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A stability condition is provided for a class of vorticity boundary formulas used withthe second order finite-difference numerical scheme for the vorticity-stream function formulation ofthe unsteady incompressible Navier-Stokes eq...
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A stability condition is provided for a class of vorticity boundary formulas used withthe second order finite-difference numerical scheme for the vorticity-stream function formulation ofthe unsteady incompressible Navier-Stokes equations. These local vorticity boundary formulas arederived using the no-slip boundary condition for the velocity. A new form of these long-stencilformulas is needed to classify the stability property, in which local terms are controlled by globalquantities via discrete elliptic regularity for the stream functions.
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We present benchmark simulations for the 8:1 differentially heated cavity problem, the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourt...
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We present benchmark simulations for the 8:1 differentially heated cavity problem, the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth-order finite difference method based on the vorticity-stream function formulation of the Boussinesq equations. The momentum equation is discretized by a compact scheme with the no-slip boundary condition forced using a local vorticity boundary conation. Long-stencil discretizations are used for the temperature transport equation with one-sided extrapolation applied near the boundary. The time stepping scheme for both equations is classical fourth-order Runge-Kutta. The main step is the solution of two discrete Poisson-like equations at each Runge-Kutta time stage, which are solved using FFT-based methods.
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Let D_t, 0 ≤ t ≤ 1 be a 1-parameter family of Dirac type operators on a two-dimensional disk with m - 1 holes. Suppose that all operators D_t have the same symbol, and that D_1 is conjugate to D_0 by a scalar gauge transformatio...
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Let D_t, 0 ≤ t ≤ 1 be a 1-parameter family of Dirac type operators on a two-dimensional disk with m - 1 holes. Suppose that all operators D_t have the same symbol, and that D_1 is conjugate to D_0 by a scalar gauge transformation. Suppose that all operators D_t are considered with the same elliptic local boundary condition. Our main result is a computation of the spectral flow for such a family of operators. The answer is obtained up to multiplication by an integer constant depending only on the number of holes in the disk. This constant is calculated explicitly for the case of the annulus (m = 2).
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Three-dimensional (3D) obstacles on the bottom are common sites for the generation of vortices, internal waves and turbulence by ocean currents. Turbulence-resolving simulations are conducted for stratified flow past a conical hil...
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Three-dimensional (3D) obstacles on the bottom are common sites for the generation of vortices, internal waves and turbulence by ocean currents. Turbulence-resolving simulations are conducted for stratified flow past a conical hill, a canonical example of 3D obstacles. Motivated by the use of slip boundary condition (BC) and drag-law (effectively partial slip) BC in the literature on geophysical wakes, we examine the sensitivity of the flow to BCs on the obstacle surface and the flat bottom. Four BC types are examined for a non-rotating wake created by a steady current impinging on a conical obstacle, with a detailed comparison being performed between two cases, namely NOSL (no-slip BC used at all solid boundaries) and SL (slip BC used at all solid boundaries). The other two cases are as follows: Hybrid, undertaken with slip at the flat bottom and no-slip at the obstacle boundaries, and case DL wherein a quadratic drag-law BC is adopted on all solid boundaries. The no-slip BC allows the formation of a boundary layer which separates and sheds vorticity into the wake. Significant changes occur in the structure of the lee vortices and wake when the BC is changed. For instance, bottom wall friction in the no-slip case suppresses unsteadiness of flow separation leading to a steady attached lee vortex. In contrast, when the bottom wall has a slip BC (the SL and Hybrid cases) or has partial slip (DL case), unsteady separation leads to a vortex street in the near wake and the enhancement of turbulence. The recirculation region is shorter and the wake recovery is substantially faster in the case of slip or partial-slip BC. In the lee of the obstacle, turbulent kinetic energy (TKE) for case NOSL is concentrated in a shear layer between the recirculating wake and the free stream, while TKE is bottom-intensified in the other three cases. DL is the appropriate BC for high-Re wakes where the boundary layer cannot be resolved. The sources of lee vorticity are also examined in this
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A new Ertel-potential-vorticity inversion method is proposed and tested in the framework of a low-order model as well as in Meteo France's operational primitive-equation spectral model, ARPEGE. The potential-vorticity (PV) inversi...
