Free Surface Profile Research Articles

Dynamic response of spar-type floating offshore wind turbine in freak wave considering the wave-current interaction effect

In this paper, the dynamic responses of a Spar-type floating offshore wind turbine (FOWT) are simulated and analyzed under the scenarios with freak wave superimposed a uniform current. The wave-current interaction is considered in the process of freak wave generation. An improved phase modulation algorithm is used to generate the free surface profile of the freak wave. Compared with the deterministic wave modeling method, this method can realize the randomness of the sea state and also achieve high efficiency. The effect of the presence of current on the wave energy spectra is firstly investigated. Then the OC3 Hywind Spar-type FOWT in the parked condition is chosen as an example to study the dynamic responses under the extreme wave scenarios. An in-house MATLAB code based on a nonlinear aero-hydro-mooring coupled model is adopted to perform these numerical investigations. The simulations are conducted in the time domain and then the results of wave forces and platform motions in the surge, heave and pitch are summarized and analyzed considering the presence of current with different velocities. The results of mooring lines tension and the acceleration at nacelle are also investigated. Through the simulation results, we can have a clear understanding of the mechanism of the wave-current interaction phenomenon for extremely high waves in Gaussian seas. Furthermore, it also allows identifying the severest wave conditions which are important for the analysis of the floating structure ultimate design conditions.

Numerical modelling of trapezoidal weir flow with RANS, LES and DES models

The characteristics of the trapezoidal weir flow are measured using a one-dimensional laser Doppler anemometer for two different flow conditions. The governing equations of the flow are solved using Standard k–e, Realizable k–e, Modified k–ω and Reynolds Stress Model based on the Reynolds-Averaged Navier–Stokes Equations and by Large Eddy and Detached Eddy Simulations. ANSYS-Fluent package program is used for the numerical analysis of flow with the same experimental conditions. The free surface of the trapezoidal weir flow is computed by the volume of fluid method. The effect of the selected grid structure on the numerical results is examined by Grid Convergence Index. Moreover, two-dimensional (2D) and three-dimensional (3D) analyses of the trapezoidal weir flow are included to estimate the effects of side walls. Experimental results of the velocity field and free surface profiles are compared to the numerical results of 2D and 3D simulations for the validation purposes. From the comparisons it is concluded that the Reynolds Stress Model estimates the flow field more accurately compared with those of the other models used in the present study. Furthermore, the flow characteristics such as turbulence kinetic energy, energy spectrum and pressure distributions for different flow rates are presented. Lastly, the discharge coefficients for different flow–weir configurations are compared experimentally and numerically.

Effect of viscosity on sloshing in a rectangular tank with intermediate liquid depth

The viscous effects on the horizontally-excited sloshing under resonant and off-resonant excitations are investigated experimentally. Both tap water and glycerin at different temperatures are chosen as the experimental fluids. The intermediate depth ratio h/L = 0.2 is chosen. The sloshing of water and glycerin at four kinematic viscosities ranging from 1.14 × 10−6 m2/s to 1.1 × 10−3 m2/s is studied. Through well-controlled experiments, by analyzing the pressure and free surface snapshot, the sloshing gradually turns from the resonant-steady state to the harmonic state for a certain viscosity threshold. The free surface profiles of low and high viscous fluids under resonant excitations are further analyzed, in connection with the dynamic pressures and excitation accelerations. The peak dynamic pressures are successively out of synchrony with the peak excitation accelerations, obvious phase shift occurs which eventually goes to one fifth of the resonant frequency. Through the fast Fourier transform, it is found that the dominant response frequencies of high viscous fluids are integral times of the forcing frequency behaving a distinct state from the low viscous fluids especially for the water.

