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Coriolis Force (Corioli + force)
Selected AbstractsConvection in the Earth's core driven by lateral variations in the core,mantle boundary heat fluxGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2000Steven John Gibbons Summary Moving core fluid maintains an isothermal core,mantle boundary (CMB), so lateral variations in the CMB heat flow result from mantle convection. Such variations will drive thermal winds, even if the top of the core is stably stratified. These flows may contribute to the magnetic secular variation and are investigated here using a simple, non-magnetic numerical model of the core. The results depend on the equatorial symmetry of the boundary heat flux variation. Large-scale equatorially symmetric (ES) heat flux variations at the outer surface of a rapidly rotating spherical shell drive deeply penetrating flows that are strongly suppressed in stratified fluid. Smaller-scale ES heat flux variations drive flows less dominated by rotation and so less inhibited by stratification. Equatorially anti-symmetric flux variations drive flows an order of magnitude less energetic than those driven by ES patterns but, due to the nature of the Coriolis force, are less suppressed by stratification. The response of the rotating core fluid to a general CMB heat flow pattern will then depend strongly on the subadiabatic temperature profile. Imposing a lateral heat flux variation linearly related to a model of seismic tomography in the lowermost mantle drives flow in a density stratified fluid that reproduces some features found in flows inverted from geomagnetic data. [source] Incorporating spatially variable bottom stress and Coriolis force into 2D, a posteriori, unstructured mesh generation for shallow water modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009D. Michael Parrish Abstract An enhanced version of our localized truncation error analysis with complex derivatives (LTEA,CD ) a posteriori approach to computing target element sizes for tidal, shallow water flow, LTEA+CD , is applied to the Western North Atlantic Tidal model domain. The LTEA + CD method utilizes localized truncation error estimates of the shallow water momentum equations and builds upon LTEA and LTEA,CD-based techniques by including: (1) velocity fields from a nonlinear simulation with complete constituent forcing; (2) spatially variable bottom stress; and (3) Coriolis force. Use of complex derivatives in this case results in a simple truncation error expression, and the ability to compute localized truncation errors using difference equations that employ only seven to eight computational points. The compact difference molecules allow the computation of truncation error estimates and target element sizes throughout the domain, including along the boundary; this fact, along with inclusion of locally variable bottom stress and Coriolis force, constitute significant advancements beyond the capabilities of LTEA. The goal of LTEA + CD is to drive the truncation error to a more uniform, domain-wide value by adjusting element sizes (we apply LTEA + CD by re-meshing the entire domain, not by moving nodes). We find that LTEA + CD can produce a mesh that is comprised of fewer nodes and elements than an initial high-resolution mesh while performing as well as the initial mesh when considering the resynthesized tidal signals (elevations). Copyright © 2008 John Wiley & Sons, Ltd. [source] Tidal dissipation in rotating fluid bodies: a simplified modelMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009Gordon I. Ogilvie ABSTRACT We study the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body. The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous incompressible fluid. Centrifugal effects are neglected, but the Coriolis force is considered in full, and dissipation occurs through viscous or frictional forces. The dissipation rate exhibits a complicated dependence on the tidal frequency and generally increases with the size of the core. In certain intervals of frequency, efficient dissipation is found to occur even for very small values of the coefficient of viscosity or friction. We discuss the results with reference to wave attractors, critical latitudes and other features of the propagation of inertial waves within the fluid, and comment on their relevance for tidal dissipation in planets and stars. [source] Coriolis effects in mesoscale flows with sharp changes in surface conditionsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 603 2004J. C. R. Hunt Abstract A general linearized ,shallow-layer' perturbation model, where the approximately neutral lower layer of thickness h0 is situated below a stable upper layer (i.e. an inversion with temperature change ,T), is developed for steady, mesoscale atmospheric flows over low-lying topography whose height is less than h0. With the Coriolis parameter f, sharp changes in surface conditions (surface roughness, terrain elevation, heat flux) are modelled as a distributed body force through the lower layer. The Froude number of this layer is small. Typical cases of mesoscale discontinuities are examined. The results are compared with those of a continuously stratified model and observations, and with numerical mesoscale model results for a meteorological case-study over the Dover Straits region of the English Channel. The main results are: (i) If the wind direction is parallel to the edge-line separating the change in surface roughness, there are marked increases and decreases in these coastal winds whose maxima can occur over the sea within a distance of order h0(,1 km) of a coast. The strength of these wind ,jets', which do not occur in the absence of Coriolis force, decrease away from the edge-line gradually over transverse length-scales of the order of the Rossby deformation radius . Changes to surface roughness lead to an increase in the wind speed perturbation in the downwind direction until limited by non-linear effects. When the wind is at an angle to a roughness change or coast, the maxima occur at the coastline. (ii) Where there are sharp changes in the orientation of contours of constant roughness length (e.g. at capes or bays on the coastline or wakes of high-drag areas), ,detached' jets are formed in the downwind direction. (iii) Changes in surface elevation at a coast produce effects different from those of roughness; a positive wind jet forms parallel to the coast in the direction of the