and decadal timescales the mean circulation is strongly modulated by changes in the large scale climate forcing associated with PDO and ENSO. Intensification of the model gyre scale circulation occurs after the 1976–1977 climate shift, as well as during 1965–1970 and 1993–1995. From the model dynamical budgets we find that when the GOA experiences stronger southeasterly winds, typical during the positive phase of the PDO and ENSO, there is net large-scale Ekman convergence in the central and eastern coastal boundary. The geostrophic adjustment to higher sea surface height (SSH) and lower isopycnals lead to stronger cyclonic gyre scale circulation. The opposite situation occurs during stronger northwesterly winds (negative phase of the PDO). Along the eastern side of the GOA basin, interannual changes in the surface winds also modulate the seasonal development of high amplitude anticyclonic eddies (e.g. Haïda and Sitka eddies). Large interannual eddy events during winter-spring, are phase-locked with the seasonal cycle. The initial eddy dynamics are consistent with a quasi-linear Rossby wave response to positive SSH anomalies forced by stronger downwelling favorable winds (e.g. southwesterly during El Niño). However, because of the fast growth rate of baroclinic instability and the geographical focusing associated with the coastal geometry, most of the perturbation energy in the Rossby wave is locally trapped until converted into large scale nonlinear coherent eddies. Coastally trapped waves of tropical origin may also contribute to positive SSH anomalies that lead to higher amplitude eddies. However, their presence does not appear essential. The model ensembles, which do not include the effects of equatorial coastally trapped waves, capture the large Haïda and Sitka eddy events observed during 1982 and 1997 and explain between 40% and 70% of the tidal gauges variance along the GOA coast. In the western side of the GOA basin, interannual eddy variability located south of the Alaskan Stream is not correlated with large scale forcing and appears to be intrinsic. A comparison of the three model ensembles forced by NCEP winds and a multi-century-long integration forced only with the seasonal cycle, shows that the internal variability alone explains most of the eddy variance. The asymmetry between the eddy forced regime in the eastern basin, and the intrinsic regime in the western basin, has important implications for predicting the GOA response to climate change. If future climate change results in stronger wintertime winds and increased downwelling in the eastern basin, then increased mesoscale activity (perhaps more or larger eddies) might occur in this region. Conversely, the changes in the western basin are not predictable based on environmental forcing. Eastern eddies transport important biogeochemical quantities such as iron, oxygen and chlorophyll-a into the gyre interior, therefore having potential upscale effects on the GOA high-nutrient-low-chlorophyll region.

Erosion of a Surface Vortex by a Seamount on the β Plane

Abstract This paper investigates the behavior of a surface-intensified anticyclone encountering a seamount on the β plane in a stratified ocean. The eddy may be strongly eroded, and sometimes subdivided, provided that it gets close enough to the seamount. In case of subdivision, the detached part has a vertical structure different from that of the initial eddy, and a subsurface vortex may result. The basic erosion mechanism previously observed with f-plane experiments is still active on the β plane. Deep fluid motions induced by the initial vortex across the isobaths generate topographic vortices whose upper parts exert a shear/strain on the initial eddy, causing its filamentation. On the β plane, this process is further complicated by the presence of additional eddies created by fluid motion across the planetary vorticity gradient. Experiments without any topography show that these eddies by themselves can erode the initial vortex. In particular, a deep positive potential vorticity pole influences the near-bottom signature of the original vortex with a strong temporal variability. This reflects on the manner in which the surface eddy feels an underlying seamount. Sensitivity experiments show that the eddy erosion rate after encountering a seamount can no longer be related to basic parameters such as the minimum eddy–seamount distance, as it was on the f plane. The additional vorticity poles influencing the eddy on the β plane make the result of the eddy–seamount encounter very sensitive to small variations of the initial conditions, and impossible to predict.

Numerical Simulation of Cloud–Clear Air Interfacial Mixing

Abstract This paper discusses results from a series of direct numerical simulations of the microscale cloud–clear air mixing, set forth in the idealized scenario of decaying moist turbulence. In the moist case, kinetic energy of microscale motions comes not only from the classical downscale energy cascade, but it can also be generated internally due to the evaporation of cloud droplets. Three sets of numerical simulations are performed for three intensities of initial large-scale eddies. In each set, a control dry simulation is performed, as well as two moist simulations applying either bulk or detailed representation of cloud microphysics. Model results suggest that, as far as the evolutions of enstrophy and turbulent kinetic energy are concerned, the most significant impact of moist processes occurs at the low intensity of initial large-scale eddies (the input turbulent kinetic energy of 2 × 10−4 m2 s−2 resulting in the maximum eddy dissipation rate of 5 × 10−4 m2 s−3). In such a case, mixing and homoge...

Maximum entropy theory and the rapid relaxation of three-dimensional quasi-geostrophic turbulence.

Turbulent flow in a rapidly rotating stably stratified fluid (quasi-geostrophic turbulence) commonly decays toward a stable pattern of large-scale jets or vortices. A formula for the most probable three-dimensional end state, the maximum entropy state (MES), is derived using a form of Lynden-Bell statistical mechanics. The MES is determined by a set of integral invariants, including energy, as opposed to a complete description of the initial condition. A computed MES qualitatively resembles the quasistationary end state of a numerical simulation that is initialized with red noise, and relaxes for a time on the order of 100 (initial) eddy turnovers. However, the potential enstrophy of the end state, obtained from a coarsened potential vorticity distribution, exceeds that of the MES by nearly a factor of 2. The estimated errors for both theory and simulation do not account for the discrepancy. This suggests that the MES, if ever realized, requires a much longer time scale to fully develop.

The effects of expansion strength on large-scale structures in compressible free shear layers

Planar visualizations of two compressible free shear layers were performed immediately downstream of centered expansions of differing strengths in order to assess the influence of expansion strength on the embedded large-scale structures. The free shear layers studied here were formed through the separation of an approach flow, either a Mach 2.0 stream or a Mach 2.5 stream, from a planar backstep. In addition to side-view and end-view visualizations, spatial correlations (computed from large image ensembles) and laser Doppler velocimetry surveys of the free shear layers were also examined to discern relationships between the structure dynamics and the underlying pre- and postexpansion velocity fields. The instantaneous images clearly illustrate that ellipsoidal, highly coherent structures were present in both shear layers downstream of the expansion corner. The dissimilar expansion strengths did not appear to produce qualitatively different structures in the shear layers; however, as compared to the weaker expansion, the stronger expansion did result in an increase in the growth rate of the large-scale structures, apparently from an augmentation of the 〈u′v′〉∂U/∂y production term in the TKE equation. Furthermore, quantitative measurements of the mean structure geometry, as determined from the spatial correlation fields, revealed that a stronger expansion strength resulted in a larger aspect ratio of the mean structures (i.e., the structures were stretched preferentially in the streamwise and transverse directions as compared to the spanwise direction during the expansion process). Quadrant decompositions of the instantaneous velocity fluctuations within the approach boundary layers and within the free shear layers indicated a definite increase in structure organization across the expansion region, which is in contrast with studies of expanded supersonic boundary layers without separation. The instantaneous image data, spatial correlations, and velocity decompositions uniformly suggest that the separation process itself, and not the expansion strength, is the primary influence on initial eddy structure in the postexpansion free shear layer.