Experimental and Numerical Analysis of a Dam-Break Flow through Different Contraction Geometries of the Channel

Dam-break wave propagation usually occurs over irregular topography, due for example to natural contraction-expansion of the river bed and to the presence of natural or artificial obstacles. Due to limited available dam-break real-case data, laboratory and numerical modeling studies are significant for understanding this type of complex flow problems. To contribute to the related field, a dam-break flow over a channel with a contracting reach was investigated experimentally and numerically. Laboratory tests were carried out in a smooth rectangular channel with a horizontal dry bed for three different lateral contraction geometries. A non-intrusive digital imaging technique was utilized to analyze the dam-break wave propagation. Free surface profiles and time variation of water levels in selected sections were obtained directly from three synchronized CCD video camera records through a virtual wave probe. The experimental results were compared against the numerical solution of VOF (Volume of Fluid)-based Shallow Water Equations (SWEs) and Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence model. Good agreements were obtained between computed and measured results. However, the RANS solution shows a better correspondence with the experimental results compared with the SWEs one. The presented new experimental data can be used to validate numerical models for the simulation of dam-break flows over irregular topography.

Quantitative comparison of experimental and Mohr-Coulomb finite element method simulation flow characteristics from quasi two-dimensional flat-bottomed bins

Four different flow characteristics obtained from Eulerian finite element method (FEM) simulations using a Mohr-Coulomb material model are quantitatively compared to experiments performed on laboratory-scale concentric and eccentric quasi two-dimensional flat-bottomed bins. Particle image velocimetry (PIV) experiments are performed on Ottawa 20–30 sand discharging through the bins. The experimental steady state velocity profiles, mass discharge rate (MDR), duration of steady MDR (TSS), and free surface profiles are compared to the FEM predictions. The significance of material dilation and associated softening (DS) on FEM flow characteristics is examined through comparisons to simulations without dilation or softening (NDNS). FEM DS simulations using a Mohr-Coulomb material model that includes material dilation and softening are shown to be capable of predicting the four flow characteristics in both discharging bins with reasonable accuracy.

On the calculation of wavenumber from measured time traces

When characterising local geometry for unsteady water waves, the accurate determination of spatial quantities such as the wavenumber from measured time traces is non-trivial. The present study investigates different methods in order to highlight the discrepancies that arise when estimating the wavenumber from fully nonlinear numerical time traces of the free surface profile. To this extent, the open research topic relating to the accuracy of the Hilbert transform in analysing broad-banded signals is addressed. The accuracy of local wavenumber estimates from the Hilbert transform are shown to have a strong dependency on the bandwidth of the underlying spectrum. For broad-banded sea-states there is a significant departure of the Hilbert transform predictions from actual wavenumber values. In contrast, the Double Fourier numerical model of Baldock and Swan (1994) [1] is shown to obtain accurate estimates of local wave geometry from just a single measured time trace, regardless of spectral characteristics; it is thus the recommended method. In addition, an empirical correction factor is proposed that can be applied to the linear dispersion equation in order to obtain an improved wavenumber estimate. The correction is tested for unidirectional deep water, nonlinear random sea-states and shown to offer considerable improvements in the local wavenumber estimates.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

Abstract A three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

Research on the Normal Use of a Plug Discharge Tunnel

This study analyzed the normal use of an unusual flood-releasing tunnel with a plug dissipator. Firstly, normal physical model tests based on the Froude criterion (1 : 50) were finished. Secondly, depression physical model tests based on the Froude criterion (1 : 50) and cavitation similarity criterion were finished. Thirdly, 3-dimensional numerical simulation of flow field was finished, and free surface profile was captured, which was based on RNGk-εtwo-equation turbulence model and VOF method. The focus of this study is on the relationship between normal use and cavitation characteristics (e.g., pressure, turbulence kinetic energy, and cavitation number). The results show that lowering the reservoir water level, reduced by 20.41 m at most, increases the risk of cavitation of a plug discharge tunnel, which means with the decrease of the flow cavitation number, the possibility of structural damage will increase dramatically, while reducing the outlet height can effectively raise the flow cavitation number, ensuring the safety of normal use. Under the conditions of free outflow, for theH1/evalues of 4.45, 4.00, and 3.55, the conditions in which the tunnel meets the requirements of anticavitation areh/D ≤ 0.42,h/D ≤ 0.39, andh/D ≤ 0.35, respectively. In addition, the discharge capacity of the tunnel is not significantly reduced with the lowering of outlet height, implying that operation under a low water head of the plug discharge tunnel, as low as 3.55 ofH1/ein the test, is feasible. The results obtained in this study can serve as reference information in engineering design of the plug discharge tunnel.

