Temporal Stability Analysis Research Articles

Field-Scale Spatial and Temporal Soil Water Variability in Irrigated Croplands

HighlightsThe greatest heterogeneity in soil water was observed at 30-60 cm depth in a corn field and 0-15 cm in a cotton field.Spatiotemporal soil water variability did not increase with increasing soil water in all soil layers in both croplands during the growing season.Water excess and water stress locations were identified in both fields. A single, temporally stable location was identified in each field, which can be used for precise uniform irrigation.Knowledge of variability and stability in soil water can be useful in determining the number and location of sensors to install in crop fields to assist irrigation scheduling decisions.Abstract. This study investigated the spatiotemporal variability and temporal stability of soil water at various depths in two croplands sown in corn and cotton during the 2018 growing season in the Tennessee Valley Region (TVR) of northern Alabama. Classical statistics and relative difference approaches were used to analyze soil water data in this study. In the corn field, the 30-60 cm depth showed the greatest variability, while the cotton field showed the greatest variability at 0-15 cm depth. A decreasing trend was noticed between mean soil water and coefficient of variation for all depths in the cotton field and at 30-60 cm depth in the corn field. However, convex upward, exponential decreasing, or no trends were found between mean soil water and standard deviation at different depths in both fields. The temporal stability analysis showed one representative sensor (S8 in corn and S1 in cotton) for the entire soil profile in both fields. Different statistical tests, i.e., Spearman’s correlation (rs), Nash-Sutcliffe efficiency (NSE), coefficient of determination (R2), etc., were used to reduce uncertainty or increase confidence in the performance of representative sensors. Among various field attributes, topography in corn and soil properties in cotton were determined as significant factors responsible for soil water variability. Crop evapotranspiration (ETc) showed significant negative weak and moderate correlations with soil water in the corn and cotton fields, respectively. However, the mean air temperature showed a significant positive correlation with soil water in the corn field and a significant negative correlation in the cotton field. Solar radiation had a significant negative correlation with soil water in the cotton field and a non-significant correlation in the corn field. Accumulated growing degree days (accGDD) showed a significant negative correlation with soil water in the corn field and a positive correlation in the cotton field. This study gives insights into soil water variability, provides useful information about temporal stability, and identifies significant factors for precision uniform irrigation scheduling. Keywords: Corn, Cotton, Croplands, Growing season, Irrigation, Soil water, Spatial and temporal variability, Temporal stability.

Unsteady hybrid nanofluid flow on a stagnation point of a permeable rigid surface

AbstractThis study investigates the unsteady flow of Al2O3‐Cu/water hybrid nanofluid on a stagnation point of a permeable rigid surface. The similarity equations are obtained using similarity variables and then solved using the bvp4c solver. The outcomes show that dual solutions exist for the negative unsteadiness and some mass flux parameters. Besides, the heat transfer rate is intensified with the hybrid nanoparticles. Moreover, the increasing of the mass flux parameter tends to increase the heat transfer rate and the skin friction on the surface. Also, the reduction of the skin friction coefficient is observed, and a higher heat transfer rate is achieved for smaller values of the unsteadiness parameter. Finally, by a temporal stability analysis, it is found that the first solution is stable and reliable as time evolves.

Temporal Stability Analysis of Magnetized Hybrid Nanofluid Propagating Through an Unsteady Shrinking Sheet: Partial Slip Conditions

Temporal Stability Analysis of Magnetized Hybrid Nanofluid Propagating Through an Unsteady Shrinking Sheet: Partial Slip Conditions

Stagnation-point flow of Ag-CuO/water hybrid nanofluids over a permeable stretching/shrinking sheet with temporal stability analysis

Present work has been studied the stagnation-point flow of hybrid Ag-CuO/water nanofluids over the stretching/shrinking sheet. The Navier-Stokes equations have reduced to the ordinary differential equations with similarity transformation. Runge-Kutta Fehlberg (RKF45), together with the shooting method, is employed to solve the differential equations. Numerical analysis showed that dual solutions exist and are connected to the specific values of the shrinking rate. All figures have the same behavior with the suction/injection parameter. Furthermore, with the intensification of the suction/injection parameter, the graphs are contracted, and the lower solutions become extended. The friction factor of Ag/water and hybrid nanofluids is increased by about 50–70% and 35–50% with suction/injection parameter, respectively. Normalized Nusselt number for Ag/water and hybrid nanofluids are increase by about 150–200% and 100% with suction/injection parameter, respectively. Time-dependent stability analysis showed that only the upper branch of solutions is stable, while the lower branch is not in actual physics.

