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Froude Number (froude + number)

Distribution by Scientific Domains

Earth and Environmental Science	53%
Engineering	46%

Selected Abstracts

Transient flow patterns in a microfluidic chip with a complicated microstructure

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2008
Wei Zhang
Abstract The transient flow patterns of the boiling flow in a microfluidic chip with a complicated microstructure were studied at low mass fluxes and high heat fluxes. The periodic flow pattern in the timescale of milliseconds and the stratified flow pattern were observed. For a specific separated zone, the liquid film thickness was increased along the flow direction and the dry-out always occurred earlier at the microchannel upstream rather than downstream. However, for different microchannel zones, the dry-out took place earlier in the downstream zone. It was determined that the low liquid Froude number was responsible for the formation of the stratified flow. The large boiling number resulted in a large shear stress at the vapor,liquid interface, leading to the accumulation of the liquid in the microchannel downstream, causing the increased liquid film thickness along the flow direction. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(4): 224,231, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20201 [source]

Shape of isolated bubble in intermittent flows in a horizontal pipe

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2007
Gu Hanyang
Abstract An experimental study on the shape of a single bubble similar to those observed in a horizontal plug/slug flow was performed using visual observation and conductance probes. The results indicated that the shapes of the bubble nose and the bubble body depend on the Froude number defined by gas/liquid mixture velocity, whereas the shape of the back region of the bubble depends on both the Froude number and bubble length. The photographic images showed that the structural feature of the bubble head is related to the motion characteristics of the bubble. The transition from plug flow to slug flow occurs when the tail of the bubble changes from a staircase to hydraulic jump pattern with the increasing of the Froude number and bubble length. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(5): 276, 285, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20161 [source]

A field-based investigation to examine underwater soundscapes of five common river habitats,

HYDROLOGICAL PROCESSES, Issue 22 2010
Diego Tonolla
Abstract Aquatic river habitat types have been characterized and classified for over five decades based on hydrogeomorphic and ecological variables. However, few studies considered the generation of underwater sound as a unique property of aquatic habitats, and therefore as a potential information source for freshwater organisms. In this study, five common habitat types along 12 rivers in Switzerland (six replicates per habitat type) were acoustically compared. Acoustic signals were recorded by submerging two parallel hydrophones and were analysed by calculating the energetic mean as well as the temporal variance of ten octave bands (31·5 Hz,16 kHz). Concurrently, each habitat type was characterized by hydraulic and geomorphic variables, respectively. The average relative roughness, velocity-to-depth ratio, and Froude number explained most of the variance of the acoustic signals created in different habitat types. The average relative roughness predominantly affected middle frequencies (63 Hz,1 kHz), while streambed sediment transport increased high-frequency sound pressure levels (2,16 kHz) as well as the temporal variability of the recorded signal. Each aquatic habitat type exhibited a distinct acoustic signature or soundscape. These soundscapes may be a crucial information source for many freshwater organisms about their riverine environment. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Errors of kinematic wave and diffusion wave approximations for time-independent flows with infiltration and momentum exchange included

HYDROLOGICAL PROCESSES, Issue 9 2005
V. P. Singh
Abstract Error equations for kinematic wave and diffusion wave approximations were derived for time-independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF , 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF , 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2003
G. S. Stelling Professor
Abstract This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A numerical method to solve the m -terms of a submerged body with forward speed

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2002
W.-Y. Duan
Abstract To model mathematically the problem of a rigid body moving below the free surface, a control surface surrounding the body is introduced. The linear free surface condition of the steady waves created by the moving body is satisfied. To describe the fluid flow outside this surface a potential integral equation is constructed using the Kelvin wave Green function whereas inside the surface, a source integral equation is developed adopting a simple Green function. Source strengths are determined by matching the two integral equations through continuity conditions applied to velocity potential and its normal derivatives along the control surface. After solving for the induced fluid velocity on the body surface and the control surface, an integral equation is derived involving a mixed distribution of sources and dipoles using a simple Green function and one component of the fluid velocity. The normal derivatives of the fluid velocity on the body surface, namely the m -terms, are then solved by this matching integral equation method (MIEM). Numerical results are presented for two elliptical sections moving at a prescribed Froude number and submerged depth and a sensitivity analysis undertaken to assess the influence of these parameters. Furthermore, comparisons are performed to analyse the impact of different assumptions adopted in the derivation of the m -terms. It is found that the present method is easy to use in a panel method with satisfactory numerical precision. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Observations of downslope winds and rotors in the Falkland Islands

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 605 2005
S. D. Mobbs
Abstract A field campaign aimed at observing the near-surface flow field across and downwind of a mountain range on the Falkland Islands, South Atlantic, is described. The objective was to understand and eventually predict orographically generated turbulence. The instrumentation was based primarily on an array of automatic weather stations (AWSs), which recorded 30 s mean surface pressure, wind speed and direction (at 2 m), temperature and relative humidity for approximately one year. These measurements were supported by twice-daily radiosonde releases. The densest part of the AWS array was located to the south of the Wickham mountain range, across Mount Pleasant Airfield (MPA). In northerly flow the array provides a detailed study of the flow downwind of the mountain range. The dataset contains several episodes in which the flow downwind of the mountains is accelerated relative to the upwind flow. During some of these episodes short-lived (typically ,1 hour) periods of unsteady flow separation are observed and these are associated with the formation of rotors aloft. Such events present a significant hazard to aviation at MPA. Examination of radiosonde profiles suggests that the presence of a strong temperature inversion at a height similar to the mountain height is a necessary condition for both downwind acceleration and the formation of rotors. The data are used to show that the downwind fractional speed-up is proportional to the non-dimensional mountain height (based on upstream near-surface winds and a depth-averaged Brunt,Väisälä frequency diagnosed from radiosonde data). Similarly, a relationship is established between a quantity that describes the spatial variability of the flow downwind of the mountains and the upstream wind and depth-averaged Brunt,Väisälä frequency. The dependence of the flow behaviour on the Froude number (defined in the usual way for two-layer shallow-water flow) and ratio of mountain height to inversion height is presented in terms of a flow regime diagram. © Royal Meteorological Society, 2005. S. B. Vosper's and P. F. Sheridan's contributions are Crown copyright [source]