wind when the coast is on the right (looking downwind) and a negative jet when the coast is on the left. These jets do not increase in strength along the flow and do not persist downwind. (iv) Coriolis effects also determine how the inversion height varies near coastlines and surface roughness changes; for example, increasing/decreasing inland over a distance LR when stable airflow approaches from the sea and the coast is on the right/left of an observer looking downwind (opposite in the southern hemisphere). This mechanism is consistent with observed increasing/decreasing cloudiness inland from a coast. (v) Other effects occur where the surface elevation changes gradually over a distance of order LR (e.g. a wide, shallow valley); frictional effects are comparable with buoyancy and Coriolis forces, and flows perpendicular to the elevation change are deflected to the left (in the northern hemisphere), as observed in the Rhine valley. (vi) The shallow-layer model simulates the major features of the low-level flow field computed using the numerical mesoscale model with a horizontal resolution of 2 km, i.e. of order h0. Broad features were captured using a coarser resolution of 12 km. (vii) The analysis provides a method of estimating errors associated with finite grid size in numerical mesoscale models. Copyright © 2004 Royal Meteorological Society [source] Boundary-layer variations due to orographic-wave breaking in the presence of rotationTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 603 2004B. Grisogono Abstract A mesoscale numerical model is used to study the atmospheric boundary-layer (ABL) response to nonlinear orographic forcing with Coriolis effect, f, over a mountain with length (the cross-wind component) comparable to the Rossby radius of deformation, LR. The orographic-wave breaking occurring for Froude number Fr<1, affected by f>0, intensifies on the northern flank for westerly flows, as also found in other recent studies. A cumulative effect occurs as the Coriolis force lifts the northern ABL top and generates a stronger low-level jet (LLJ) than on the southern side. A differential layering also appears, since the specific humidity is higher in the lower southern ABL than in the related northern ABL, and vice versa. By contrast, there are higher values of the turbulent kinetic energy and humidity in the upper northern ABL. The breaking of flow symmetry around the orography due to f changes both the vertical vorticity and horizontal divergence field, (,, D), it modulates eddies and turbulence leading to the differential layering of the ABL. The stronger northern LLJ and its weaker southern counterpart, both meandering, together with the asymmetric wave breaking, induce strong lee-side fluctuations of the (,, D) field in the presence of f. The enhanced (,, D) production due to wave breaking over the distance , LR, the primary atmosphere,orography resonance occurs mainly in the vertical, while the ,f -enhancement' occurs in the horizontal plane. In this way, the initial mesoscale forcing may extend its effects over the synoptic scale. Copyright © 2004 Royal Meteorological Society [source] Mean electromotive force proportional to mean flow in MILD turbulenceASTRONOMISCHE NACHRICHTEN, Issue 1 2010K.-H. Rädler Abstract In mean-field magnetohydrodynamics the mean electromotive force due to velocity and magnetic-field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the , effect, is important for large-scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross-helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Prediction of turbulent flow and heat transfer within rotating U-shaped passagesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 6 2006Liu Chuan Kai Abstract Numerical predictions of three-dimensional flow and heat transfer are presented for rotating serpentine passages with and without rib turbulators. The coolant air is pressurized and its operating conditions are selected closely to match actual turbine operating parameters. Two different arrangements of rib turbulators were studied: (1) transverse ribs on the leading and trailing walls and (2) transverse ribs on all four walls. The rib height-to-hydraulic diameter ratio (e/Dh) is 0.143; the rib pitch-to-height ratio (s/e) is 7. Results for the rib-roughened serpentine passages were compared with those of smooth ones calculated in the literature. It was shown that a significant enhancement is achieved by means of rib turbulators in a serpentine passage at a stationary state as well as in a rotating state. In the radially-outward flow passages, the effect of rotation on heat transfer is relatively prominent. The secondary flows induced by the Coriolis forces are most intensive in the channel with four ribbed surfaces. The heat transfer after a 180° sharp turn in the smooth channel is influenced more by the sharp-turn-induced flow than the rib-roughened ones. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(6): 410,420, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20125 [source] Solution of non-linear dispersive wave problems using a moving finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2007Abigail Wacher Abstract The solution of the fully non-linear time-dependent two-dimensional shallow water equations is considered. Dispersive effects due to the Coriolis forces are taken into account. Such effects are of major importance in geophysical fluid dynamics applications. The recently proposed string gradient weighted moving finite element method is extended for this class of problems. This method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to non-dispersive wave problems; here its performance under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation, is studied. Optimal rates of convergence are obtained. Results for some example problems of water hump release are presented. Non-linear and linearized solutions are compared. Copyright © 2006 John Wiley & Sons, Ltd. [source] Swelling effect on the dynamic behaviour of composite cylindrical shells conveying fluidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006M. H. Toorani Abstract This paper presents a semi-analytical investigation of a fluid,structure system. Both isotropic and composite cylindrical shells filled with or subjected to a flowing fluid have been considered in this study. The structure may be uniform or non-uniform in the circumferential direction. The hybrid finite element approach, shearable shell theory and velocity potential flow theory have been combined to establish the dynamic equations of the coupled system. