Stability of a liquid film flowing down an inclined anisotropic and inhomogeneous porous layer: an analytical description

2016 ◽  
Vol 807 ◽  
pp. 135-154 ◽  
Author(s):  
P. Deepu ◽  
Srinivas Kallurkar ◽  
Prateek Anand ◽  
Saptarshi Basu
Keyword(s):  
Surface Waves ◽  
Porous Layer ◽  
Fluid Layer ◽  
Dominant Role ◽  
Analytical Description ◽  
Order Effects ◽  
Layer System ◽  
Gravity Driven ◽  
The Stability ◽  
Long Wave Approximation

We study the effect of anisotropy and inhomogeneity in the permeability of the porous layer on the stability of surface waves of an inclined fluid–porous double-layer system. The fluid is assumed to be Newtonian and the porous layer to be Darcian. The porous layer is saturated with the same fluid and the two layers are coupled at the interface via the Beavers–Joseph condition. Linear stability analysis is performed based on a long-wave approximation. The resulting eigenvalue problem is exactly solved up to third order in the wavenumber. The anisotropic behaviour of permeability, cross-stream component of permeability, surface tension and porosity are found to have only higher-order effects on the stability characteristics of the system. On the other hand, the inhomogeneous feature in the streamwise component of permeability play a dominant role in determining the stability of the gravity-driven surface waves; as do other system parameters such as the thickness of the fluid layer relative to that of the porous layer and the Beavers–Joseph coefficient.

Stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous layer

2017 ◽  
Vol 826 ◽  
pp. 376-395 ◽  
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Couette Flow ◽  
Porous Layer ◽  
Poiseuille Flow ◽  
Fluid Layer ◽  
Maximum Velocity ◽  
Stability Characteristic ◽  
Layer System ◽  
Neutral Curves ◽  
Layer Mode ◽  
The Stability

This paper performs a linear stability analysis to investigate the stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous medium saturated with the same fluid. The effect of superimposed Couette flow on the associated Poiseuille flow in such a two-layer system is explored carefully. The result shows that the presence of Couette flow may destabilize the Poiseuille flow at small depth ratio $\hat{d}$, defined by the ratio of the depth of the fluid layer to the depth of the porous layer, and induce a tri-modal structure to the neutral curves. At moderate $\hat{d}$, the Couette component generally produces a stabilization effect on the flow. When the velocity of the upper moving wall is large enough, a bi-modal behaviour of the neutral curves appears and a shift of instability mode occurs from the long-wave fluid-layer mode to the porous-layer mode with higher wavenumber. These stability characteristics are remarkably different from those of the plane Poiseuille–Couette flow in a single fluid layer in that the flow becomes absolutely stable when the wall velocity is over 70 % of the maximum velocity of the Poiseuille component of flow. The stability of pure Couette flow in such a two-layer system is also studied. It is found that the flow is still absolutely stable with respect to infinitesimal disturbances, which is the same as the stability characteristic of a single-layer plane Couette flow.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

scholarly journals Wave-induced Lagrangian drift in a porous seabed

2021 ◽  
Author(s):  
Jan Erik H. Weber ◽  
Peygham Ghaffari
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Lagrangian Formulation ◽  
Stokes Drift ◽  
Porous Bed ◽  
Wave Approximation ◽  
Long Wave ◽  
The Mean ◽  
Long Wave Approximation ◽  
The Waves

AbstractThe mean drift in a porous seabed caused by long surface waves in the overlying fluid is investigated theoretically. We use a Lagrangian formulation for the fluid and the porous bed. For the wave field we assume inviscid flow, and in the seabed, we apply Darcy’s law. Throughout the analysis, we assume that the long-wave approximation is valid. Since the pressure gradient is nonlinear in the Lagrangian formulation, the balance of forces in the porous bed now contains nonlinear terms that yield the mean horizontal Stokes drift. In addition, if the waves are spatially damped due to interaction with the underlying bed, there must be a nonlinear balance in the fluid layer between the mean surface gradient and the gradient of the radiation stress. This causes, through continuity of pressure, an additional force in the porous layer. The corresponding drift is larger than the Stokes drift if the depth of the porous bed is more than twice that of the fluid layer. The interaction between the fluid layer and the seabed can also cause the waves to become temporally attenuated. Again, through nonlinearity, this leads to a horizontal Stokes drift in the porous layer, but now damped in time. In the long-wave approximation only the horizontal component of the permeability in the porous medium appears, so our analysis is valid for a medium that has different permeabilities in the horizontal and vertical directions. It is suggested that the drift results may have an application to the transport of microplastics in the porous oceanic seabed.

