Showing papers on "Fluid parcel published in 1991"

Some Interesting Issues in Incompressible Fluid Dynamics, Both in the Continuum and in Numerical Simulation

Abstract: Publisher Summary This chapter presents some issues in incompressible fluid dynamics, both in the continuum and in numerical simulation. One of the principle themes considered is the common, simple, and convenient mathematical model of a fluid that states that the mass conservation law is one that requires the fluid to be incompressible everywhere and for all time. It is found that the process of differentiating the constraint equation can have far-reaching consequences, especially while discussing the semi-discrete form of the NS equations through differential-algebraic equations. The PPE provides the hope of separating the velocity calculation from the pressure calculation. Boundary situations other than impenetrable, no-slip walls, or specified inflow velocities occur quite frequently, perhaps most often in flow-thru domains in which part of the boundary sees fluid leaving the domain. It is found that the Kinney model invokes a discrete time approximation and introduces vortex sheets to reduce the spurious slip velocity to zero.

Static Stability—An Update

Abstract: Static stability should not be evaluated from the local lapse rate. There is a growing body of observations, such as within portions of mixed layers and forest canopies, showing that the whole sounding should be considered to evaluate stability. Air parcels can move across large vertical distances to create turbulence within regions that would otherwise have been considered stable or neutral according to classical local definitions. A nonlocal determination of static stability is presented that accounts for both the local lapse rate and for convective air parcels moving across finite distances. Such a method is necessary to properly estimate turbulence, dispersion, and vertical fluxes that affect our weather and climate forecasts. Teachers of introductory meteorology courses and textbook authors are encouraged to revise their static stability discussions to follow air parcel displacements from beginning to end.

Coriolis-effect in mass flow metering

Abstract: The paper aims at a detailed description of the physical background, for the so-called Coriolis mass flow meter. It presents essentially an analysis of the (free) vibration modes of a fluid conveying straight pipe segment. Due to the inertial effects of the flowing fluid, mainly the Coriolis force, these modes deviate in shape (and in frequency) from those appearing in the absence of fluid motion. The effect of fluid inertia may, therefore, be exploited for the purpose of flow measurement. The analysis is performed under a simplifying approximation: The pipe is considered as a beam, the fluid as a moving string. This approximation leaves the fluid with only one degree of freedom, connected with its mean velocity, and eliminates an infinity of degrees of freedom of the pipe. Yet it keeps, the essential features of the phenomenon. The equations describing the vibrations are derived variationally, with the constraint of a common vibration amplitude of both fluid and pipe. The Lagrange multiplier associated with the constraint gives the interaction force between pipe and fluid. The modes are determined by a perturbation procedure, wherein the small (perturbation) parameter is related to the fluid velocity. The analysis shows, as main result, how the time delay between the vibrations of two appropriately chosen points of the pipe may serve to determine the mass flow rate of the fluid. Other aspects of the problem, like the precise role of the Coriolis force, are considered. The possible improvement of the used approximation is discussed.

A Simple Model of the Climatology and Variability of the Low-Level Wind Field in the Tropics

Abstract: A simple model of the low-level wind field in the entire tropics is presented. The dynamics are the same as those within the familiar Gill model, i.e., linear, steady state, contained within a single vertical mode and damped by Rayleigh friction. Convective atmospheric heating can occur if a lifted air parcel is buoyant relative to its surroundings, and the heating is computed with reference to the cloud model of Yanai et al. Radiative cooling is represented by a Newtonian cooling to an equilibrium lapse rate. The model is forced by surface temperature and humidity. A qualitatively correct representation of the climatological flow is achieved. The main differences between model and observations relate to the model's inability to reproduce the intensity and limited spatial scale of the convergence zones. Model simulations of anomalous circulations are subject to the same limitations. Problems related to the lack of an explicit boundary layer in the model, the poor representation of radiation, and ...

The compressible mixing layer

Abstract: Despite important efforts of many scientists over the decades, turbulence continues to persist as one of the least understood field of fluid mechanics, and therefore much improvements in fluid flow systems are still expected from a better understanding of this physics.

Numerical simulation of incompressible fluid flows

Abstract: In this paper we discuss temporal, spatial, and architectural aspects of the numerical simulation of time-dependent incompressible fluid flows. In particular, we consider: high-order operator-integration-factor time-splitting methods; sliding-mesh spectral mortar-element spatial discretizations; and data-parallel distributed-memory medium-grained parallel solution techniques. Numerous flow examples are presented.

Theoretical Determination of the Fractal Dimension of Fluid Parcel Trajectories in Large and Meso-Scale Flows

Abstract: Recent work suggests that Lagrangian parcel trajectories in large and meso-scale flows can have a fractal dimension. Drifting buoy trajectories may be viewed as fractal curves in the plane of the ocean’s surface and have typical fractal dimensions of about D = 1.30 ± 0.06 in a range of scales normally attributed to geostrophic turbulence. Herein we address some of the theoretical issues and show that a simple Hamiltonian system with Eulerian velocity spectrum k-δ (δ ~0.5) can describe many of the measured properties of the drifter motions. Generally speaking the dimension D is related to δ, to the dispersion relation of the flow and to nonlinear dynamics. It is tempting to use the dimension D to describe some of the variability inherent in some oceanic motions; in particular we show that fluid parcels do not obey the classical diffusion law (Dt, D the diffusion coefficient) but instead diffuse anomalously (Dt2/D). The mixing and transport of passive tracers are generally enhanced in flows of this type. We emphasize that the focus herein is on dynamic fractality, i.e. fractality arises as a consequence of the Hamiltonian equations of motion and hence may be used as a tool for probing dynamical behavior. This contrasts to more traditional studies in which fractality is often studied for its own sake or for artistic stimulation, independent of physical content.

Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow

Abstract: This presentation introduces a low-dimensional model for an incompressible, viscous, rotating fluid flow in a cylindrical vessel. The low-dimensional model is formed by projecting the transport equations on some subspace, spanned by known solutions to the discretized Navier-Stokes equations. Using the software package PATH, a program that analyses finite non-linear ODE-systems, such as our low-dimensional model, we find the bifurcation path with the Reynolds number as modelparameter. Thus, the transition from a stationary to a periodic solution in physical space is recognized as a super-critical Hopf-bifurcation in low-dimensional space.