Base Flow Parameters Research Articles

Hydrodynamic influence on thermal management of flexible heatsink devices embedded with out-of-plane intricate microchannel design

This study examines the thermal management efficacy of a 3-D printed microfluidic heat sink device with an intricate microchannel design. The performance of the presented device was experimentally compared to device with contemporary rectangular microchannel for different base material compositions and flow parameters to further understand the complex heat transfer trade-off between heat conduction and convection. The study found that upon tuned with a relatively low flow rate of 10 μLmin−1, the heatsink device made from nanocomposite material, featuring an intricate 3D design, generates the lowest hotspot temperature due to uniform heat dissipation. However, when flow rate was increased to 120 μLmin−1, the phenomenon reverses and PDMS-based devices with intricate channel perform better compared to PDMS nanocomposite-based devices. There was concurrent occurrence of the aforementioned phenomena at various temperature settings of 338 K, 358 K, 373 K, and 388 K. Numerical simulation reveals that relatively high flow rates create vortices, which significantly alter the heat transfer characteristics of the devices. Along with its primary application of on-demand flexible electronic cooling, with optimal flow tuning, the applications of the proposed device can be further extended to the thermal management of batteries, industrial 3D-printer nozzle heads, and artificial organ cooling, etc.

Quantification technique of transition to turbulence in boundary layers using infrared thermography

The problem of accurate experimental detection of laminar-turbulent transition in three-dimensional boundary layers is discussed. A high-resolving panoramic experimental technique to estimate the onset and length of the transition for aerodynamic applications is proposed and described in detail. The technique includes multistage processing of recorded infrared image sequences to provide a robust detection of the transition in a broad range of base flow parameters. The data processing is fast and virtually hands-free that allows extensive parametric investigation of the transition in experiments. Moreover, an application of statistics procedures to obtain various spanwise-averaged values quantifying different aspects of the transition important for calibrating and validating engineering transition prediction methods is possible.

Diffusive effects in local instabilities of a baroclinic axisymmetric vortex

We present a local stability analysis of an idealized model of the stratified vortices that appear in geophysical settings. The base flow comprises an axisymmetric vortex with background rotation and an out-of-plane stable stratification, and a radial stratification in the thermal wind balance with the out-of-plane momentum gradient. Solving the local stability equations along fluid particle trajectories in the base flow, the dependence of short-wavelength instabilities on the Schmidt number $Sc$ (ratio between momentum and mass diffusivities) is studied, in the presence of curvature effects. In the diffusion-free limit, the well-known symmetric instability is recovered. In the viscous, double-diffusive regime, instability characteristics are shown to depend on three non-dimensional parameters (including $Sc$ ), and two different instabilities are identified: (i) a monotonic instability (same as symmetric instability at $Sc = 1$ ), and (ii) an oscillatory instability (absent at $Sc = 1$ ). Separating the base flow and perturbation characteristics, two each of base flow and perturbation parameters (apart from $Sc$ ) are identified, and the entire parameter space is explored for the aforementioned instabilities. In comparison with $Sc = 1$ , monotonic and oscillatory instabilities are shown to significantly expand the instability region in the space of base flow parameters as $Sc$ moves away from unity. Neutral stability boundaries on the plane of $Sc$ and a modified gradient Richardson number are then identified for both these instabilities. In the absence of curvature effects, our results are shown to be consistent with previous studies based on normal mode analysis, thus establishing that the local stability approach is well suited to capturing symmetric and double-diffusive instabilities. The paper concludes with a discussion of curvature effects, and the likelihood of monotonic and oscillatory instabilities in typical oceanic settings.

