Topic

# Froude number

About: Froude number is a research topic. Over the lifetime, 6231 publications have been published within this topic receiving 121944 citations. The topic is also known as: Froude number for mass transfer.

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TL;DR: A mathematical model for terrestrial running is presented, based on a leg with the properties of a simple spring, which shows that at high forward speed, KLEG is a nearly linear function of both U and V, while the effective vertical stiffness is a quadratic function of U.

1,107 citations

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TL;DR: In this article, it was shown that the log-law can be applied strictly only to the nearwall region and the von K´rm´n constant κ and integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number.

Abstract: A powerful two‐color Laser Doppler Anemometer (LDA) system, with direct digital signal processing has been used to measure accurately the longitudinal and vertical velocity components in two‐dimensional, fully‐developed open‐channel flow over smooth beds. The law of the wall and the velocity defect law were re‐examined because the log‐law has been often applied to open channels without detailed verification. It was found that the log‐law can be applied strictly only to the near‐wall region. In this region, the von K´rm´n constant κ and the integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number. As the Reynolds number becomes larger, the deviation from the log‐law cannot be neglected in the outer region. This deviation can be expressed well by Coles' wake function which involves a Reynolds‐number dependent parameter Π. The distributions of eddy viscosity and mixing length were evaluated and found to depend on Π. All the data including the...

892 citations

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TL;DR: In this article, a simple model is given that describes the response of the upper ocean to an imposed wind stress, which is taken to mix thoroughly a layer of depth h, and to erode the stably stratified fluid below.

Abstract: A simple model is given that describes the response of the upper ocean to an imposed wind stress. The stress drives both mean and turbulent flow near the surface, which is taken to mix thoroughly a layer of depth h, and to erode the stably stratified fluid below. A marginal stability criterion based on a Froude number is used to close the problem, and it is suggested that the mean momentum has a strong role in the mixing process. The initial deepening is predicted to obey where u. is the friction velocity of the imposed stress, N the ambient buoyancy frequency, and t the time. After one-half inertial period the deepening is arrested by rotadeon at a depth h = 22/4 u.{(Nf)+ where f is the Coriolis frequency. The flow is then a “mixed Ekman” layer, with strong inertial oscillations superimposed on it. Three quarters of the mean energy of the deepening layer is found to be kinetic, and only one-quarter potential. Heating and cooling are included in the model, but stress dominates for time-scales of ...

632 citations

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Brown University

^{1}TL;DR: In this paper, the Taylor expansion of the Dirichlet Neumann operator in homogeneous powers of the surface elevation η and the velocity potential ϕ is proposed to simulate the water wave problem in a channel for a fluid of finite or infinite depth.

610 citations

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TL;DR: The literature on the structure and behaviour of gravity currents is reviewed in this paper, with particular attention to turbidity currents, though reference is also made to comparable behaviour in pyroclastic flows.

Abstract: Summary
The literature on the structure and behaviour of gravity currents is reviewed, with emphasis on some recent studies, and with particular attention to turbidity currents, though reference is also made to comparable behaviour in pyroclastic flows. Questions of definition are discussed, in particular the distinction between dense currents, which may deposit en masse, and more dilute currents. High-density dispersions may exist as a discrete, independently moving layer beneath a more dilute flow, as the basal part of a continuous density distribution or possibly as a transient depositional layer. Existing theory appears inadequate to explain the behaviour of some high-density dispersions. Surge-type currents are contrasted with quasi-steady currents, which may be generated by a variety of mechanisms including direct feed by rivers in flood. Such fluvially generated currents provide one means of generating currents with reversing buoyancy. Geologically significant turbidity currents are impractical for direct study owing to their large scale and (often) destructive nature. Small-scale laboratory currents offer a wealth of insights into turbidity current behaviour. This paper summarizes recent experimental studies that focus on the physical structure of gravity currents, with emphasis on the velocity and turbulence structure, the vertical density distribution and the stability of stratification. Preliminary quantification of the turbulence structure (including controls on turbulent entrainment, turbulent kinetic energy, Reynolds stresses and turbulence production) has been facilitated by recent technological developments that have allowed the measurement of instantaneous fluctuations in both velocity and concentration. Laboratory models, however, generally involve substantial simplification, and require compromises in some parameters to achieve adequate scaling of the parameters of most interest. Mathematical modelling also provides important insights into turbidity current behaviour. We discuss various approaches to modelling, ranging from simple hydraulic equations to systems of partial differential equations that explicitly treat conservation of momentum, fluid and sediment mass, and turbulent kinetic energy. The application for which the model is designed (i.e. to calculate mean head velocity or to create an instantaneous two-dimensional contour plot of downstream velocity in a current) determines the complexity of the mathematical model required. The behaviour of suspension currents around topography is complex and depends upon the relative height of the topography, and upon the density and velocity structure of the current. Many interactions with topography are well described by the internal Froude number, Fri. Both reflection and deflection of currents may occur on the upstream side of topography, depending upon Fri. On the downstream side of topography, flow separation, lee waves or hydraulic jumps may occur.

550 citations