The nonlinear phase of wave growth leading to chaos and breakdown to turbulence in a boundary layer as an example of an open system

1990 ◽  
Vol 430 (1878) ◽  
pp. 3-24 ◽  
Keyword(s):  
Boundary Layer ◽  
Time Series ◽  
Differential Equations ◽  
Mathematical Models ◽  
Flow Regime ◽  
Open System ◽  
Broadband Noise ◽  
Periodic Component ◽  
Velocity Fluctuations ◽  
Nonlinear Phase

The spatial development of boundary-layer instabilities has been investigated experimentally in a flow régime where nonlinearities are important. Detailed measurements of the evolution of a regular periodic wavetrain into an irregular or chaotic one are reported. It was found that the broadband noise content of the motion grew very rapidly downstream when the amplitude of the periodic component was sufficiently large. The almost explosive growth of the broadband element provided velocity fluctuations with chaotic time series similar to those generated by mathematical models based on low-order differential equations.

Prediction of Atmospheric Turbulence Characteristics for Surface Boundary Layer using Empirical Spectral Methods

2020 ◽  
Author(s):  
Yagya Dutta Dwivedi ◽  
Vasishta Bhargava Nukala ◽  
Satya Prasad Maddula ◽  
Kiran Nair
Keyword(s):  
Boundary Layer ◽  
Time Series ◽  
Surface Roughness ◽  
Wind Speed ◽  
Atmospheric Turbulence ◽  
Surface Boundary ◽  
Low Frequencies ◽  
Surface Boundary Layer ◽  
Power Spectral ◽  
Mean Wind Speed

Abstract Atmospheric turbulence is an unsteady phenomenon found in nature and plays significance role in predicting natural events and life prediction of structures. In this work, turbulence in surface boundary layer has been studied through empirical methods. Computer simulation of Von Karman, Kaimal methods were evaluated for different surface roughness and for low (1%), medium (10%) and high (50%) turbulence intensities. Instantaneous values of one minute time series for longitudinal turbulent wind at mean wind speed of 12 m/s using both spectra showed strong correlation in validation trends. Influence of integral length scales on turbulence kinetic energy production at different heights is illustrated. Time series for mean wind speed of 12 m/s with surface roughness value of 0.05 m have shown that variance for longitudinal, lateral and vertical velocity components were different and found to be anisotropic. Wind speed power spectral density from Davenport and Simiu profiles have also been calculated at surface roughness of 0.05 m and compared with k−1 and k−3 slopes for Kolmogorov k−5/3 law in inertial sub-range and k−7 in viscous dissipation range. At high frequencies, logarithmic slope of Kolmogorov −5/3rd law agreed well with Davenport, Harris, Simiu and Solari spectra than at low frequencies.

Removal of trichloroethylene and trichloroethane using a novel hollow-fibre gas-permeable membrane

2003 ◽  
Vol 3 (5-6) ◽  
pp. 67-72
Author(s):  
S. Takizawa ◽  
T. Win
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Removal Efficiency ◽  
Residence Time ◽  
Flow Rate ◽  
Air Flow ◽  
Hollow Fibre ◽  
Permeation Rate ◽  
Permeable Membrane ◽  
Diffusional Boundary Layer

In order to evaluate effects of operational parameters on the removal efficiency of trichloroethylene and 1,1,1-trichloroethene from water, lab-scale experiments were conducted using a novel hollow-fibre gaspermeable membrane system, which has a very thin gas-permeable membrane held between microporous support membranes. The permeation rate of chlorinated hydrocarbons increased at higher temperature and water flow rate. On the other hand, the effects of the operational conditions in the permeate side were complex. When the permeate side was kept at low pressure without sweeping air (pervaporation), the removal efficiency of chlorinated hydrocarbon, as well as water permeation rate, was low probably due to lower level of membrane swelling on the permeate side. But when a very small amount of air was swept on the membrane (air perstripping) under a low pressure, it showed a higher efficiency than in any other conditions. Three factors affecting the permeation rate are: 1) reduction of diffusional boundary layer within the microporous support membrane, 2) air/vapour flow regime and short cutting, and 3) the extent of membrane swelling on the permeate side. A higher air flow, in general, reduces the diffusional boundary layer, but at the same time disrupts the flow regime, causes short cutting, and makes the membrane dryer. Due to these multiple effects on gas permeation, there is an optimum operational condition concerning the vacuum pressure and the air flow rate. Under the optimum operational condition, the residence time within the hollow-fibre membrane to achieve 99% removal of TCE was 5.25 minutes. The log (removal rate) was linearly correlated with the average hydraulic residence time within the membrane, and 1 mg/L of TCE can be reduced to 1 μg/L (99.9% removal).

