Optimal Homotopy Asymptotic Method for Viscous Boundary Layer Flow in Unbounded Domain

2014 ◽  
Author(s):  
R.D. Ene ◽  
V. Marinca ◽  
R. Negrea
Keyword(s):  
Boundary Layer ◽  
Unbounded Domain ◽  
Asymptotic Method ◽  
Boundary Layer Flow ◽  
Viscous Boundary Layer ◽  
Optimal Homotopy Asymptotic Method ◽  
Layer Flow ◽  
Viscous Boundary

Boundary layer flow and bed shear stress under a solitary wave

2007 ◽  
Vol 574 ◽  
pp. 449-463 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
YONG SUNG PARK ◽  
EDWIN A. COWEN
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Solitary Wave ◽  
Analytical Solutions ◽  
Boundary Layer Flow ◽  
Inertia Force ◽  
Bed Shear Stress ◽  
Viscous Boundary Layer ◽  
Layer Flow ◽  
Viscous Boundary

Liu & Orfila (J. Fluid Mech. vol. 520, 2004, p. 83) derived analytical solutions for viscous boundary layer flows under transient long waves. Their analytical solutions were obtained with the assumption that the nonlinear inertia force was negligible in the momentum equations. In this paper, using Liu & Orfila's solution and the solutions for the nonlinear boundary layer equations, we examine the boundary layer flow characteristics under a solitary wave. It is found that while the horizontal component of the free-stream velocity outside the boundary layer always moves in the direction of wave propagation, the fluid particle velocity near the bottom inside the boundary layer reverses direction as the wave decelerates. Consequently, the bed shear stress also changes sign during the deceleration phase. Laboratory measurements, including the free-surface displacement, particle image velocimetry (PIV) resolved velocity fields of the viscous boundary layer, and the calculated bed shear stress were also collected to check the theoretical results. Excellent agreement is observed.

An experimental study of the instability of the laminar Ekman boundary layer

1963 ◽  
Vol 15 (4) ◽  
pp. 560-576 ◽  
Author(s):  
Alan J. Faller
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Rotating Disk ◽  
Homogeneous Fluid ◽  
Viscous Boundary Layer ◽  
Ekman Boundary Layer ◽  
Characteristic Angle ◽  
Layer Flow ◽  
The Stability ◽  
Viscous Boundary

This study concerns the stability of the steady laminar boundary-layer flow of a homogeneous fluid which occurs in a rotating system when the relative flow is slow compared to the basic speed of rotation. Such a flow is called an Ekman boundary-layer flow after V. W. Ekman who considered the theory of such flows with application to the wind-induced drift of the surface waters of the ocean.Ekman flow was produced in a large cylindrical rotating tank by withdrawing water from the centre and introducing it at the rim. This created a steady-state symmetrical vortex in which the flow from the rim to the centre took place entirely in the shallow viscous boundary layer at the bottom. This boundary-layer flow became unstable above the critical Reynolds number$Re_c = vD|v = 125 \pm 5$wherevis the tangential speed of flow,$D = (v| \Omega)^{\frac {1}{2}}$is the characteristic depth of the boundary layer,vis the kinematic viscosity, and Ω is the basic speed of rotation. The initial instability was similar to that which occurs in the boundary layer on a rotating disk, having a banded form with a characteristic angle to the basic flow and with the band spacing proportional to the depth of the boundary layer.

scholarly journals Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet

2019 ◽  
pp. 1-7
Author(s):  
S. Alao ◽  
R. A. Oderinu ◽  
F. O. Akinpelu ◽  
E. I. Akinola
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Analysis Method ◽  
Viscous Boundary Layer ◽  
New Approach ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Viscous Boundary ◽  
Adomian Polynomial

This paper investigates a new approach called Homotopy Analysis Decomposition Method (HADM) for solving nonlinear differential equations, the method was developed by incorporating Adomian polynomial into Homotopy Analysis Method. The Adomian polynomial was used to decompose the nonlinear term in the equation then apply the scheme of homotopy analysis method. The accuracy and efficiency of the proposed method was validated by considering algebraically decaying viscous boundary layer  flow due to a moving sheet. Diagonal Pade approximation was used to get the skin friction. The obtained results were presented along with other methods in the literature in tabular form to show the computational efficiency of the new approach. The results were found to agree with those in literature. Owing to its small size of computation, the method is not aected by discretization error as the results are presented in form of polynomials.

Instabilities and inertial waves generated in a librating cylinder

2011 ◽  
Vol 687 ◽  
pp. 171-193 ◽  
Author(s):  
J. M. Lopez ◽  
F. Marques
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Boundary Layer Flows ◽  
Viscous Boundary Layer ◽  
Navier Stokes Equations ◽  
Damping Rate ◽  
Layer Flow ◽  
Viscous Boundary

AbstractA librating cylinder consists of a rotating cylinder whose rate of rotation is modulated. When the mean rotation rate is large compared with the viscous damping rate, the flow may support inertial waves, depending on the frequency of the modulation. The modulation also produces time-dependent boundary layers on the cylinder endwalls and sidewall, and the sidewall boundary layer flow in particular is susceptible to instabilities which can introduce additional forcing on the interior flow with time scales different from the modulation period. These instabilities may also drive and/or modify the inertial waves. In this paper, we explore such flows numerically using a spectral-collocation code solving the Navier–Stokes equations in order to capture the dynamics involved in the interactions between the inertial waves and the viscous boundary layer flows.

Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

1992 ◽  
Vol 237 ◽  
pp. 231-260 ◽  
Author(s):  
M. E. Goldstein ◽  
S. J. Leib ◽  
S. J. Cowley
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Leading Edge ◽  
Uniform Flow ◽  
Viscous Boundary Layer ◽  
Layer Flow ◽  
Viscous Boundary ◽  
Flat Plate Boundary Layer

We consider a nominally uniform flow over a semi-infinite flat plate. Our analysis shows how a small streamwise disturbance in the otherwise uniform flow ahead of the plate is amplified by leading-edge bluntness effects and eventually leads to a small-amplitude but nonlinear spanwise motion far downstream from the leading edge of the plate. This spanwise motion is then imposed on the viscous boundary-layer flow at the surface of the plate – causing an order-one change in its profile shape. This ultimately reduces the wall shear stress to zero – causing the boundary layer to undergo a localized separation, which may be characterized as a kind of bursting phenomenon that could be related to the turbulent bursts observed in some flat-plate boundary-layer experiments.

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