Hydrological simulation evaluation with WRF-Hydro in a large and highly complicated watershed: The Xijiang River basin

Study regionXijiang River, South China. Study focusThis paper discusses the application of WRF-Hydro, a distributed hydrological model, to a complicated watershed. The model performance on simulating streamflow, soil moisture, soil temperature and evapotranspiration is evaluated. Changes and characteristics of streamflow and related variables simulated by the model are analyzed. New hydrological insights for the regionIn this study, thirteen sensitive parameters used in this model are tested in large and small watersheds of the basin. It is found that large basins are more sensitive to base flow parameters than small basins. The WRF default soil type dataset is replaced by the Beijing Normal University (BNU) soil type dataset that is more accurate. The model can simulate temporal changes of streamflow as well as temporary variabilities of hydrological variables. The model can be applied in small and large watersheds. The trend of streamflow in the basin is spatially uneven with an increasing trend in the upper part and a decreasing trend in the lower part. The changes in streamflow are partly related to precipitation and evapotranspiration trends. The trends of 30-day maximum/minimum streamflow are not significant, but the reversals demonstrate significant changes during 1980–2018. This study is expected to serve as a reference for the application of the model in this basin and model calibration over different sizes of study area.

URBAN CONFIGURATION AND WATER BALANCE WITH AQUACYCLE MODEL IN THE BELÉM CATCHMENT, SOUTHERN BRAZIL

The influence of anthropogenic activities on drainage basins increases the complexity of hydrological systems in urban watersheds due to the increased amount of impervious surfaces and the interaction between natural and constructed drainage systems. Herein, the aim is to verify how water balance components respond to anthropogenic changes in different configurations of urban space. The study focuses on the Belém catchment, located in Curitiba, Southern Brazil city. Simulations were performed using the Aquacycle model to evaluate the water balance of fourteen Hydrologic Similarity Areas, which were delimited based on the integrated analysis of zoning law, and demographic density data. The results show a direct and linear interaction between an increase in impervious areas with an increase in surface runoff and decreases in infiltration and evapotranspiration, demonstrating the relationship among urban configuration and components of hydrological cycle. Linear regression analysis indicates R² of 0.986 between impervious surfaces and surface runoff, 0.956 for evapotranspiration and 0.934 for groundwater recharge. However, streamflow and baseflow parameters showed no sensitivity to the percentage of impervious surfaces, with R² 0.557 and 0.244, respectively. Finally, the results indicate a significant contribution to the water balance resulting from water-supply system leakage and wastewater discharge into the drainage system.

Potensi Debit Aliran Lokal Waduk Saguling Menggunakan Model Hujan Limpasan

Saguling reservoir is one of the three largest reservoirs in the Citarum River Basin. The water source of its reservoir originates from Upper Citarum river basin, with gauging station located in Citarum-Nanjung and local discharge from tributaries around the reservoir. The problem is there is no observation of local discharge from the tributaries, thus its potential is estimated. The purpose of this study is to analyze the potential of local discharge with the Hydrology Engineering Center-Hydrologic Modeling System (HEC-HMS) model. The HEC-HMS Rainfall-runoff method is used for calculating the potential of the local discharge that flows into Saguling resevrvoir. The parameters used in the model are deficit constant (loss parameter), linear reservoir (baseflow parameter), dan lag time (transform parameter). Rainfall-runoff model produced good calibration values for Citarum-Nanjung Gauging Station with R2 of 0.8 and the Nash-Sutcliffe efficiency (NSE) value of 0.788. The verification result carried out in Saguling reservoir gives NSE of 0.8343 and R2 value of 0.83. The simulation shows that the potential discharge from local river contributes about 21.64% of the total discharge that enters into the reservoir with monthly dependable flow for power plants, Q80 and Q85 values at 8,23 m3/s and 5,69 m3/s, respectively. The average discharge of local rivers can generate electricity of 3.89 MW - 162 MW.Keywords: Local discharge, rainfall runoff, potential discharge, Saguling reservoir

