scholarly journals Visualization of three-dimensional incompressible flows by quasi-two-dimensional divergence-free projections

2014 ◽  
Vol 97 ◽  
pp. 143-155 ◽  
Author(s):  
Alexander Yu. Gelfgat
Keyword(s):  
Incompressible Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Divergence Free

scholarly journals Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking

2013 ◽  
Vol 45 (3) ◽  
pp. 1871-1885 ◽  
Author(s):  
C. Bardos ◽  
M. C. Lopes Filho ◽  
Dongjuan Niu ◽  
H. J. Nussenzveig Lopes ◽  
E. S. Titi
Keyword(s):  
Symmetry Breaking ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Viscous Incompressible Flows

scholarly journals Stratified Kelvin-Helmholtz turbulence of compressible shear flows

2018 ◽  
Author(s):  
Romit Maulik ◽  
Omer San
Keyword(s):  
Power Density ◽  
Spatial Resolution ◽  
Shear Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Structure Functions ◽  
Compressible Turbulence ◽  
Power Density Spectrum ◽  
Two Dimensional ◽  
Density Spectrum

Abstract. We study the scaling laws and structure functions of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin-Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16,3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k−5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k−5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum flattens to k−1/4. This flattening may be assumed to be a reason for the k−7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of second and third order velocity structure functions where it is noticed that scaling behavior differs between the two- and three-dimensional cases wherein only the latter is seen to follow trends from K41 theory.

scholarly journals On two-dimensional ferromagnetism

2009 ◽  
Vol 139 (3) ◽  
pp. 575-594 ◽  
Author(s):  
Pablo Pedregal ◽  
Baisheng Yan
Keyword(s):  
Minimization Problem ◽  
Integral Functional ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
New Energy ◽  
Non Local ◽  
Free Fields ◽  
Divergence Free ◽  
Future Work

We present a new method for solving the minimization problem in ferromagnetism. Our method is based on replacing the non-local non-convex total energy of magnetization by a new local non-convex energy of divergence-free fields. Such a general method works in all dimensions. However, for the two-dimensional case, since the divergence-free fields are equivalent to the rotated gradients, this new energy can be written as an integral functional of gradients and hence the minimization problem can be solved by some recent non-convex minimization procedures in the calculus of variations. We focus on the two-dimensional case in this paper and leave the three-dimensional situation to future work. Special emphasis is placed on the analysis of the existence/non-existence depending on the applied field and the physical domain.

scholarly journals Stratified Kelvin–Helmholtz turbulence of compressible shear flows

2018 ◽  
Vol 25 (2) ◽  
pp. 457-476 ◽  
Author(s):  
Omer San ◽  
Romit Maulik
Keyword(s):  
Power Density ◽  
Spatial Resolution ◽  
Shear Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Compressible Turbulence ◽  
Power Density Spectrum ◽  
Two Dimensional ◽  
Density Spectrum ◽  
Significant Difference

Abstract. We study scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin–Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16 3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both the kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k-5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k-5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum yields a k-5/3 scaling. This difference may be assumed to be a reason for the k-7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of the Helmholtz decomposition of both the kinetic velocity and density-weighted velocity fields. We observe that the scaling results are invariant with respect to the compressibility parameter when the density-weighted definition is used. Our two-dimensional results also confirm that a large inertial range of the solenoidal component with the k−3 scaling can be obtained when we simulate with a lower compressibility parameter; however, the compressive spectrum converges to k−2 for a larger compressibility parameter.

scholarly journals Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 1. Fields with divergence

2005 ◽  
Vol 47 (1) ◽  
pp. 21-38 ◽  
Author(s):  
G. D. McBain
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Cartesian Coordinates ◽  
Scalar Representation ◽  
The Mean ◽  
Free Fields ◽  
Divergence Free ◽  
Wave Coordinates

AbstractIt is shown how to decompose a three-dimensional field periodic in two Cartesian coordinates into five parts, three of which are identically divergence-free and the other two orthogonal to all divergence-free fields. The three divergence-free parts coincide with the mean, poloidal and toroidal fields of Schmitt and Wahl; the present work, therefore, extends their decomposition from divergence-free fields to fields of arbitrary divergence. For the representation of known and unknown fields, each of the five subspaces is characterised by both a projection and a scalar representation. Use of Fourier components and wave coordinates reduces poloidal fields to the sum of two-dimensional poloidal fields, and toroidal fields to the sum of unidirectional toroidal fields.

Using Viscous Calculations in Pump Design

1990 ◽  
Vol 112 (3) ◽  
pp. 272-280 ◽  
Author(s):  
F. Martelli ◽  
V. Michelassi
Keyword(s):  
High Performance ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Computer Code ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Complex Flow ◽  
Pump Design

A viscous computer code for designing the meridional channels of high-performance pumps is presented. An averaging technique is used to reduce the three-dimensional flow to a two-dimensional model. The code, based upon an implicit finite difference method for steady two-dimensional incompressible flows, was validated in complex flow geometries prior to application in the design analysis of an actual pump. Viscous effects are taken into account by two different turbulence models. The Navier-Stokes solver is used in conjunction with a standard blade-to-blade calculation by means of an automatic graphic procedure that exchanges geometric and flowfield data. Various meridional shape solutions are presented and discussed in relation to physical evidence.

A Marker-VOF Algorithm for Incompressible Flows With Interfaces

2002 ◽  
Author(s):  
Ruben Scardovelli ◽  
Eugenio Aulisa ◽  
Sandro Manservisi ◽  
Valerio Marra
Keyword(s):  
Incompressible Flows ◽  
Piecewise Linear ◽  
High Surface ◽  
Three Dimensional ◽  
Grid Cell ◽  
Reconstruction Algorithm ◽  
Two Dimensional ◽  
Thin Filaments ◽  
Smooth Interface ◽  
Lagrangian Scheme

In this paper, we present a three-dimensional (3D) reconstruction algorithm for Cartesian grids and a split advection algorithm which is based on a two-dimensional (2D) Eulerian-Lagrangian scheme that conserves mass exactly for incompressible flows. In the Volume-of-Fluid/Piecewise Linear Interface Calculation (VOF/PLIC) method a linear function in every grid cell cut by the interface approximates the free surface or the surface between two immiscible phases. The reconstruction is not continuous, and not accurate in regions with high surface curvature or when the interface develops thin filaments. Therefore, we have developed a new 2D mixed markers and VOF algorithm that follows the motion of a smooth interface with a good conservation of volume. Results are shown for flows with nonconstant vorticity.

Studies of the Eulerian–Lagrangian transformation in two-dimensional random flows

1991 ◽  
Vol 224 ◽  
pp. 485-505 ◽  
Author(s):  
J. P. Lynov ◽  
A. H. Nielsen ◽  
H. L. Pécseli ◽  
J. Juul Rasmussen
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Time Varying ◽  
Two Dimensional ◽  
Vortex Model ◽  
Individual Structure ◽  
Random Flow ◽  
Analytical Expressions ◽  
Random Flows

Two-dimensional, incompressible flows are discussed by a generalization of the line-vortex model. A large number of structures are randomly distributed initially. Each individual structure is convected by the superposed flow field of all the others. The statistical properties of the resulting space–time varying random flow are studied. Analytical expressions for both Eulerian and Lagrangian correlation functions are obtained for the limit where the density of structures is large. The analytical results compare favourably with numerical simulations. The study serves as a special test on proposed relations between Eulerian and Lagrangian averages which can be generally valid, i.e. also for three-dimensional, turbulent flows.

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