Boundary-layer variations due to orographic-wave breaking in the presence of rotation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 603 2004
B. 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]

On the representation of gravity waves in numerical models of the shallow-water equations

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 563 2000
A. R. Mohebalhojeh
Abstract Gravity waves, or imbalanced motions, that develop during the evolution of vortical flows in numerical models of the shallow water (SW) equations are examined in detail. The focus here is on nearly-balanced flows, with small but non-zero gravity-wave activity. For properly initialized flows, it is reasonable to expect small GW activity when Froude numbers Fr < 1 and Rossby numbers Ro , 1. The guiding principle in the present study is that an accurate representation of potential vorticity (PV) is the pre-requisite to a fair assessment of the generation of gravity waves. The contour-advective semi-Lagrangian (CASL) algorithm for the SW equations is applied, as it shows a remarkable improvement in the simulation of PV. However, it is shown that the standard CASL algorithm for SW leads to a noticeable numerical generation of gravity waves. The false generation of gravity waves can equivalently be thought of as the false, or numerical, breakdown of balance. In order to understand the maintenance of balance in the SW equations, a hierarchy of CASL algorithms is introduced. The main idea behind the new hierarchy is to implement PV inversion partially, balancing algorithms directly within the SW algorithm, while still permitting imbalanced motions. The results of the first three members of the hierarchy, CA0 (standard CASL), CA1, and CA2, are described and are compared with the results of two other SW algorithms, a pseudo-spectral and a semi-Lagrangian one. The main body of results is obtained for a highly ageostrophic regime of flow, with|Ro|max , 1 and Frmax , 0.5, where sub-index 'max' denotes maximum over the domain. Other flow regimes in the relevant parts of the Ro-Fr parameter space are also explored. It is found that, for a given resolution and Froude number, there is an optimal CASL algorithm, i.e. one which gives rise to the least numerical generation of gravity waves. [source]

Effects of fish size, time-to-fatigue and turbulence on swimming performance: a case study of Galaxias maculatus

JOURNAL OF FISH BIOLOGY, Issue 6 2003
V. I. Nikora
A simple relationship for the inanga Galaxias maculatus swimming velocity is suggested and tested in low and high turbulence channels. The relationship connects the swimming velocity with fish Reynolds and Froude numbers and can be used in both ecological analysis (e.g. habitat requirements) and management strategies (e.g. fishways design). Contrary to some previous studies and intuition, effects of turbulence on swimming performance appeared to be negligible. The most likely explanation for this result relates to mechanics of fish,turbulence interactions that may be dependent on both the turbulence scales and energy. The data suggest that future studies of turbulence effects on fish behaviour should involve, in addition to turbulence energetics, consideration of fish dimensions in relation to the spectrum of turbulence scales. [source]

Stability of some exact solutions of the shallow-water equations for testing numerical models in spherical geometry

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 632 2008
A. Staniforth
Abstract Five families of exact axisymmetric solutions of the nonlinear shallow-water equations in spherical geometry have recently been proposed as an aid to the development and testing of global numerical models. Sufficient conditions for the stability of these solutions are here derived to guide the choice of values for the family parameters. Thus it can be ensured that any significant time evolution occurring in a numerical model initialised with one of these exact solutions is of numerical origin, and does not reflect an inherent physical instability. With the caveat that only sufficient conditions for stability are examined, it appears that planetary rotation stabilises the solutions (as would be so if the flow were governed by barotropic vorticity dynamics), and that low Rossby and Froude numbers favour their stability. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd [source]

Agradient velocity, vortical motion and gravity waves in a rotating shallow-water model

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 601 2004
Georgi G. Sutyrin
Abstract A new approach to modelling slow vortical motion and fast inertia-gravity waves is suggested within the rotating shallow-water primitive equations with arbitrary topography. The velocity is exactly expressed as a sum of the gradient wind, described by the Bernoulli function, B, and the remaining agradient part, proportional to the velocity tendency. Then the equation for inverse potential vorticity, Q, as well as momentum equations for agradient velocity include the same source of intrinsic flow evolution expressed as a single term J(B, Q), where J is the Jacobian operator (for any steady state J(B,Q)=0). Two components of agradient velocity are responsible for the fast inertia-gravity wave propagation similar to the traditionally used divergence and ageostrophic vorticity. This approach allows for the construction of balance relations for vortical dynamics and potential vorticity inversion schemes even for moderate Rossby and Froude numbers assuming the characteristic value of |J(B,Q)|=, to be small. The components of agradient velocity are used as the fast variables slaved to potential vorticity that allows for diagnostic estimates of the velocity tendency, the direct potential vorticity inversion with the accuracy of ,2 and the corresponding potential vorticity-conserving agradient velocity balance model (AVBM). The ultimate limitations of constructing the balance are revealed in the form of the ellipticity condition for balanced tendency of the Bernoulli function which incorporates both known criteria of the formal stability: the gradient wind modified by the characteristic vortical Rossby wave phase speed should be subcritical. The accuracy of the AVBM is illustrated by considering the linear normal modes and coastal Kelvin waves in the f -plane channel with topography. Copyright © 2004 Royal Meteorological Society [source]