Adjoint-based parametric sensitivity analysis for swirling M-flames

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

Transient energy growth of optimal streaks in parallel round jets

We present a linear optimal perturbation analysis of streamwise invariant disturbances evolving in parallel round jets. The potential for transient energy growth of perturbations with azimuthal wavenumber m≥1 is analyzed for different values of Reynolds number Re. Two families of steady (frozen) and unsteady (diffusing) base flow velocity profiles have been used, for different aspect ratios α = R/θ, where R is the jet radius and θ is the shear layer momentum thickness. Optimal initial conditions correspond to infinitesimal streamwise vortices, which evolve transiently to produce axial velocity streaks, whose spatial structure and intensity depend on base flow and perturbation parameters. Their dynamics can be characterized by a maximum optimal value of the energy gain Gopt, reached at an optimal time τopt after which the perturbations eventually decay. Optimal energy gain and time are shown to be, respectively, proportional to Re2 and Re, regardless of the frozen or diffusing nature of the base flow. Besides, it is found that the optimal gain scales like Gopt∝1/m3 for all m except m = 1. This quantitative difference for azimuthal wavenumber m = 1 is shown to be based on the nature of transient mechanisms. For m = 1 perturbations, the shift-up effect [J. I. Jiménez-González et al., “Modal and non-modal evolution of perturbations for parallel round jets,” Phys. Fluids 27, 044105-1–044105-19 (2015)] is active: an initial streamwise vorticity dipole induces a nearly uniform velocity flow in the jet core, which shifts the whole jet radially. By contrast, optimal perturbations with m≥2 are concentrated along the shear layer, in a way that resembles the classical lift-up mechanism in wall-shear flows. The m = 1 shift-up effect is more energetic than the m≥2 lift-up, but it is slower, with optimal times considerably shorter in the case of m≥2 disturbances. This suggests that these perturbations may emerge very quickly in the flow when injected as initial conditions. When the base flow diffuses, the large time scale for m = 1 disturbances allows the shear layer to spread and the jet core velocity to decrease substantially, thus lowering the values of corresponding optimal gain and time. For m≥2, results are less affected, since the shorter transient dynamics does not leave room for significant modifications of the base flow velocity profiles, and the scaling laws obtained in the frozen case are recovered. Nevertheless, base flow diffusion hinders the transient growth, as a consequence of a weaker component-wise non-normality and a smoother, radially spread structure of optimal disturbances.

Assessment of land use land cover change impact on hydrological regime of a basin

The sustainability of water resources mainly depends on planning and management of land use; a small change in it may affect water yield largely, as both are linked through relevant hydrological processes, explicitly. However, human activities, especially a significant increase in population, in-migration and accelerated socio-economic activities, are constantly modifying the land use and land cover (LULC) pattern. The impact of such changes in LULC on the hydrological regime of a basin is of widespread concern and a great challenge to the water resource engineers. While studying these impacts, the issue that prevails is the selection of a hydrological model that may be able to accommodate spatial and temporal dynamics of the basin with higher accuracy. Therefore, in the present study, the capabilities of variable infiltration capacity hydrological model to hydrologically simulate the basin under varying LULC scenarios have been investigated. For the present analysis, the Pennar River Basin, Andhra Pradesh, which falls under a water scarce region in India, has been chosen. The water balance components such as runoff potential, evapotranspiration (ET) and baseflow of Pennar Basin have been simulated under different LULC scenarios to study the impact of change on hydrological regime of a basin. Majorly, increase in built-up (13.94% approx.) and decrease in deciduous forest cover (2.44%) are the significant changes observed in the basin during the last three decades. It was found that the impact of LULC change on hydrology is balancing out at basin scale (considering the entire basin, while routing the runoff at the basin outlet). Therefore, an analysis on spatial variation in each of the water balance components considered in the study was done at grid scale. It was observed that the impact of LULC is considerable spatially at grid level, and the maximum increase of 265 mm (1985–2005) and the decrease of 48 mm (1985–1995) in runoff generation at grid were estimated. On the contrary, ET component showed the maximum increase of 400 and decrease of 570 mm under different LULC change scenario. Similarly, in the base flow parameter, an increase of 70 mm and the decrease of 100 mm were observed. It was noticed that the upper basin is showing an increasing trend in almost all hydrological components as compared to the lower basin. Based on this basin scale study, it was concluded that change in the land cover alters the hydrology; however, it needs to be studied at finer spatial scale rather than the entire basin as a whole. The information like the spatial variation in hydrological components may be very useful for local authority and decision-makers to plan mitigation strategies accordingly.