An ISPH with k–ε closure for simulating turbulence under solitary waves

In this paper an Incompressible Smoothed Particle Hydrodynamics (ISPH) method solving the 2D RANS (Reynolds Averaged Navier-Stokes) equations with the k–ε turbulence closure is constructed. In the present model, the concept of “massless ISPH” utilizing the definition of “particle density” (number of computational particles within unit volume) is stressed. The skills of this numerical model are tested by applying to two laboratory experiments: (1) A non-breaking solitary wave propagating over a bottom-mounted barrier and (2) a solitary wave breaking on a 1 on 50 slope. In the former case flow separation occurs behind the barrier as the wave crest passes by and a vortex is generated, which later interacts with free surface causing breaking. In the latter case wave breaking and bottom friction both generate significant turbulence. For both cases, the effects of initial seeding of turbulent kinetic energy, required in the k–ε model, are studied and it is concluded that initial values of O (10−10) to O (10−8) m2/s2 should be used. An adaptive wall boundary condition for k–ε turbulence model is employed to avoid the unrealistic production of turbulence near the wall boundary. The numerical results, in terms of free surface profile, mean velocity field, vorticity field, turbulent kinetic energy and turbulent shear stress, are compared with experimental data. Very reasonable agreement is observed. This paper presents the first comprehensively validated 2D ISPH model with the k–ε turbulence closure, which can be applied to transient free surface wave problems.

Investigating impact of converging training walls of the ogee spillways on hydraulic performance

Due to their economical and structural aspects, ogee-crested spillways can be constructed and operated in a wide variety of situations. In this study, a three-dimensional physical model (1:50 scale) was planned and constructed to investigate the impact of converging training walls of the ogee spillways with a curve axis on flow characteristics such as the discharge coefficient, free surface profile, flow depth and pressure on the spillway. For this purpose, the spillway was constructed, tested and verified in both the symmetrical and asymmetrical convergence of training walls ranging from 0° to 120°. Observations from flow depth and piezometric pressure along the spillway in various convergence angles indicate that as θ increases, the flow depth and piezometric pressure increase at the bottom and the toe of the spillway model. Also, in convergence angles of 60° and 90° tested in both symmetric and asymmetric states, the angles with lower Lch/L have larger flow depth and piezometric pressure. The results of the experiments indicated that in the converging ogee spillway, by increasing the total upstream head, the discharge coefficient shows increment for each of the convergence angles (θ’s) and eventually the downstream flow changes its condition to either supercritical or critical stages. It must be considered that the discharge coefficient is independent of symmetric or asymmetric situations. On the other hand, at the submergence stage for the spillway, the difference in the discharge coefficient can be due to tailwater submergence occurring in some convergence angles. Also, the flow depth and the piezometric pressure on the bottom and the toe of the spillway increased more in the symmetrical convergence angles in comparison with the asymmetrical convergence angles. Also, by decreasing the downstream channel width to the crest length (Lch/L), the flow depth and piezometric pressure increase subsequently. Results approved that the 60° convergence is the most economic convergence angle due to its capability in passing the largest flow discharge in the maximum head. The reason for this choice is that the crest length of this angle is 33% lesser than that of 120° convergence.

On the mass source internal wave making method for ALE based numerical wave tank

In this study, we perform simulations for free surface wave tracking inside a numerical tank. A Navier–Stokes solver, combined with the arbitrary Lagrangian–Eulerian method, is introduced. To generate free surface waves, a mass source internal wave-maker, proposed by Lin and Liu (J Waterw Port Coast Ocean Eng 125(4):207–215, 1999), is employed and implemented in OpenFOAM. A line mass source distribution throughout the water depth is used to mimic a real-world wave-maker. Specifically, two types of line source wave-makers for shallow water, namely the piston and flap types, are established, together with the block mass source model used by Lin and Liu (J Waterw Port Coast Ocean Eng 125(4):207–215, 1999) . Numerical results of free surface profiles and horizontal velocity profiles are validated by experimental data (Umeyama in J Waterw Port Coast Ocean Eng 137(2):85–94, 2010) . It is concluded that in the case of shallow-water wave propagation, the line source model is better than the block source model at maintaining the wave form. The internal wave-making method has its ceiling (wave height and water depth ratio $$H/h = 0.1$$ ) for applications in numerical wave-making. Flow contamination induced by the wave-maker itself must be considered in complex flow situations such as wave-current interactions.