Dynamics of shear-layer coherent structures in a forced wall-bounded flow

Abstract

Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

Dual solutions of a magnetohydrodynamic stagnation point flow of a non-Newtonian fluid over a shrinking sheet and a linear temporal stability analysis

The present study accentuates the magnetohydrodynamic and suction/injection effects on the two-dimensional stagnation point flow and heat transfer of a non-Newtonian fluid over a shrinking sheet. The set of Navier-Stokes equations are converted into a system of highly non-linear ordinary differential equations by employing suitable similarity variables. The obtained self-similar equations are then solved numerically with the aid of shooting technique. The similarity equations exhibit dual solutions over a certain range of the shrinking strength. It is observed that the solution domain increases as the suction/injection parameter, the non-Newtonian parameter and the magnetic parameter increase. Moreover, it is further noticed that these two solution branches show opposite behavior on the velocity and temperature profiles for the combined effects of the several flow parameters. Emphasis has been given to determine the most feasible and physically stable solution branch. Thus a linear temporal stability analysis has been carried out and the stability of the these two branches are tested by the sign of the smallest eigenvalue. The smallest eigenvalues are found numerically which suggest that the upper solution branch is stable and the flow dynamics can be describe by the behavior of the upper solution branch.

Hybrid nanofluid flow on a shrinking cylinder with prescribed surface heat flux

PurposeThis study aims to investigate the flow impinging on a stagnation point of a shrinking cylinder subjected to prescribed surface heat flux in Al2O3-Cu/water hybrid nanofluid.Design/methodology/approachUsing similarity variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed.FindingsThe outcomes show that dual solutions are possible for the shrinking case, in the range , where is the bifurcation point of the solutions. Meanwhile, the solution is unique for . Besides, the boundary layer is detached on the surface at , where the value of is affected by the hybrid nanoparticle and the curvature parameter . Moreover, the friction and the heat transfer on the surface increase with the rising values and . Finally, the temporal stability analysis shows that the first solution is stable in the long run, whereas the second solution is not.Originality/valueThe present work considers the problem of stagnation point flow impinging on a shrinking cylinder containing Al2O3-Cu/water hybrid nanofluid, with prescribed surface heat flux. This paper shows that two solutions are obtained for the shrinking case. Further analysis shows that only one of the solutions is stable as time evolves.

Melting heat transfer of a hybrid nanofluid flow towards a stagnation point region with second-order slip

This paper examines the behaviour of a hybrid nanofluid flow towards a stagnation point on a stretching or shrinking surface with second-order slip and melting heat transfer effects. Copper (Cu) and alumina (Al2O3) are considered as the hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in MATLAB software through the bvp4c solver to obtain the numerical solutions. The results reveal that two solutions are possible for the shrinking case [Formula: see text], where the bifurcation of the solutions occurs in this region. Moreover, the heat transfer rate and the skin friction coefficient enhance with the rise of the melting parameter. Meanwhile, these quantities decrease for a smaller second-order slip parameter. The temporal stability analysis shows that only one of the two solutions is stable as time evolves.