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration of the equilibrium equations. The linear potential flow theory is applied to describe the fluid effects that lead to the inertial, centrifugal and Coriolis forces. The axisymmetric, beam-like and shell modes of vibrations in both cases of uniform and non-uniform cylindrical shells are investigated. Fluid elastic stability of a structure subjected to a flowing fluid is also studied. This theory yields the high and the low eigenvalues and eigenmodes with comparably high accuracy. Reasonable agreement is found with other theories and experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Dynamics and Coupling Actuation of Elastic Underactuated ManipulatorsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2003Tie Shi Zhao This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton-Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three-link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc. [source] Coriolis effects in mesoscale flows with sharp changes in surface conditionsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 603 2004J. C. R. Hunt Abstract A general linearized ,shallow-layer' perturbation model, where the approximately neutral lower layer of thickness h0 is situated below a stable upper layer (i.e. an inversion with temperature change ,T), is developed for steady, mesoscale atmospheric flows over low-lying topography whose height is less than h0. With the Coriolis parameter f, sharp changes in surface conditions (surface roughness, terrain elevation, heat flux) are modelled as a distributed body force through the lower layer. The Froude number of this layer is small. Typical cases of mesoscale discontinuities are examined. The results are compared with those of a continuously stratified model and observations, and with numerical mesoscale model results for a meteorological case-study over the Dover Straits region of the English Channel. The main results are: (i) If the wind direction is parallel to the edge-line separating the change in surface roughness, there are marked increases and decreases in these coastal winds whose maxima can occur over the sea within a distance of order h0(,1 km) of a coast. The strength of these wind ,jets', which do not occur in the absence of Coriolis force, decrease away from the edge-line gradually over transverse length-scales of the order of the Rossby deformation radius . Changes to surface roughness lead to an increase in the wind speed perturbation in the downwind direction until limited by non-linear effects. When the wind is at an angle to a roughness change or coast, the maxima occur at the coastline. (ii) Where there are sharp changes in the orientation of contours of constant roughness length (e.g. at capes or bays on the coastline or wakes of high-drag areas), ,detached' jets are formed in the downwind direction. (iii) Changes in surface elevation at a coast produce effects different from those of roughness; a positive wind jet forms parallel to the coast in the direction of the wind when the coast is on the right (looking downwind) and a negative jet when the coast is on the left. These jets do not increase in strength along the flow and do not persist downwind. (iv) Coriolis effects also determine how the inversion height varies near coastlines and surface roughness changes; for example, increasing/decreasing inland over a distance LR when stable airflow approaches from the sea and the coast is on the right/left of an observer looking downwind (opposite in the southern hemisphere). This mechanism is consistent with observed increasing/decreasing cloudiness inland from a coast. (v) Other effects occur where the surface elevation changes gradually over a distance of order LR (e.g. a wide, shallow valley); frictional effects are comparable with buoyancy and Coriolis forces, and flows perpendicular to the elevation change are deflected to the left (in the northern hemisphere), as observed in the Rhine valley. (vi) The shallow-layer model simulates the major features of the low-level flow field computed using the numerical mesoscale model with a horizontal resolution of 2 km, i.e. of order h0. Broad features were captured using a coarser resolution of 12 km. (vii) The analysis provides a method of estimating errors associated with finite grid size in numerical mesoscale models. Copyright © 2004 Royal Meteorological Society [source] A study of the Coriolis effect on the fluid flow profile in a centrifugal bioreactorBIOTECHNOLOGY PROGRESS, Issue 4 2009Christopher J. Detzel Abstract Increasing demand for tissues, proteins, and antibodies derived from cell culture is necessitating the development and implementation of high cell density bioreactors. A system for studying high density culture is the centrifugal bioreactor (CCBR), which retains cells by increasing settling velocities through system rotation, thereby eliminating diffusional limitations associated with mechanical cell retention devices. This article focuses on the fluid mechanics of the CCBR system by considering Coriolis effects. Such considerations for centrifugal bioprocessing have heretofore been ignored; therefore, a simpler analysis of an empty chamber will be performed. Comparisons are made between numerical simulations and bromophenol blue dye injection experiments. For the non-rotating bioreactor with an inlet velocity of 4.3 cm/s, both the numerical and experimental results show the formation of a teardrop shaped plume of dye following streamlines through the reactor. However, as the reactor is rotated, the simulation predicts the development of vortices and a flow profile dominated by Coriolis forces resulting in the majority of flow up the leading wall of the reactor as dye initially enters the chamber, results are confirmed by experimental observations. As the reactor continues to fill with dye, the simulation predicts dye movement up both walls while experimental observations show the reactor fills with dye from the exit to the inlet. Differences between the simulation and experimental observations can be explained by excessive diffusion required for simulation convergence, and a slight density difference between dyed and un-dyed solutions. Implications of the results on practical bioreactor use are also discussed. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source] | ||||||||||||||||