Generating stable solitary waves with a piston-type wavemaker

The generation of stable and pure solitary waves in large-scale experimental flumes and numerical models is the focus of this study. Such waves give a better description of the target wave amplitude, has minimal amplitude dissipation during propagation and has negligible trailing waves. In the present study, the two solitary wave generation methodologies, namely, Goring's Method (GM) and the Malek-Mohammadi and Testik Method (MMTM), described in Goring (1979) and Malek-Mohammadi and Testik (2010) respectively, have been used to examine the solitary wave solutions of Boussinesq, Rayleigh, Grimshaw and Fenton, both experimentally and numerically for three different relative wave height (ε), ratios of 0.1, 0.3 and 0.6. Numerical modeling is done within a Smoothed Particle Hydrodynamics (SPH) framework developed in Valizadeh and Rudman (2017). For each ε value, we have compared the experimental and numerical results in terms of the free surface profiles and the phase speeds to give recommendations for the solitary wave solution and the generation methodology that demonstrates the best performance. Our results indicate that the Rayleigh solitary wave solution gives more accurate profiles in both experiments and numerical simulations. With respect to wave generation methodology, the MMTM gives the best results in the experiments, whereas, the GM describes the target waves better in our numerical SPH simulations.

Numerical investigation of waves slamming on a rotating flap in free motion using a fully nonlinear HOBEM

A time-domain higher-order boundary element method (HOBEM) with fully non-linear boundary conditions is established to investigate the slamming problem on a rotating flap in free motion. The mixed Eulerian-Lagrangian (MEL) boundary conditions with numerical damping layers are adopted to track the time-dependent free surface nodes, through which the influences of coupled disturbed waves from the outer boundaries are eliminated. The potential of each element within the thin long jet is calculated in the rotating coordinate system to overcome numerical instability induced by the local highly oscillatory pressure. The domain decomposition method and the unequal distribution scheme of meshes are simultaneously adopted to capture the falling jet with strong non-linearity. The auxiliary function method is then employed to calculate the pressure distribution, through which the mutual dependence between the body motion and the fluid flow is decoupled. The present numerical model is verified through comparing the flap motion response, dynamic characteristics and free surface elevations against the published experimental data and the Computational Fluid Dynamics (CFD) results. The parameter studies are performed to investigate the influences of flap properties and wave parameters. Detailed results are provided through free surface profile, rotation angle, angular velocity, torque response and pressure distribution.

Experimental reconstruction of extreme sea waves by time reversal principle

We report an experimental study of the reconstruction of real-ocean rogue waves in a laboratory environment using the time reversal (TR) methodology (Chabchoub & Fink, Phys. Rev. Lett. , vol. 112, 2014, 124101). Three different rogue wave measurements are used to validate the TR approach. The generation and accurate control of target free-surface profiles in a unidirectional wave flume using standard techniques, such as the New Wave theory (Tromans, Anaturk & Hagemeier, Proceedings of the First International Offshore and Polar Engineering Conference , 1991, pp. 64–71), are fairly challenging, especially for very steep and, thus, highly nonlinear extreme waves. The TR method, making use of the time reversibility of wave propagation and symmetry of the governing hydrodynamic equations of motion, leads to a simple two-step experimental procedure, the accuracy of which is investigated in this paper. The use of the TR procedure requires the appropriate Froude scaling in designing the model-scale experiments. The present study represents the first validation of the TR method to realistic irregular seas containing rogue waves. Three extreme wave profiles are tested to assess the applicability of the TR scheme to different wave configurations taking into account variable characteristics. This includes the famed New Year wave. The accuracy of the TR method is demonstrated with varying wave steepness values and propagation distances of the reverse reconstruction. It is demonstrated that the unidirectional TR reconstruction is robust, even in the presence of unavoidable wave breaking, known to be an irreversible process within the framework of any wave hydrodynamic evolution equation, and independently of complex environmental conditions or focusing mechanism at play in the sea.

