Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems

2005 ◽  
Vol 175 (826) ◽  
pp. 0-0 ◽  
Author(s):  
Guy Métivier ◽  
Kevin Zumbrun
Keyword(s):  
Boundary Layers ◽  
Hyperbolic Problems ◽  
Viscous Boundary

scholarly journals Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

2011 ◽  
Vol 671 ◽  
pp. 96-120 ◽  
Author(s):  
J. C. R. HUNT ◽  
D. D. STRETCH ◽  
S. E. BELCHER
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Lower Layer ◽  
Coupling Mechanism ◽  
Viscous Layer ◽  
Viscous Coupling ◽  
Viscous Effects ◽  
Horizontal Structure ◽  
Velocity Fluctuations ◽  
Viscous Boundary

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

scholarly journals Tidal rectification in lateral viscous boundary layers of a semi-enclosed basin

1987 ◽  
Vol 184 ◽  
pp. 381-397 ◽  
Author(s):  
H. E. De Swart ◽  
J. T. F. Zimmerman
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Boundary ◽  
Stokes Number ◽  
Residual Current ◽  
Residual Flow ◽  
Oscillatory Boundary Layer ◽  
Tidal Rectification ◽  
Vorticity Flux ◽  
Viscous Boundary

The rectified flow, induced by divergence of the vorticity flux in lateral oscillatory viscous boundary layers along the sidewalls of a semi-enclosed basin, is studied as a function of the Strouhal number, k, equivalent to the Reynolds number of the viscous inner oscillatory boundary layer, and of the Stokes number. The squared ratio of these numbers defines another Reynolds number, measuring the strength of the self-advection by the residual flow. For strong self-advection the residual current decays to zero in an outer boundary, its width being large compared to the width of the inner layer. The regimes of small, moderate and strong self-advection are analysed.

A Numerical Method for Calculating Viscous Flow Round Multiple-Section Aerofoils

1975 ◽  
Vol 26 (3) ◽  
pp. 176-188 ◽  
Author(s):  
T Seebohm ◽  
B G Newman
Keyword(s):  
Numerical Method ◽  
Boundary Layers ◽  
Inviscid Flow ◽  
List Type ◽  
Attached Flow ◽  
Flow Round ◽  
High Reynolds ◽  
Viscous Boundary ◽  
Viscous Solutions ◽  
Outer Potential

A numerical method is described for predicting incompressible, attached flow round multiple-section aerofoils at high Reynolds number. Interaction between wakes and boundary layers is not accounted for, but the method is nevertheless suitable for optimisation of design in the take-off condition. The solution is obtained in three steps: (i)The calculation of the outer, potential flow using a conventional Kutta condition for each aerofoil section.(ii)The calculation of viscous boundary layers and wakes.(iii)The combination of the inviscid and viscous solutions to effect proper matching at the edges of the boundary layers and wakes and a more accurate specification of the circulation in the inviscid flow.

Progressive internal waves on slopes

1969 ◽  
Vol 35 (1) ◽  
pp. 131-144 ◽  
Author(s):  
Carl Wunsch
Keyword(s):  
Boundary Layers ◽  
Internal Waves ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Inhomogeneous Waves ◽  
Usual Manner ◽  
Propagating Waves ◽  
Viscous Boundary ◽  
The Waves ◽  
Interior Solutions

The refraction of progressive internal waves on sloping bottoms is treated for the case of constant Brunt—Väisälä frequency. In two dimensions simple, explicit expressions for the changing wavelengths and amplitudes are found. For small slopes, the solutions reduce to simple propagating waves at infinity.The singularity along a characteristic is shown to be removable, though the solutions are now inhomogeneous waves. The viscous boundary layers of the wedge geometry are briefly considered with the inviscid solutions remaining as interior solutions.A theory valid for small slopes is obtained for three-dimensional waves. The waves are refracted in the usual manner, turning parallel to the beach in shallow water.

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