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A new Ertel-potential-vorticity inversion method is proposed and tested in the framework of a low-order model as well as in Meteo France's operational primitive-equation spectral model, ARPEGE. The potential-vorticity (PV) inversion procedure is designed so that its result lies within the subspace of model solutions, without the use of any explicit balance condition. The inversion is based on a variational problem in which one minimizes simultaneously the distance to the dynamical initialized solution following a digital-filter method and the PV to be inverted. Since the inverted solution results from model backward and forward integrations, and not from a set of algebraic equations, it possesses a strong dynamical consistency. In the framework of a low-order model, it is found that for small Rossby number, digital-filter initialization lies between nonlinear normal-mode initialization and quasi-geostrophic methods. The method has also been successfully used to rebuild the non-divergent flow, the temperature, and a significant part of the divergent flow, knowing only the three-dimensional PV field and a boundary condition.
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We consider different computational issues related to the three-dimensionalities of the flow around an oscillating circular cylinder. The full time-dependent Navier-Stokes equations are directly solved in a moving reference frame ...
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We consider different computational issues related to the three-dimensionalities of the flow around an oscillating circular cylinder. The full time-dependent Navier-Stokes equations are directly solved in a moving reference frame by introducing a forcing term. The choice of quantitative validation criteria is discussed and discrepancies of previously published results are addressed. The development of Honji vortices shows that short simulation times may lead to incorrect quasi-stable vortex patterns. The viscous decay of already established Honji vortices is also examined.
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We study the vortices of energy minimizers in the London limit for the Ginzburg_Landau model with periodic boundary condi_tions. For applied fields well below the second critical field we are able to describe the location and numb...
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We study the vortices of energy minimizers in the London limit for the Ginzburg_Landau model with periodic boundary condi_tions. For applied fields well below the second critical field we are able to describe the location and number of vortices. Many of the results presented appeared in [H. Aydi, Doctoral Dissertation, Université Paris-XII, 2004], others are new. _ 2008 Elsevier Masson SAS. All rights reserved.
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Taking advantage of alternative expressions for potential vorticity (PV) in divergence forms, we derive balances between volume integral of PV and boundary conditions, that are then applied to practical computations of PV:
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Direct numerical simulation (DNS) of forced plumes arising from input of both momentum and buoyancy into an ambient fluid is presented. The large vortical structures in the near field of thermal and reactive plumes are investigate...
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Direct numerical simulation (DNS) of forced plumes arising from input of both momentum and buoyancy into an ambient fluid is presented. The large vortical structures in the near field of thermal and reactive plumes are investigated. Boundary conditions associated with the spatial DNS of open-boundary buoyant flows that are compatible with the modern non-dissipative, high-order, finite-difference schemes have been developed. The governing equations for flow and combustion at the plume centerline are put into a special form to circumvent the singularity at the axis associated with the cylindrical coordinates. Mixing is found to be stronger in the planar thermal plume than in the axisymmetric case. An explanation is provided based on the vorticity budget. Axisymmetric reactive plumes with a one-step reaction governed by the Arrhenius kinetics have also been studied. The unsteady effects of chemical heat release and combustion-induced buoyancy on the flow structures are investigated. Budgets of the vorticity transport are examined to reveal the mechanisms leading to the formation and evolution of large vortical structures in forced plumes. It is found that volumetric expansion due to chemical heat release tends to destroy vorticity, while combustion-induced buoyancy under the gravitational effect generates vorticity. The gravitational term in the vorticity transport equation is found to be the main mechanism for the buoyant flow instability and the development of counter-rotating vortices in reactive plumes.
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We study the minimizers of the Ginzburg–Landau free energy functional in the class (u, A) ∈ H1(Ω; ℂ) × H1(Ω; ℝ2) with |u| = 1 on ∂Ω, where Ω is a bounded simply connected domain in ℝ2. We consider the connected componen...
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We study the minimizers of the Ginzburg–Landau free energy functional in the class (u, A) ∈ H1(Ω; ℂ) × H1(Ω; ℝ2) with |u| = 1 on ∂Ω, where Ω is a bounded simply connected domain in ℝ2. We consider the connected components of this class defined by the prescribed topological degree d of u on the boundary ∂Ω. We show that for d ≠ 0 the minimizers exist if 0 < λ ≤ 1 and do not exist if λ > 1, where λ is the coupling constant ( is the Ginzburg–Landau parameter). We also establish the asymptotic locations of vortices for λ → 1 - 0 (the critical value λ = 1 is known as the Bogomol'nyi integrable case).
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