Planar hydraulic jumps in thin film flow

We reformulate shallow water theory to understand viscous shear induced natural hydraulic jumps in channels slightly deviated from the horizontal. One of the interesting contributions of the study is a modified expression for Froude number to predict jumps in inclined channels. The proposed Froude number is different from the conventional expression which incorporates channel inclination as a straight forward component of gravity. This highlights the complexity that a jump can generate even in single phase laminar flow. We also obtain an analytical expression for predicting jump strength and show that the scaling relationship originally proposed for jump location in horizontal channels is applicable for both upslope and downslope flows. As expected, upslope flow aids jump formation and beyond a critical adverse tilt, a submerged jump results in subcritical flow right from the entry. On the other hand, both Reynolds number and channel tilt suppress the tendency to jump in downslope flows and below a critical downslope inclination, the flow remains supercritical throughout the channel length. The film thickness for fully developed flow can be predicted from the exact solution of the Navier–Stokes equations. As the theory encounters a singularity in the jump region, numerical simulations and experimental results have been used to obtain additional insights into the physics of jump formation. They have revealed the existence of submerged jump, wavy jump, smooth jump and no jump conditions as a function of liquid Reynolds number, scaled channel length and channel inclination. Such a variety of jump geometries in planar laminar flow has not been reported earlier. Both theory and simulations also reveal that the linear free surface profile upstream of the jump is a function of Reynolds number only, while the downstream profiles can be tuned by changing both Reynolds number as well as the channel length and tilt over the range of parameters studied. We thus demonstrate that, despite the simplicity and the approximations involved, shallow water equations formulated assuming self-similar velocity profiles can elucidate the physics of planar laminar jumps over slight inclinations, difficult to avoid in practice. The analytical and simulated results have been extensively validated with experimental data obtained from a specially designed test rig which ensures laminar flow before and after the jump. To the authors’ knowledge, almost no experimental study has to date been reported on films ‘thin enough’ to remain laminar even after the planar jump.

A 3D Lagrangian gradient smoothing method framework with an adaptable gradient smoothing domain‐constructing algorithm for simulating large deformation free surface flows

SummaryA novel smoothing particle hydrodynamics (SPH)‐like Lagrangian meshfree method, named as Lagrangian gradient smoothing method (L‐GSM), has been proposed to avoid the “tensile instability” issue in SPH simulation by replacing the SPH particle‐summation gradient approximation technique with a local grid‐based GSM gradient smoothing operator. The L‐GSM model has been proven effective and efficient when applied to a wide range of large deformation problems for fluids and flowing solids in two‐dimensional case. In this study, a three‐dimensional (3D) L‐GSM numerical framework is proposed for simulating large deformation problems with the existence of free surfaces through developing a widely adaptable 3D gradient smoothing domain (GSD) constructing algorithm. It includes three key novel ingredients: (i) the localized GSD based on an efficient distance‐oriented particle‐searching algorithm enabling both easy implementation and efficient computation; (ii) a novel algorithm for constructing 3D GSD to guarantee the effectiveness of the 3D GSM gradient operator adaptable to any extreme cases; (iii) a robust normalized 3D GSM gradient operator formulation that can restore the accuracy of gradient approximation even on boundary interface. The effectiveness of the proposed 3D GSD‐constructing algorithm is first verified under various distribution conditions of particles. The accuracy of the proposed adaptable 3D GSM gradient algorithm is then examined through conducting a series of numerical experiments with different spacing ratios. Finally, the 3D L‐GSM numerical framework is applied to solve a practical problem of free surface flows with large deformation: collapse of a soil column. The results reveal that the present adaptable 3D L‐GSM numerical framework can effectively handle the large deformation problems, like flowing solids, with a constantly changing arbitrary free surface profile.

