Hyperbolic approximation and inviscid limit

1998 ◽  
pp. 97-133
Author(s):  
Wojbor A. Woyczyński
Keyword(s):  
Inviscid Limit

scholarly journals On the linear stability of compressible plane Couette flow

1994 ◽  
Vol 258 ◽  
pp. 131-165 ◽  
Author(s):  
Peter W. Duck ◽  
Gordon Erlebacher ◽  
M. Yousuff Hussaini
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Small Amplitude ◽  
Reynolds Numbers ◽  
Inviscid Limit ◽  
Plane Couette Flow ◽  
Moving Wall ◽  
Type Boundary ◽  
The Stability ◽  
Radiation Type

The linear stability of compressible plane Couette flow is investigated. The appropriate basic velocity and temperature distributions are perturbed by a small-amplitude normal-mode disturbance. The full small-amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instabilities can occur, although the corresponding growth rates are often quite small; the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wave speed of the disturbances approaches the velocity of either of the walls, and these regimes are also analysed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

A Numerical Simulation Algorithm of the Inviscid Dynamics of Axisymmetric Swirling Flows in a Pipe

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
J. Granata ◽  
L. Xu ◽  
Z. Rusak ◽  
S. Wang
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Difference Scheme ◽  
Second Order ◽  
Swirling Flows ◽  
Inviscid Limit ◽  
Simulation Algorithm ◽  
Spatial Integration ◽  
Order Difference ◽  
Breakdown Process

Current simulations of swirling flows in pipes are limited to relatively low Reynolds number flows (Re < 6000); however, the characteristic Reynolds number is much higher (Re > 20,000) in most of engineering applications. To address this difficulty, this paper presents a numerical simulation algorithm of the dynamics of incompressible, inviscid-limit, axisymmetric swirling flows in a pipe, including the vortex breakdown process. It is based on an explicit, first-order difference scheme in time and an upwind, second-order difference scheme in space for the time integration of the circulation and azimuthal vorticity. A second-order Poisson equation solver for the spatial integration of the stream function in terms of azimuthal vorticity is used. In addition, when reversed flow zones appear, an averaging step of properties is applied at designated time steps. This adds slight artificial viscosity to the algorithm and prevents growth of localized high-frequency numerical noise inside the breakdown zone that is related to the expected singularity that must appear in any flow simulation based on the Euler equations. Mesh refinement studies show agreement of computations for various mesh sizes. Computed examples of flow dynamics demonstrate agreement with linear and nonlinear stability theories of vortex flows in a finite-length pipe. Agreement is also found with theoretically predicted steady axisymmetric breakdown states in a pipe as flow evolves to a time-asymptotic state. These findings indicate that the present algorithm provides an accurate prediction of the inviscid-limit, axisymmetric breakdown process. Also, the numerical results support the theoretical predictions and shed light on vortex dynamics at high Re.

Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow

1997 ◽  
Vol 9 (4) ◽  
pp. 876-882 ◽  
Author(s):  
Koji Ohkitani ◽  
Michio Yamada
Keyword(s):  
Limit Behavior ◽  
Inviscid Limit

Subharmonic resonance of short internal standing waves by progressive surface waves

1996 ◽  
Vol 321 ◽  
pp. 217-233 ◽  
Author(s):  
D. F. Hill ◽  
M. A. Foda
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Growth Rates ◽  
Evolution Equations ◽  
Standing Waves ◽  
Second Order ◽  
Inviscid Limit ◽  
Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

scholarly journals The inviscid limit for the incompressible stationary magnetohydrodynamics equations in three dimensions

2021 ◽  
pp. 2150006
Author(s):  
Weiping Yan ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Unbounded Domain ◽  
Three Dimensional ◽  
Viscosity Coefficient ◽  
Three Dimensions ◽  
Mhd Equations ◽  
Inviscid Limit ◽  
Magnetohydrodynamics Equations ◽  
Zero Viscosity Limit ◽  
Viscosity Limit ◽  
Zero Viscosity

This paper is concerned with the zero-viscosity limit of the three-dimensional (3D) incompressible stationary magnetohydrodynamics (MHD) equations in the 3D unbounded domain [Formula: see text]. The main result of this paper establishes that the solution of 3D incompressible stationary MHD equations converges to the solution of the 3D incompressible stationary Euler equations as the viscosity coefficient goes to zero.

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

2021 ◽  
Vol 933 ◽  
Author(s):  
Yongyun Hwang ◽  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Turbulence Intensity ◽  
Streamwise Velocity ◽  
Early Observation ◽  
Wall Turbulence ◽  
Inviscid Limit ◽  
Necessary Condition ◽  
Outer Length ◽  
Power Spectral ◽  
Parallel Direction ◽  
Logarithmic Layer

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

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