scholarly journals Cooling and instabilities in colliding flows

2021 ◽  
Author(s):  
R N Markwick ◽  
A Frank ◽  
J Carroll-Nellenback ◽  
B Liu ◽  
E G Blackman ◽  
...  
Keyword(s):  
Thermal Instability ◽  
Three Dimensional ◽  
Oscillation Period ◽  
Three Dimensions ◽  
Temperature Dependent ◽  
Radiative Shock ◽  
Hydrodynamic Simulations ◽  
Protostellar Jets ◽  
The One ◽  
Cooling Function

Abstract Collisional self-interactions occurring in protostellar jets give rise to strong shocks, the structure of which can be affected by radiative cooling within the flow. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in both one and three dimensions with a power law cooling function. The characteristic length and time scales for cooling are temperature dependent and thus may vary as shocked gas cools. When the cooling length decreases sufficiently rapidly the system becomes unstable to the radiative shock instability, which produces oscillations in the position of the shock front; these oscillations can be seen in both the one and three dimensional cases. Our simulations show no evidence of the density clumping characteristic of a thermal instability, even when the cooling function meets the expected criteria. In the three-dimensional case, the nonlinear thin shell instability (NTSI) is found to dominate when the cooling length is sufficiently small. When the flows are subjected to the radiative shock instability, oscillations in the size of the cooling region allow NTSI to occur at larger cooling lengths, though larger cooling lengths delay the onset of NTSI by increasing the oscillation period.

scholarly journals Numerical simulation of Faraday waves

2009 ◽  
Vol 635 ◽  
pp. 1-26 ◽  
Author(s):  
NICOLAS PÉRINET ◽  
DAMIR JURIC ◽  
LAURETTE S. TUCKERMAN
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Oscillation Period ◽  
Finite Amplitude ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Faraday Waves ◽  
Temporal Behaviour ◽  
Two Fluids ◽  
Front Tracking Method

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier–Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, p. 49). The finite-amplitude results are compared with the experiments of Kityk et al (Phys. Rev. E, vol. 72, 2005, p. 036209). In particular, we reproduce the detailed spatio-temporal spectrum of both square and hexagonal patterns within experimental uncertainty. We present the first calculations of a three-dimensional velocity field arising from the Faraday instability for a hexagonal pattern as it varies over its oscillation period.

scholarly journals A Three-Dimensional Polar Ice-Sheet Model

1977 ◽  
Vol 18 (80) ◽  
pp. 373-389 ◽  
Author(s):  
D. Jenssen
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Phase Changes ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Polar Ice ◽  
Three Dimensional Model ◽  
Temperature Dependent ◽  
Mass Depletion

AbstractA three-dimensional model of the temperature and velocity distribution within any arbitrary-shaped ice mass is described. There is a mutual interaction in the model between the flow of the ice and its thermodynamics, since the flow law used in the model is temperature-dependent.Ice growth in three dimensions is governed by mass accumulation through precipitation, by mass depletion through loss of ice over the ocean, and by continuity requirements. Phase changes at the base of the ice are accounted for. The model has been applied in art exploratory manner to the Greenland ice sheet. Changes in the ice shape and temperature are presented and discussed. The basic shortcoming of the model as here presented appears primarily due to the coarse finite-difference mesh used, and to an unsophisticated approach to modelling the boundary ice.

On the Recovery of 3D Spatial Statistics of Particles from 1D Measurements: Implications for Airborne Instruments

2014 ◽  
Vol 31 (10) ◽  
pp. 2078-2087 ◽  
Author(s):  
Michael L. Larsen ◽  
Clarissa A. Briner ◽  
Philip Boehner
Keyword(s):  
Point Processes ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
Cloud Droplets ◽  
Sampling Variability ◽  
One Dimensional ◽  
Natural Sampling ◽  
The One

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

Three-dimensional effects in low-strain integrity testing of piles: analytical solution

2016 ◽  
Vol 53 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Changjie Zheng ◽  
George P. Kouretzis ◽  
Xuanming Ding ◽  
Hanlong Liu ◽  
Harry G. Poulos
Keyword(s):  
Impact Load ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Integrity Testing ◽  
Integrity Tests ◽  
The One ◽  
Propagation Of Waves ◽  
The Impact ◽  
Pile Integrity ◽  
Elastic Soil

The interpretation of low-strain integrity tests of piles is commonly based on methods developed around the one-dimensional wave propagation theory. In reality, waves resulting from the impact of a hammer on a pile head propagate in three dimensions, and the validity of the plane-front assumption is rather questionable for cases where the size of the hammer is small relative to that of the pile. This paper presents an analytical model of the dynamic response of a pile to an impact load on its head, considering propagation of waves in both vertical and radial directions. The proposed formulation applies to a pile of finite length embedded in multilayered elastic soil, and allows for considering both shape and material pile defects, by reducing locally the radius of the pile cross section or the Young’s modulus of its material. Arithmetic examples are used to depict the effect of high-frequency interferences on the interpretation of pile integrity tests, which can only be accounted for in the three-dimensional formulation of the problem, and lead to practical suggestions for the interpretation of such tests.