A qualitative model structure sensitivity analysis method to support model selection

Summary The selection and identification of a suitable hydrological model structure is a more challenging task than fitting parameters of a fixed model structure to reproduce a measured hydrograph. The suitable model structure is highly dependent on various criteria, i.e. the modeling objective, the characteristics and the scale of the system under investigation and the available data. Flexible environments for model building are available, but need to be assisted by proper diagnostic tools for model structure selection. This paper introduces a qualitative method for model component sensitivity analysis. Traditionally, model sensitivity is evaluated for model parameters. In this paper, the concept is translated into an evaluation of model structure sensitivity. Similarly to the one-factor-at-a-time (OAT) methods for parameter sensitivity, this method varies the model structure components one at a time and evaluates the change in sensitivity towards the output variables. As such, the effect of model component variations can be evaluated towards different objective functions or output variables. The methodology is presented for a simple lumped hydrological model environment, introducing different possible model building variations. By comparing the effect of changes in model structure for different model objectives, model selection can be better evaluated. Based on the presented component sensitivity analysis of a case study, some suggestions with regard to model selection are formulated for the system under study: (1) a non-linear storage component is recommended, since it ensures more sensitive (identifiable) parameters for this component and less parameter interaction; (2) interflow is mainly important for the low flow criteria; (3) excess infiltration process is most influencing when focussing on the lower flows; (4) a more simple routing component is advisable; and (5) baseflow parameters have in general low sensitivity values, except for the low flow criteria.

Hydrological modelling of the Zambezi River Basin taking into account floodplain behaviour by a modified reservoir approach

ABSTRACTFloodplains are regions of great interest for environmental assessment as they constitute important ecological reserves and contribute efficiently to natural flood attenuation. However, the implementation of a model describing the basic hydrological behaviour of floodplains is not an easy task due to the complexity of the processes included. Although several attempts have been made to simulate floodplain effects in global rainfall-runoff models, no satisfactory routines have been developed yet. In this study, an adapted version of the Soil and Water Assessment Tool (2009) reservoir model is proposed and applied to the Zambezi Basin at daily time step with the intention of adequately modelling floodplain behaviour. The model separates the outflow of the reservoir simulating the floodplain into main channel flow and flow over the floodplain area. The improved solution was compared with the original model regarding its potential to simulate observed discharges in terms of volume ratio, the Nash–Sutcliffe coefficient and hydrograph plots. These evaluation criteria attest, for both calibration and validation periods, that the modified model is superior to the original one for simulating the discharge downstream of large floodplains. A sensitivity analysis is carried out at two geographical levels: at the outlet of a floodplain and at the outlet of the entire basin. The results show that upper flow parameters are more sensitive than base flow parameters.

