322,848 research outputs found
Viscous spreading of non-Newtonian gravity currents on a plane
No full textA gravity current originated by a power-law viscous fluid propagating on a horizontal rigid plane below a fluid of lower density is examined. The intruding fluid is considered to have a pure Ostwald power-law constitutive equation. The set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces. The conditions under which the above assumptions are valid are examined and a self-similar solution in terms of a nonlinear ordinary differential equation is derived. For the release of a time-variable volume of fluid, the shape of the gravity current is determined numerically using an approximate analytical solution derived close to the current front as a starting condition. A closed-form analytical expression is derived for the special case of the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes
Stokes flow between sinusoidal walls
No full textIn this paper, we study two-dimensional Stokes flow between sinusoidal walls. A stream function is introduced, thus transforming the Stokes equation into a biharmonic one, whose solution is then derived for a single periodic cell of length equal to the wall fluctuation wavelength, and for a given pressure drop. Relevant boundary conditions are the no-slip and no-flow conditions on the boundary, as well as those deriving from the periodicity and an auxiliary condition based on an energy argument. For such a mathematical problem, an approximate solution is possible via a series expansion in terms of a small parameter equal to the ratio between the mean channel width and the wavelength. We present closed-form second-order expressions for stream function, flow rate, and velocity components, and discuss the implications of the zero-order solution (lubrication approximation) for different values of two dimensionless parameters. Expressions derived for the velocity components show flow reversal for strong channel sinuosity; they will be useful for several purposes, such as study of solute transport in rough-walled fractures or of heat and mass transfer in conduits with wavy wall
Viscous spreading of non-Newtonian gravity currents in radial geometry
No full textA gravity current originated by a power-law viscous fluid propagating in axisymmetric geometry on a horizontal rigid plane below a fluid of lesser density is examined. The intruding fluid is considered to have a pure power-law constitutive equation. The set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces. The conditions under which the above assumptions are valid are examined and a self-similar solution in terms of a nonlinear ordinary differential equation is derived for the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes
Generating and scaling fractional Brownian motion on finite domains
No full textPower variograms of statistically isotropic or anisotropic fractal fields (common in earth science) are weighted integrals of variograms representing statistically homogeneous fields (modes) having mutually uncorrelated increments. Large- and small-scale cutoffs were previ-ously assumed proportional to length scales of the sampling window and data support. We verify this assumption numerically for two-dimensional isotropic fractional Brownian motion (fBm). It was previously concluded semi-empirically that, for Hurst coefficient H = 0.25, the constant of proportionality is μ = 1/3. We confirm this but find μ to vary with mode type and H. We find that due to lack of ergodicity, sample fBm variograms generated on finite windows exhibit directional dependence and differ sharply between realizations. Many realizations are required to obtain an average sample variogram resembling the theoretical power model, especially for persistent fields. We propose generating fBm on finite windows using truncated power variograms and provide guidance for doing so effectively
Scaling Effects on Finite-Domain Fractional Brownian Motion
No full textPower variograms of statistically isotropic or anisotropic fractal fields are weighted integrals of variograms representing statistically homogeneous fields (modes) having mutually uncorrelated increments. Large- and small-scale cutoffs were previ-ously assumed proportional to length scales of the sampling window and data support. We verify this assumption numerically for two-dimensional isotropic fractional Brownian motion (fBm). It was previously concluded semi-empirically that, for Hurst coefficient H = 0.25, the constant of proportionality is μ = 1/3. We confirm this but find μ to vary with mode type and H. We find that due to lack of ergodicity, sample fBm variograms generated on finite windows exhibit directional dependence and differ sharply between realizations. Many realizations are required to obtain an average sample variogram resembling the theoretical power model, especially for persistent fields. We propose generating fBm on finite windows using truncated power variograms and provide guidance for doing so effectively
Stokes flow between sinusoidal walls
No full textIn this paper, we study two-dimensional Stokes flow between sinusoidal walls. A stream function is introduced, thus transforming the Stokes equation into a biharmonic one, whose solution is then derived for a single periodic cell of length equal to the wall fluctuation wavelength, and for a given pressure drop. Relevant boundary conditions are the no-slip and no-flow conditions on the boundary, as well as those deriving from the periodicity and an auxiliary condition based on an energy argument. For such a mathematical problem, an approximate solution is possible via a series expansion in terms of a small parameter equal to the ratio between the mean channel width and the wavelength. We present closed-form second-order expressions for stream function, flow rate, and velocity components, and discuss the implications of the zero-order solution (lubrication approximation) for different values of two dimensionless parameters. Expressions derived for the velocity components show flow reversal for strong channel sinuosity; they will be useful for several purposes, such as study of solute transport in rough-walled fractures or of heat and mass transfer in conduits with wavy walls
Laminar flow of a Harschel-Bulkley fluid in channels of finite width
No full textLaminar flow of a viscoplastic fluid in a shallow and wide channel is examined under the long-wave approximation. The fluid is described by the three-parameter Herschel-Bulkley constitutive equation. The complete set of equations governing the flow is presented, generalizing earlier results for a Bingham fluid. The paper then focuses on steady uniform flow: for different geometries of the channel (polynomials like triangular and parabolic, trapezoidal, and rectangular), the velocity distribution and the total discharge are derived analytically as functions of the fluid properties and of the channel cross-section. Results show the existence of dead zones close to bed and banks of the channel; discharges through any given cross-section are higher for dilatant than for pseudo-plastic fluids
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