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

scholarly journals Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Variable Thickness ◽  
Heat Mass Transfer ◽  
Mathematical Formulation ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

Study of Thermal Activity in The Mixing Layer During First Generated Single Cloud by Using Combined Observation From Boundary Layer Radar, Doppler Lidar and Time Lapse Camera 

2021 ◽  
Author(s):  
Ginaldi Ari Nugroho ◽  
Kosei Yamaguchi ◽  
Eiichi Nakakita ◽  
Masayuki K. Yamamoto ◽  
Seiji Kawamura ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Time Series ◽  
Atmospheric Boundary Layer ◽  
Vertical Velocity ◽  
Time Lapse ◽  
Small Scale ◽  
Thermal Activity ◽  
Doppler Lidar ◽  
Cumulus Cloud ◽  
Scale Perturbation

<p>Detailed observation of small scale perturbation in the atmospheric boundary layer during the first generated cumulus cloud are conducted. Our target is to study this small scale perturbation, especially related to the thermal activity at the first generated cumulus cloud. The observation is performed during the daytime on August 17, 2018, and September 03, 2018. Location is focused in the urban area of Kobe, Japan. High-resolution instruments such as Boundary Layer Radar, Doppler Lidar, and Time Lapse camera are used in this observation. Boundary Layer Radar, and Doppler Lidar are used for clear air observation. Meanwhile Time Lapse Camera are used for cloud existence observation. The atmospheric boundary layer structure is analyzed based on vertical velocity profile, variance, skewness, and estimated atmospheric boundary layer height. Wavelet are used to observe more of the period of the thermal activity. Furthermore, time correlation between vertical velocity time series from height 0.3 to 2 km and image pixel of generated cloud time series are also discussed in this study.</p>

Dual similarity solutions because of mixed convective flow of a double-nanoparticles hybrid nanofluid: critical points and stability analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ioan Pop ◽  
Mohammadreza Nademi Rostami ◽  
Saeed Dinarvand
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Flow Regime ◽  
Magnetic Parameter ◽  
Volume Fraction ◽  
Similarity Solutions ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Buoyancy Parameter ◽  
Mixed Convective Flow

Purpose The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical nanoparticles over a vertical permeable plate with focus on dual similarity solutions. Design/methodology/approach The single-phase hybrid nanofluid modeling is based on nanoparticles and base fluid masses instead of volume fraction of first and second nanoparticles as inputs. After substituting pertinent similarity variables into the basic partial differential equations governing on the problem, the authors obtain a complicated system of nondimensional ordinary differential equations, which has non-unique solution in a certain range of the buoyancy parameter. It is worth mentioning that, the stability analysis of the solutions is also presented and it is shown that always the first solutions are stable and physically realizable. Findings It is proved that the magnetic parameter and the wall permeability parameter widen the range of the buoyancy parameter for which the solution exists; however, the opposite trend is valid for second nanoparticle mass. Besides, mass suction at the surface of the plate as well as magnetic parameter leads to reduce both hydrodynamic and thermal boundary layer thicknesses. Moreover, the assisting flow regime always has higher values of similarity skin friction and Nusselt number relative to opposing flow regime. Originality/value A novel mass-based model of the hybridity in nanofluids has been used to study the foregoing problem with focus on dual similarity solutions. The results of this paper are completely original and, to the best of the authors’ knowledge, the numerical results of the present paper were never published by any researcher.

Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow

2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat Generation ◽  
Axisymmetric Flow ◽  
Convective Transport ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

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