Nonlinear interfacial dynamics in stratified multilayer channel flows

AbstractThe dynamics of viscous immiscible pressure-driven multilayer flows in channels are investigated using a combination of modelling, analysis and numerical computations. More specifically, the particular system of three stratified layers with two internal fluid–fluid interfaces is considered in detail in order to identify the nonlinear mechanisms involved due to multiple fluid surface interactions. The approach adopted is analytical/asymptotic and is valid for interfacial waves that are long compared with the channel height or individual undisturbed liquid layer thicknesses. This leads to a coupled system of fully nonlinear partial differential equations of Benney type that contain a small slenderness parameter that cannot be scaled out of the problem. This system is in turn used to develop a consistent coupled system of weakly nonlinear evolution equations, and it is shown that this is possible only if the underlying base-flow and fluid parameters satisfy certain conditions that enable a synchronous Galilean transformation to be performed at leading order. Two distinct canonical cases (all terms in the equations are of the same order) are identified in the absence and presence of inertia, respectively. The resulting systems incorporate all of the active physical mechanisms at Reynolds numbers that are not large, namely, nonlinearities, inertia-induced instabilities (at non-zero Reynolds number) and surface tension stabilization of sufficiently short waves. The coupled system supports several instabilities that are not found in single long-wave equations including, transitional instabilities due to a change of type of the flux nonlinearity from hyperbolic to elliptic, kinematic instabilities due to the presence of complex eigenvalues in the linearized advection matrix leading to a resonance between the interfaces, and the possibility of long-wave instabilities induced by an interaction between the flux function of the system and the surface tension terms. All of these instabilities are followed into the nonlinear regime by carrying out extensive numerical simulations using spectral methods on periodic domains. It is established that instabilities leading to coherent structures in the form of nonlinear travelling waves are possible even at zero Reynolds number, in contrast to single interface (two-layer) systems; in addition, even in parameter regimes where the flow is linearly stable, the coupling of the flux functions and their hyperbolic–elliptic transitions lead to coherent structures for initial disturbances above a threshold value. When inertia is present an additional short-wave instability enters and the systems become general coupled Kuramoto–Sivashinsky-type equations. Extensive numerical experiments indicate a rich landscape of dynamical behaviour including nonlinear travelling waves, time-periodic travelling states and chaotic dynamics. It is also established that it is possible to regularize the chaotic dynamics into travelling wave pulses by enhancing the inertialess instabilities through the advective terms. Such phenomena may be of importance in mixing, mass and heat-transfer applications.

Modeling of Event and Continuous Flow Hydrographs with HEC–HMS: Case Study in the Kelani River Basin, Sri Lanka

AbstractThis paper describes a case study of event and continuous hydrologic modeling in the Kelani River basin in Sri Lanka using the Hydrologic Engineering Center—Hydrologic Modeling System (HEC–HMS). An extremely high rainfall event in November 2005 was used to calibrate model parameters, and extremely high rainfall events in April–May 2008, May–June 2008, and May 2010 were used to validate the event model. The calibrated, direct runoff and base flow parameters were then used in the continuous hydrologic model. The Green and Ampt infiltration loss method was used to account for infiltration loss in event-based modeling and a five-layer soil moisture accounting loss method was employed in continuous modeling. The Clark unit hydrograph method and the recession base flow method were used to simulate direct runoff and base flow, respectively. The results depict the capability of HEC–HMS to reproduce streamflows in the basin to a high accuracy with averaged computed Nash–Sutcliffe efficiencies of 0.91 for e...

Flood Analysis On The Tailing Dam At Way Linggo, Lampung Province

Abstract : The Soil Conservation Service (SCS) runoff Curve Number (CN) was developed as an index that represents the combination of a hydrologic soil group and a land use and treatment class.Tailling Dam Way Linggo is located in Lampung Province.Due to the absence of an automatic water level recorder in the project site , another recorder in neighbouring catchment that is Banjaragung, catchment, which is the smallest catchment area in the Way Seputih Sekampung River basin, had to be selected.Calibration of model parameters for Banjaragung catchment to validate the CN method for use at the Tailing location. Reconstitution of two Flood Hydrographs for the 1981 and 1982 events are are sufficient for conclusion that parameters are representing actual hydrological conditions for losses composed in Curve Numbers, Baseflow parameters and unit hydrograph of Soil Conservation Service (SCS) parameters (time lag depending on river length) in Tailling Dam Way Linggo, or in other words, the Curve Number can also be applied in the Tailing Dam catchment.