On dual solutions of the unsteady MHD flow on a stretchable rotating disk with heat transfer and a linear temporal stability analysis

The present paper is an extension of the work done by Fang and Tao (2012) in the presence of a magnetic field. The external magnetic field is applied normal to a stretchable disk surface and heat is transferred from the disk surface to the ambient fluid which gives a new family of unsteady viscous flow over a stretchable rotating disk with deceleration. The Navier–Stokes equations and the energy equation admit similarity solutions depending on unsteadiness parameter. The resulting set of highly nonlinear ordinary differential equations are solved numerically. Two solution branches are found due to the effect of unsteadiness parameter for several values of magnetic parameter and stretching parameter. The effects of pertinent flow parameters on the shear stresses on radial and tangential directions, Nusselt numbers, torque, dimensionless velocity and temperature profiles are shown graphically for both the solution branches and their physical interpretation are discussed in detail. Emphasis has been laid to check the stability of dual solution branches. The stability is tested by the sign of the smallest eigenvalue, and our analysis reveals that the lower solution branches are unstable.

Stability of laminar flames on upper and lower inclined fuel surfaces

Experiments have found substantial morphological differences between buoyancy-driven flames developing on the upper and lower surfaces of inclined burning plates. These differences cannot be explained on the basis of existing analytical solutions of steady semi-infinite flames, which provide identical descriptions for the top and bottom configurations. To investigate the potential role of flame instabilities in the experimentally observed flow differences, a temporal linear stability analysis is performed here. The problem is formulated in the limit of infinitely fast reaction, taking into account the non-unity Lewis number of the fuel vapor. The stability analysis incorporates non-parallel effects of the base flow and considers separately spanwise traveling waves and Görtler-like streamwise vortices. The solution to the stability eigenvalue problem determines the downstream location at which the flow becomes unstable, characterized by a critical value of the relevant Grashof number, whose value varies with the plate inclination angle. The results for the flame formed on the underside of the fuel surface indicate that instabilities emerge farther downstream than they do for a flame developing over the top of the fuel surface, in agreement with experimental observations. Increased buoyancy-induced vorticity production is reasoned to be responsible for the augmented instability tendency of topside flames.

Stability of surfactant-laden liquid film flow over a cylindrical rod

The stability of surfactant-laden liquid film flow over a cylindrical rod is examined in creeping flow limit using standard temporal linear stability analysis. The clean film flow configuration (i.e., in absence of surfactant) is well-known to become unstable owing to Rayleigh-Plateau instability of cylindrical liquid interfaces. Previous studies demonstrated that for a static liquid film (i.e., zero basic flow) coating a rod, the presence of interfacial surfactant decrease the growth of Rayleigh-Plateau instability, but is unable to suppress it completely. Further, the presence of interfacial surfactant is known to introduce an additional mode, referred to as surfactant mode in the present work. To the best of our knowledge, the stability of surfactant mode has not been analyzed in the context of cylindrical film flows. Thus, we reexamined the stability of surfactant-laden cylindrical liquid film flow to analyze the stability behavior of the above said two modes when the basic flow is turned on. The present study reveals that the incorporation of basic flow in stability analysis leads to the complete suppression of Rayleigh-Plateau instability due to the presence of interfacial surfactants as compared to the partial suppression obtained for a stationary liquid film. Three nondimensional parameters appear for this problem: Bond number (denoted as Bo) which characterizes the strength of basic flow, Marangoni number (denoted as Ma) which signifies the presence of surfactant, and ratio of rod radius to film thickness denoted as S. In creeping flow limit, the characteristic equation is quadratic with one root belonging to Rayleigh-Plateau mode and the other to surfactant mode. We first carried out an asymptotic analysis to independently capture the eigenvalues corresponding to both the modes in limit of long-wave disturbances. The long-wave results show that the Rayleigh-Plateau instability is completely suppressed on increasing the Marangoni number above a critical value while the surfactant mode always remains stable in low wave-number limit. The continuation of long-wave results to arbitrary wavelength disturbances show that the suppression of Rayleigh-Plateau instability mode still holds, however, the surfactant mode becomes unstable at sufficiently high values of Marangoni number. Further, this surfactant mode instability shifts toward low wave numbers with critical Marangoni number for instability scaling with wave number in a particular fashion. We used this scaling and carried out an asymptotic analysis to capture this instability in low wave-number limit. Depending on S and Bo, we observed the existence of a stable gap in terms of Ma where both the eigen-modes remain stable. Our results indicate that for a given Bond number, the width of stable gap in terms of Ma decreases with decrease in S and the stable gap vanishes when S is sufficiently small. The effect of increasing Bond number (or equivalently, the strength of basic flow) is found to be stabilizing for the film flow configuration.