scholarly journals Non-Darcian-Bènard Double Diffusive Magneto-Marangoni Convection in a Two Layer System with Constant Heat Source/Sink

2021 ◽  
pp. 4039-4055
Author(s):  
N. Manjunatha ◽  
R. Sumithra
Keyword(s):  
Porous Layer ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Type I ◽  
Layer System ◽  
Constant Heat ◽  
Double Diffusive

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection   is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field.   The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects.  The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); these are type (i) Adiabatic-Adiabatic and type (ii) Adiabatic-Isothermal.  The corresponding two TMNs   are obtained and the impacts of the porous parameter, solute Marangoni number, modified internal Rayleigh numbers, viscosity ratio, and the diffusivity ratios on the non-Darcian-Bènard double diffusive magneto - Marangoni convection are studied in detail.

scholarly journals Magneto Binary Nanofluid Convection in Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Jyoti Sharma ◽  
Urvashi Gupta ◽  
R. K. Wanchoo
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Comparative Analysis ◽  
Galerkin Method ◽  
Fluid Layer ◽  
Layer System ◽  
Water Based ◽  
The Stability ◽  
Mode Technique

The effect of an externally impressed magnetic field on the stability of a binary nanofluid layer in porous medium is considered in this work. The conservation equations related to the system are solved using normal mode technique and Galerkin method to analyze the problem. The complex expressions are approximated to get useful results. Mode of heat transfer is stationary for top heavy distribution of nanoparticles in the fluid layer and top heavy nanofluids are very less stable than regular fluids. Oscillatory motions are possible for bottom heavy distribution of nanoparticles and they are not much influenced by properties of different nanoparticles. A comparative analysis of the instability of water based nanofluids with metallic (Cu, Ag) and semiconducting (TiO2, SiO2) nanoparticles under the influence of magnetic field is examined. Semiconducting nanofluids are found to be more stable than metallic nanofluids. Porosity destabilizes the layer while solute difference (at the boundaries of the layer) stabilizes it. Magnetic field stabilizes the fluid layer system significantly.

scholarly journals Stokes drift through corals

2021 ◽  
Author(s):  
Joseph J. Webber ◽  
Herbert E. Huppert
Keyword(s):  
Coral Reef ◽  
Coral Reefs ◽  
Porous Layer ◽  
Large Scale ◽  
Fluid Layer ◽  
Ocean Waves ◽  
Stokes Drift ◽  
Inviscid Fluid ◽  
Porous Bed ◽  
Vertical Drift

AbstractMotivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

scholarly journals Coupled THM and Matrix Stability Modeling of Hydroshearing Stimulation in a Coupled Fracture-Matrix Hot Volcanic System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yong Xiao ◽  
Jianchun Guo ◽  
Hehua Wang ◽  
Lize Lu ◽  
John McLennan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Dominant Role ◽  
Injection Well ◽  
Time Step ◽  
Volcanic System ◽  
Induced Stress ◽  
The Matrix ◽  
Matrix Stability ◽  
The Stability

A coupled thermal-hydraulic-mechanical (THM) model is developed to simulate the combined effect of fracture fluid flow, heat transfer from the matrix to injected fluid, and shearing dilation behaviors in a coupled fracture-matrix hot volcanic reservoir system. Fluid flows in the fracture are calculated based on the cubic law. Heat transfer within the fracture involved is thermal conduction, thermal advection, and thermal dispersion; within the reservoir matrix, thermal conduction is the only mode of heat transfer. In view of the expansion of the fracture network, deformation and thermal-induced stress model are added to the matrix node’s in situ stress environment in each time step to analyze the stability of the matrix. A series of results from the coupled THM model, induced stress, and matrix stability indicate that thermal-induced aperture plays a dominant role near the injection well to enhance the conductivity of the fracture. Away from the injection well, the conductivity of the fracture is contributed by shear dilation. The induced stress has the maximum value at the injection point; the deformation-induced stress has large value with smaller affected range; on the contrary, thermal-induced stress has small value with larger affected range. Matrix stability simulation results indicate that the stability of the matrix nodes may be destroyed; this mechanism is helpful to create complex fracture networks.

Attitude reconstruction from strap-down rate gyros using power series

2021 ◽  
pp. 1-19
Author(s):  
Habib Ghanbarpourasl
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Direction Cosine ◽  
Analytical Description ◽  
Double Precision ◽  
Angular Velocity Vector ◽  
Higher Order Terms ◽  
Direction Cosine Matrix ◽  
The Stability ◽  
Better Than

Abstract This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

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