Baseflow control on sediment flux connectivity: Insights from a nested catchment study in Central Mexico

In order to assess the extent of sediment connectivity between uplands and lowlands and to quantify the processes of in-channel deposition and remobilization, measurements of suspended sediment fluxes were conducted in a nested rural catchment of the Mexican Volcanic Belt. Data were collected over one year at three upland sites (3 to 12 km2) and two downstream stations (390-630 km2). Our results show that a structural discontinuity in the catchment (i.e. abrupt slope decrease at the junction between piedmonts and the alluvial plain from 2 to 10% to < 0.1%) could be compensated by functional continuity during floods. Direct conveyance of fine sediment to the outlet occurred when a high stream transport capacity was reached. Erosion of the streambed was observed on various occasions and accounted for up to 50% of the flux leaving the catchment during one event. Conversely, temporary in-channel storage was apparent on other occasions, amounting to up to 52% of the flux recorded upstream during one storm. These two distinct behaviours were approximately equally distributed along the rainy season and strongly driven by the extent of coupling between surface and subsurface water. This work indeed highlights the role of baseflow spatial variations in determining the extent of lowland sediment conveyance. Riverbed erosional processes occurred when large differences in pre-event baseflow values (i.e. at least a twofold longitudinal increase) were observed between the 5-km distant lowland stations. Our findings outline the importance of systematically taking into consideration the baseflow parameter in research focusing on fine sediment transport across scales.

Entry, start up and stability effects in visco-plastically lubricated pipe flows

Interfacial instabilities of multi-layer shear flows may be eliminated by astute positioning of yield stress fluid layers that remain unyielded at the interface(s). We study the initiation, development lengths and temporal stability of such flows in the setting of a Newtonian core fluid surrounded by a Bingham lubricated fluid, within a pipe. Flow initiation is effected by starting the flow with a pipe full of stationary Bingham fluid and injecting both inner and outer fluids simultaneously. Initial instability and dispersive mixing at the front remains localised and is advected from the pipe leaving behind a stable multi-layer configuration, found for moderate Reynolds numbers (Re), for a broad range of interface radii (ri) and for different inlet diameters (Ri), whenever the base flow parameters admit a multi-layer flow with unyielded interface. The established flows have three distinct entry lengths. These relate to: (i) establishment of the first unyielded plug close to the interface (shortest); (ii) establishment of the interface radius; (iii) establishment of the velocity profile (longest). The three entry lengths increase with Re and decrease with both the Bingham number (B) and the viscosity ratio (m). Nonlinear temporal stability to axisymmetric perturbations is studied numerically, considering initial perturbations that are either localised in yielded parts of the flow or that initially break the unyielded plug regions. The aim is to understand structural aspects of the flow stability, not easily extracted from the energy stability results of Moyers-Gonzalez, Frigaard &amp; Nouar (J. Fluid Mech., vol. 506, 2004, p. 117). The initial stages of a stable perturbed flow are characterised by a very rapid decay of the perturbation kinetic energy during which time the unyielded plug reforms (or breaks and reforms). This is followed by slower exponential decay on a viscous timescale (t ~ Re). For smaller Re and moderate initial amplitudes A, the perturbations decay to the numerical tolerance. As either Re or A is increased sufficiently, a number of interesting phenomena arise. The amount of dispersion increases, making the interfacial region increasingly diffuse and limiting the final decay. At larger Re or A, we find secondary flow structures that persist. A first example of these is when the shear stress decays below the yield stress before the velocity perturbation has decayed, leading to freezing in of the interface shape. This can lead to flows with a rigid wavy interface. Secondly, depending on the core fluid radius and thickness of the surrounding plug region, we may observe a range of dispersive structures akin to the pearls and mushrooms of d'Olce et al. (Phys. Fluids, vol. 20, 2008, art. 024104).

Estimating runoff in ungauged catchments from rainfall, PET and the AWBM model

Multiple linear regressions are used to relate average annual runoff to average annual rainfall and areal potential evapotranspiration (PET) using data from 213 catchments grouped according to location in six of the major Drainage Divisions of Australia. A method is presented for estimating daily runoff from daily rainfall data using the AWBM model, which self-calibrates its surface storage parameters to the estimate of average annual runoff from the regressions, and using default values for its baseflow parameters. Two-thirds of the estimates of average annual runoff were within ±25% of the actual value. The approach can also estimate satisfactorily the monthly and annual runoff series in many catchments, with the simulations being only slightly poorer than those obtained by directly calibrating the AWBM against recorded runoff.