Radiative hybrid nanofluid flow past a rotating permeable stretching/shrinking sheet

Purpose This paper aims to discuss a stability analysis on Cu-Al2O3/water nanofluid having a radiation and suction impacts over a rotating stretching/shrinking sheet. Design/methodology/approach The partial differential equations are converted into nonlinear ordinary differential equations using similarity transformation and then being solved numerically using built in function in Matlab software (bvp4c). The effects of pertinent parameters on the temperature and velocity profiles together with local Nusselt number and skin friction are reported. Findings Compared to previously published studies, the current work is noticed to be in good deal. The analysis further shows that the non-unique solutions exist for certain shrinking parameter values. Hence, a stability analysis is executed using a linear temporal stability analysis and concluded that the second solution is unstable, while the first solution is stable. The effect of suction parameter is observed to be significant in obtaining the solutions. The improvement of the local skin friction and the decrease of the local Nusselt number on the shrinking surface are observed with the increment of the copper nanoparticle volume fractions. Originality/value The originality of current work is the numerical solutions and stability analysis of hybrid nanofluid in rotating flow. This work has also resulted in producing the non-unique solutions for the shrinking sheet, and a stability analysis has also been executed for this flow showing that the second solution is unstable, while the first solution is stable. This paper is therefore valuable for engineers and scientist to get acquainted with the properties of the flow, its behavior and the way to predict it. The authors admit that all the findings are original and were not published anywhere else.

Dual solutions of magnetohydrodynamic boundary layer flow and a linear temporal stability analysis

In this paper, we have considered the two-dimensional stagnation point flow and heat transfer of an electrically conducting viscous fluid over an exponentially stretching sheet. The Navier-Stokes equations are reduced into a system of highly non-linear ordinary differential equations by similarity transformations. The resulting systems are then solved numerically by shooting method. The effects of suction/injection parameters on the boundary layer are discussed in detail. Our numerical results reveal that for a particular range of the velocity ratio parameter, dual solutions exist. Interestingly these two solution branches show opposite characters in the velocity and temperature profiles. Thus, it is worthwhile to carry a stability analysis of these two solutions to determine the feasible solution. A linear temporal stability analysis has been carried out, and the stability is tested by the sign of the smallest eigenvalue. The smallest eigenvalues are found by two different numerical schemes, which agree well up to the desired accuracy. The effects of the pertinent flow parameters in the velocity and temperature profiles are discussed in detail and are shown graphically.

Squeezed Hybrid Nanofluid Flow Over a Permeable Sensor Surface

This paper examines the squeezed hybrid nanofluid flow over a permeable sensor surface with magnetohydrodynamics (MHD) and radiation effects. The alumina (Al2O3) and copper (Cu) are considered as the hybrid nanoparticles, while water is the base fluid. The governing equations are reduced to the similarity equations, using the similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain the numerical solutions. It was found that the heat transfer rate was greater for the hybrid nanofluid, compared to the regular nanofluid. It was observed that dual solutions exist for some values of the permeable parameter S. The upper branch solutions of the skin friction coefficient ( Re x 1 / 2 C f ) and the heat transfer rate at the surface ( Re x − 1 / 2 N u x ) enhance with the added Cu nanoparticle ( φ 2 ) and for larger magnetic strength ( M ). Moreover, the values of Re x 1 / 2 C f decrease, whereas the values of Re x − 1 / 2 N u x increase for both branches, with the rise of the squeeze flow index ( b ). Besides, an increment of the heat transfer rate at the sensor surface for both branches was observed in the presence of radiation ( R ). Temporal stability analysis was employed to determine the stability of the dual solutions, and it was discovered that only one of them was stable and physically reliable as time evolves.

Validation of the Achievement Emotions Questionnaire for Physical Education (AEQ-PE).

