scholarly journals Some aspects in Kelvin-Helmholtz instability with and without Boussinesq approximation

2021 ◽  
Vol 13 (4) ◽  
pp. 25-33
Author(s):  
Ilinca-Laura BURDULEA ◽  
Alina BOGOI
Keyword(s):  
Shear Flow ◽  
Boussinesq Approximation ◽  
Euler System ◽  
Uniform Grid ◽  
Helmholtz Instability ◽  
Density Profiles ◽  
Runge Kutta Method ◽  
Fluid Instability ◽  
Grid Points ◽  
Parallel Shear Flow

The topic of this paper is the Kelvin-Helmholtz instability, a phenomenon which occurs on the interface of a stratified fluid, in the presence of a parallel shear flow, when there is a velocity and density difference across the interface of two adjacent layers. This paper focuses on a numerical simulation modelled by the Taylor-Goldstein equation, which represents a more realistic case compared to the basic Kelvin-Helmholtz shear flow. The Euler system is solved with new modelled smooth velocity and density profiles at the interface. The flux at cell boundaries is reconstructed by implementing a third order WENO (Weighted Essentially Non-Oscillatory) method. Next, a Riemann solver builds the fluxes at cell interfaces. The use of both Rusanov and HLLC solvers is investigated. Temporal discretization is done by applying the second order TVD (total variation diminishing) Runge-Kutta method on a uniform grid. Numerical simulations are performed comparatively for both Kelvin-Helmholtz and Taylor-Goldstein instabilities, on the same simulation domains. We find that increasing the number of grid points leads to a better accuracy in shear layer vortices visualization. Thus, we can conclude that applying the Taylor-Goldstein equation improves the realism in the general fluid instability modelling.

The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow

1960 ◽  
Vol 7 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Alar Toomre
Keyword(s):  
Shear Flow ◽  
Lateral Displacement ◽  
Reynolds Numbers ◽  
Infinite Cylinder ◽  
List Type ◽  
Displacement Effect ◽  
Simple Method ◽  
Viscous Shear ◽  
Parallel Shear Flow ◽  
Viscous Shear Flow

A simple method is presented in this paper for calculating the secondary velocities, andthe lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’) in the plane of symmetry ahead of an infinitely long cylinder situated normal to a steady, incompressible, slightly viscous shear flow; the cylinder is also perpendicular to the vorticity, which is assumed uniform but small. The method is based on lateral gradients of pressure, these being calculated from the primary flow alone. Profiles of the secondary velocities are obtained at several Reynolds numbers ahead of two specific cylindrical shapes: a circular cylinder, and a flat plate normal to the flow. The displacement effect is derived and, rathe surprisingly, is found to be virtually independent of the Reynolds number.

On the effect of parallel shear flow on the plasmoid instability

2018 ◽  
Vol 25 (10) ◽  
pp. 102117
Author(s):  
M. Hosseinpour ◽  
Y. Chen ◽  
S. Zenitani
Keyword(s):  
Shear Flow ◽  
Parallel Shear Flow

The extension of the Miles-Howard theorem to compressible fluids

1970 ◽  
Vol 43 (4) ◽  
pp. 833-836 ◽  
Author(s):  
G. Chimonas
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Upper Bound ◽  
Unstable Mode ◽  
Vertical Gradient ◽  
Flow Speed ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Sufficient Condition ◽  
Parallel Shear Flow

A statically stable, gravitationally stratified compressible fluid containing a parallel shear flow is examined for stability against infinitesimal adiabatic perturbations. It is found that the Miles–Howard theorem of incompressible fluids may be generalized to this system, so that n2 ≥ ¼U′2 throughout the flow is a sufficient condition for stability. Here n2 is the Brunt–Väissälä frequency and U’ is the vertical gradient of the flow speed. Howard's upper bound on the growth rate of an unstable mode also generalizes to this compressible system.

Second-order recombination in a parallel shear flow

1989 ◽  
Vol 200 ◽  
pp. 389-407 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shear Flow ◽  
Concentration Distribution ◽  
Second Order ◽  
Explicit Solutions ◽  
Far Field ◽  
First Order ◽  
Parallel Shear Flow

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

Direct simulations of turbulent flow in a pipe rotating about its axis

1997 ◽  
Vol 343 ◽  
pp. 43-72 ◽  
Author(s):  
P. ORLANDI ◽  
M. FATICA
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Radial Direction ◽  
Uniform Grid ◽  
Grid Refinement ◽  
Streamwise Vorticity ◽  
Vorticity Field ◽  
Vortical Structures ◽  
The Mean ◽  
Grid Points

Flow in a circular pipe rotating about its axis, at low Reynolds number, is investigated. The simulation is performed by a finite difference scheme, second-order accurate in space and in time. A non-uniform grid in the radial direction yields accurate solutions with a reasonable number of grid points. The numerical method has been tested for the non-rotating pipe in the limit ν→0 to prove the energy conservation properties. In the viscous case a grid refinement check has been performed and some conclusions about drag reduction have been reached. The mean and turbulent quantities have been compared with the numerical and experimental non-rotating pipe data of Eggels et al. (1994a, b). When the pipe rotates, a degree of drag reduction is achieved in the numerical simulations just as in the experiments. Through the visualization of the vorticity field the drag reduction has been related to the modification of the vortical structures near the wall. A comparison between the vorticity in the non-rotating and in the high rotation case has shown a spiral motion leading to the transport of streamwise vorticity far from the wall.

scholarly journals Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

2017 ◽  
Vol 815 ◽  
pp. 243-256
Author(s):  
Philippe Odier ◽  
Robert E. Ecke
Keyword(s):  
Shear Flow ◽  
Linear Theory ◽  
Length Distribution ◽  
Quantitative Measure ◽  
Stability Parameter ◽  
Helmholtz Instability ◽  
Thorpe Scale ◽  
Stratified Shear Flow ◽  
Miscible Fluid ◽  
Turbulent Wall

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. We explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers$0.05\lesssim Ri\lesssim 1$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small$Ri$the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger$Ri$interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest$Ri$but decreases rapidly as$Ri$increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. The distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.

High-precision potential-field and gradient-component transformations and derivative computations using cubic B-splines

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. I35-I42 ◽  
Author(s):  
Bingzhu Wang ◽  
Edward S. Krebes ◽  
Dhananjay Ravat
Keyword(s):  
High Precision ◽  
Potential Field ◽  
Theoretical Data ◽  
Gravity Gradient ◽  
Uniform Grid ◽  
Computational Domain ◽  
B Splines ◽  
Direct Interpretation ◽  
Gradient Component ◽  
Grid Points

Potential-field and gradient-component transformations and derivative computations are necessary for many techniques of data enhancement, direct interpretation, and inversion. We advance new unified formulas for fast interpolation, differentiation, and integration and propose flexible high-precision algorithms to perform 3D and 2D potential-field- and gradient component transformations and derivative computations in the space domain using cubic B-splines. The spline-based algorithms are applicable to uniform or nonuniform rectangular grids for the 3D case and to regular or irregular grids for the 2D case. The fast Fourier transform (FFT) techniques require uniform grid spacing. The spline-based horizontal-derivative computations can be done at any point in the computational domain, whereas the FFT methods use only grid points. Comparisons between spline and FFT techniques through two gravity-gradient examples and one magnetic example show that results computed with the spline technique agree better with the exact theoretical data than do results computed with the FFT technique.

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