Approximate analytical solution for supercritical flow in rectangular curved channels

In this study, we present an asymptotical mathematical model and an analytical solution for a supercritical flow in curved rectangular open channels. An original approach is proposed for solving the free-surface configuration and features of the flow in the presence of cross shock waves. The two-dimensional steady depth-averaged shallow water equations are transformed into an equivalent one-dimensional (1D) unsteady flow problem and a first order approximation is then obtained using small perturbation theory. Furthermore, the 1D asymptotic model is solved analytically by Laplace integral transformation and the two-dimensional flow field solution is reconstructed according to the translating planes. The free-surface profile along the outer chute wall and downstream channel was compared with the available experimental data, and the results indicated the satisfactory agreement of the maximum flow depth, peak positions, and wavelength. The proposed approach provides accurate predictions of the flow features and it facilitates the safe design of curved channel transitions.

Flow and Sediment Flux Asymmetry in a Branching Channel Delta

AbstractRiver deltas form complex branching patterns that distribute sediment to the coastal sea. The routing and storage of this sediment in deltas are poorly understood. We present results of a 1‐month study of the sediment and water transport through two branches of the Wax Lake Delta on the coast of Louisiana. The two channels maintained near‐equal total partitioning of flow and sediment discharge. East Pass was narrower and had higher tidally averaged velocities, lower tidal velocity fluctuations, more sediment flux, and less alluvial bed cover than Main Pass. We connected these differences to small differences in the geometry of the channels and feedbacks between these differences. East Pass was slightly shorter than Main Pass, leading to a steeper mean free surface profile, yielding higher subtidal currents and advective sediment fluxes. Main Pass received the tides from Atchafalaya Bay earlier than East Pass, allowing tides to reach their junction earlier from Main Pass. This led to Main Pass capturing tidal prism from East Pass and higher tidal velocity fluctuations in Main Pass. These fluctuations caused larger flow convergences in Main Pass, pumping sediment out of East Pass on tidal timescales. Since East Pass had higher mean velocities and lower tidal fluctuations, it spent less time in flow regimes that would allow the formation of alluvial bed cover. By explaining these asymmetries with physical arguments, we showed how geometric differences drive asymmetries in branching systems. Barrier island inlets, coastal lagoons, and other systems may display similar behavior.

Fully nonlinear investigation of focused wave slamming on a freely rotating flap

This paper concerns the focused wave slamming induced by a freely rotating flap using domain-decomposition higher-order boundary element method (HOBEM) with fully nonlinear conditions through which the process of jet detaching from body is successfully captured. The stable results of splash jet are obtained through linearly-varying-potential hypothesis. The time derivative of velocity potential on the body surface is calculated through the auxiliary function method, and the strong mutual dependence between the flap and the fluid flow is further decoupled accordingly. The non-uniform mesh scheme is adopted in the computational domain to guarantee both efficiency and accuracy, i.e., using fine meshes in the slamming region with strong nonlinearity. The abilities of present model to generate the focused wave and simulate wave slamming on a rotating flap, are respectively, verified. Relatively comprehensive parametric studies are performed, and the results based on flap's motion states, free surface profiles and pressure distributions point out the effects of frequency bandwidth, focused position, input wave amplitude, water depth and phase angle on the slamming specifically. It has been found the slamming occurs before wave groups focus completely and focused trough further enlarges the slamming pressure compared with focused crest.

Free-surface laminar flow of a Herschel–Bulkley fluid over an inclined porous bed

The current work presents a mathematical solution for the flow of a Herschel--Bulkley fluid over a porous bed. To obtain the velocity profile, a dimensional analysis is firstly conducted for the Darcian-like flow, showing that the ratio between pore and flow scales impose the domain of validity for the Beaver-like kinematic boundary condition. A friction velocity dependent only on fluid and porous medium properties was found to identify the scale of the Darcian velocity. After applying a modified kinematic boundary condition between free flow and Darcian-like flow, free-surface flow velocity profile was obtained, which can effectively predicts non-porous solutions for less rheological complex fluids. Dimensional analysis was then performed for the velocity profile solution, which allowed to identify the effect of the porous bed on flow properties. Experimental results from the literature were employed to identify the necessary conditions for yield stress fluids to have Darcian-like flow in natural open-channel flows. Sensitivity analysis pointed out that the porous medium permeability and non-Newtonian fluid parameters have greater influence on the velocity profile for pseudoplastic fluids than for dilatant ones.