Diffraction of Electrons by Two and Three Mutually Orthogonal Standing Light Waves

1975 ◽  
Vol 53 (2) ◽  
pp. 157-164 ◽  
Author(s):  
F. Ehlotzky
Keyword(s):  
Electron Scattering ◽  
Light Wave ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Standing Light Wave ◽  
Light Waves ◽  
The One ◽  
Rectangular Lattices

The one-dimensional problem of electron scattering by a standing light wave, known as the Kapitza–Dirac effect, is shown to be easily extendable to two and three dimensions, thus showing all characteristics of diffraction of electrons by simple two- and three-dimensional rectangular lattices.

scholarly journals A Three-Dimensional Polar Ice-Sheet Model

1977 ◽  
Vol 18 (80) ◽  
pp. 373-389 ◽  
Author(s):  
D. Jenssen
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Phase Changes ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Polar Ice ◽  
Three Dimensional Model ◽  
Temperature Dependent ◽  
Mass Depletion

Abstract A three-dimensional model of the temperature and velocity distribution within any arbitrary-shaped ice mass is described. There is a mutual interaction in the model between the flow of the ice and its thermodynamics, since the flow law used in the model is temperature-dependent. Ice growth in three dimensions is governed by mass accumulation through precipitation, by mass depletion through loss of ice over the ocean, and by continuity requirements. Phase changes at the base of the ice are accounted for. The model has been applied in art exploratory manner to the Greenland ice sheet. Changes in the ice shape and temperature are presented and discussed. The basic shortcoming of the model as here presented appears primarily due to the coarse finite-difference mesh used, and to an unsophisticated approach to modelling the boundary ice.

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

On the Interpretation of Vowel “Quality”: The Dimension of Rounding

1989 ◽  
Vol 19 (1) ◽  
pp. 24-30 ◽  
Author(s):  
Leigh Lisker
Keyword(s):  
Vocal Tract ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Vowel Space ◽  
Tongue Position ◽  
Two Measures ◽  
The One ◽  
Jaw Position ◽  
Three Dimensional Space

The usual description of vowels in respect to their “phonetic quality” requires the linguist to locate them within a so-called “vowel space,” apparently articulatory in nature, and having three dimensions labeled high-low (or close-open), front-back, and unrounded-rounded. The first two are coordinates of tongue with associated jaw position, while the third specifies the posture of the lips. It is recognized that vowels can vary qualitatively in ways that this three-dimensional space does not account for. So, for example, vowels may differ in degree of nasalization, and they may be rhotacized or r-colored. Moreover, it is recognized that while this vowel space serves important functions within the community of linguists, both the two measures of tongue position and the one for the lips inadequately identify those aspects of vocal tract shapes that are primarily responsible for the distinctive phonetic qualities of vowels (Ladefoged 1971). With all this said, it remains true enough that almost any vowel pair of different qualities can be described as occupying different positions with the space. Someone hearing two vowels in sequence and detecting a quality difference will presumably also be able to diagnose the nature of the articulatory shift executed in going from one vowel to the other.

The mechanical effects of deposition patterns in welding-based layered manufacturing

2007 ◽  
Vol 221 (10) ◽  
pp. 1499-1509 ◽  
Author(s):  
M P Mughal ◽  
R A Mufti ◽  
H Fawad
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Layered Manufacturing ◽  
Source Material ◽  
Structural Effects ◽  
Temperature Dependent ◽  
Deposition Patterns ◽  
Finite Element Software ◽  
The One

This paper presents a finite element (FE)-based three-dimensional analysis to study the structural effects of deposition patterns in welding-based layered manufacturing (LM). A commercial finite element software ANSYS is used to simulate the deposition incorporating a double ellipsoidal heat source, material addition, and temperature-dependent material properties. Simulations carried out with various deposition sequences revealed that the thermal and structural effects on the workpiece are different for different patterns. The sequence starting from outside and ending at the centre is identified as the one which produces minimum warpage.

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