Dynamics in coalescing critical layers
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This article continues an exploration of instabilities of jets in two-dimensional, inviscid fluid on the beta-plane. At onset, for particular choices of the physical parameters, the normal modes responsible for instability have critical levels that coalesce along the axis of the jet. Matched asymptotic expansion (critical layer theory) is used to derive a reduced model describing the dynamics of these modes. Because the velocity profile is locally parabolic in the vicinity of the critical levels the dynamics is richer than in standard critical layer problems. The model captures the inviscid saturation of unstable modes, the excitation of neutral Rossby waves, and the decay of disturbances when there are no discrete normal modes. Inviscid saturation occurs when the vorticity distribution twists up into vortical structures that take the form of either a pair of ‘cat's eye’ patterns straddling the jet axis, or a single row of vortices. The addition of weak viscosity destroys these cat's eye structures and causes the critical layer to spread diffusively. The results are compared with numerical simulations of the governing equations.Keywords:
Inviscid flow
Saturation (graph theory)
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Geophysical fluid dynamics
Stream function
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Inviscid flow
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An analysis is performed of the evolution in time of the structure- and vorticity fields in viscousand inviscid-fluid numerically simulated wave-diffraction cases. It is shown that numerical integration of the Euler equations gives rather meaningful results in terms of structure- and vorticity fields in the cases considered, as compared with the physically rigorous approach represented by the solution of the full Navier−Stokes equations.
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Inviscid flow
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This paper extends a previous modified axisymmetric analog method to predict heating rates on hypersonic vehicles in conjunction with inviscid computational fluid dynamic (CFD) codes which can provide more accurate inviscid solutions and are suited for complex configurations. The major problem is the heating anomalies encountered in the stagnation region, as the quality of the heating solution is very sensitive to the quality of the inviscid solution in the high-gradient stagnation region. To overcome this problem, a hybrid approach is developed to eliminate noise in the inviscid solution in the near-stagnation region by recalculating a noise-free inviscid solution in that region using an engineering method. As a result, there is no need to spend much effort to compute a high-quality inviscid solution in the near-stagnation region when solving the inviscid solution using an inviscid CFD code, thus significantly reducing run times. The proposed method is applied to several typical hypersonic vehicles and compared with existing approaches to validate its effectiveness. The results show that the proposed method can predict surface heating rates on complex configurations with reasonable accuracy but requires much shorter computational times.
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Inviscid flow
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Abstract : A viscous inviscid interaction method for three dimensional flows, in which the partially parabolic Reynolds equations are coupled with an inviscid flow solution procedure in an interactive and iterative manner, is applied to two simple three dimensional bodies for which experimental data are available for comparison. The relative merits of interactive and global solution procedures are evaluation by comparing the viscous inviscid interaction solutions with noninteractive large domain solutions of only the viscous flow equations. Both methods yield satisfactory results, although the interaction solutions are found to be computationally more efficient for the cases considered. Keywords: Thick Three Dimensional Layer; Viscous Inviscid Interaction; Partially parabolic Equations; Computational Fluid Dynamics.
Inviscid flow
Viscous liquid
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General equations are derived for the rate of change of vorticity in compressible, inviscid flow into which fluid may be introduced, and in which nonuniform body forces may exist. Examples of vorticity transfer and change are given and analogies are drawn between these examples.
Inviscid flow
Compressible flow
Vortex stretching
Burgers vortex
Incompressible Flow
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We prove global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. One of the key steps is a reformulation of the problem into a symmetric quasilinear Klein-Gordon system, for which the global existence of classical solutions is then proved with combination of the vector field approach and the normal forms. We also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity.
Inviscid flow
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