The fundamental role of emotions in education has been revealed in recent years. The control-value theory of achievement emotions has been postulated as one of the most used theories in this field. Thanks to the Achievement Emotions Questionnaire (AEQ), achievement emotions have been measured in different subjects and countries. The purpose of this research was to adapt and validate this questionnaire to assess achievement emotions in physical education. The sample of participants consisted of 902 (Mage = 13.15, SD = 1.17) secondary education students from various secondary schools in Spain. The psychometric properties of the Achievement Emotions Questionnaire for Physical Education (AEQ-PE) indicate that the scales are reliable and valid, as demonstrated by exploratory and confirmatory factor analysis, temporal stability, internal consistency and regression analysis. Considering the results achieved in the present study, the AEQ-PE opens a range of possibilities for both teachers and researchers. This instrument will help to understand the role of emotions in student learning and their motivation towards physical education.

Stability Analysis of MHD Fluid Flow over a Moving Plate with Pressure Gradient Using the Chebyshev Spectral Method

The purpose of this paper is to investigate the magnetohydrodynamic stability external flow of a viscous, incompressible and electrically conducting fluid over a moving flat plate using temporal linear stability analysis. Using a similarity variables based on the Skan-Falkner transformation, the governing differential equations of mean flow are transformed into a nonlinear ordinary differential equation, which is then solved numerically by the Runge-Kutta method. The MHD stability equation is solved numerically by using the Chebyshev spectral collocation method, which is based on the eigenfunction expansion in terms of Chebyshev polynomials, collocation points, and the subsequent solution of the resulting generalized eigenvalue problem with the QZ algorithm. The influence of the pressure gradient, magnetic field and wall velocity on the dimensionless mean velocity are presented graphically and discussed. For the disturbance flow in the presence of magnetic field and moving wall, the critical Reynolds number increases with increasing the magnetic field parameter and wall velocity, indicating that these parameters stabilize the flow.

Non-modal stability analysis in viscous fluid flows with slippery walls

A study of optimal temporal and spatial disturbance growths is carried out for three-dimensional viscous incompressible fluid flows with slippery walls. The non-modal temporal stability analysis is performed under the framework of normal velocity and normal vorticity formulations. A Chebyshev spectral collocation method is used to solve the governing equations numerically. For a free surface flow over a slippery inclined plane, the maximum temporal energy amplification intensifies with the effect of wall slip for the spanwise perturbation, but it attenuates with the wall slip when perturbation considers both streamwise and spanwise wavenumbers. It is found that the boundary for the regime of transient growth appears far ahead of the boundary for the regime of exponential growth, which raises a question on the critical Reynolds number for the shear mode predicted from the eigenvalue analysis. Furthermore, the eigenvalue analysis or the modal stability analysis reveals that the unstable region for the shear mode decays rapidly in the presence of wall slip, which is followed by the successive amplification of the critical Reynolds number for the shear mode and ensures the stabilizing effect of slip length on the shear mode. On the other hand, for a channel flow with slippery bounding walls, the maximum spatial energy amplification intensifies with the effect of wall slip in the absence of angular frequency, but it reduces with the wall slip if the angular frequency is present in the disturbance. Furthermore, the maximum spatial energy disturbance growth can be achieved if the disturbance excludes the angular frequency. Furthermore, it is observed that the angular frequency plays an essential role in the pattern formation of optimal response. In addition, the pseudo-resonance phenomenon occurs due to external temporal and spatially harmonic forcings, where the pseudo-resonance peak is much higher than the resonance peak.

Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid

The mixed convection flow and heat transfer over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid is considered in this paper. Copper (Cu) and alumina (Al2O3) are employed as the hybrid nanoparticles while water as the base fluid. It is shown that the heat transfer rate enhances in the presence of nanoparticles. However, the reduction in heat transfer rate is observed for the shrinking case, caused by the imposition of stronger suction at the boundary. It is also found that the bifurcation of the solutions occurs for both stretching and shrinking regions as well as for both buoyancy aiding and opposing flows. The temporal stability analysis shows that only one of the solutions is stable and thus physically reliable as time evolves.

Flow and heat transfer of a hybrid nanofluid past a permeable moving surface

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al2O3) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al2O3/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.