Short-wave cooperative instabilities in representative aircraft vortices

This paper considers the short-wave cooperative instabilities in a family of vortices representative of aircraft wakes. These vortices are characterized by two core scales, an internal core scale a1 and an external core scale a2, and their azimuthal velocity follows a power law V(r)∼r−α in the intermediate zone (a1&amp;lt;r&amp;lt;a2). The results are compared to the cases of the Rankine (constant) and Lamb–Oseen (Gaussian) vortices, and to the elliptic instability theory. The unstable wavelengths and the structure of the unstable modes are characterized as functions of the base flow parameters α and a2/a1. For 0.5⩽α⩽1, the wavelength of the instability is of the order of the internal scale a1 and the unstable modes only affect the internal core. In this case the growth rate of the instability is in accordance with the predictions of the elliptical instability theory and is a growing function of the parameter a2/a1. For 0⩽α&amp;lt;0.4, the wavelength of the instability is of the order of the external scale a2 and the unstable modes extend into the intermediate zone. In this case the growth rate of the instability differs from the predictions of the elliptical instability theory and is independent upon the parameter a2/a1. Interestingly, a sharp transition between these two regimes occurs for 0.4&amp;lt;α&amp;lt;0.5, in a range of parameters corresponding to experimentally measured trailing wakes. In this range, the bands of wave numbers affected by the instability are particularly large and may coalesce into a broadband spectrum.

Implementation of the Variational Riemann Problem Solution for Calculating Propagation of Sound Waves in Nonuniform Flow Fields

The variational Riemann problem (VRP) is defined as the first variation of the solution to Riemann's initial-value problem, also known as the problem of breakup of an arbitrary discontinuity in a gas, when the initial data undergo small variations. We show that the solution to the VRP can be analytically obtained, provided that the solution to the baseline Riemann problem is known. This solution describes the interaction of two abutting parcels of small disturbances against the background of a given base flow and therefore can be efficiently implemented in numerical methods for aeroacoustics. When the spatial distribution of disturbances and base flow parameters are given at a time moment at mesh points of a computational grid, one can exactly determine the disturbance evolution for a short lapse of time by solving the VRP at mesh interfaces. This can then be applied to update disturbance values to a new time moment by using the standard finite-volume scheme. In other words, the VRP can be used in computational aeroacoustics in the similar way to the Riemann problem used in Godunov-type methods for computational fluid dynamics. The present paper elaborates on this idea and adopts the solution to the VRP as a building block for a finite-volume Godunov-type method for aeroacoustics.

A SIMPLE METHOD FOR ESTIMATING BASEFLOW AT UNGAGED LOCATIONS1

ABSTRACT: Baseflow, or water that enters a stream from slowly varying sources such as ground water, can be critical to humans and ecosystems. We evaluate a simple method for estimating base‐flow parameters at ungaged sites. The method uses one or more baseflow discharge measurements at the ungaged site and longterm streamflow data from a nearby gaged site. A given baseflow parameter, such as the median, is estimated as the product of the corresponding gage site parameter and the geometric mean of the ratios of the measured baseflow discharges and the concurrent discharges at the gage site. If baseflows at gaged and ungaged sites have a bivariate lognormal distribution with high correlation and nearly equal log variances, the estimated baseflow parameters are very accurate. We tested the proposed method using long‐term streamflow data from two watershed pairs in the Driftless Area of southwestern Wisconsin. For one watershed pair, the theoretical assumptions are well met; for the other the log‐variances are substantially different. In the first case, the method performs well for estimating both annual and long‐term baseflow parameters. In the second, the method performs remarkably well for estimating annual mean and annual median baseflow discharge, but less well for estimating the annual lower decile and the long‐term mean, median, and lower decile. In general, the use of four measurements in a year is not substantially better than the use of two.