Analysis of Neutrally Stable Atmospheric Flow over a Two-Dimensional Forward-Facing Step

AIAA Journal ◽  
1980 ◽  
Vol 18 (1) ◽  
pp. 32-38 ◽  
Author(s):  
Walter Frost ◽  
Juergen Bitte ◽  
Chih Fang Shieh
Keyword(s):  
Two Dimensional ◽  
Atmospheric Flow ◽  
Forward Facing Step

Two-dimensional turbulence on the surface of a sphere

1978 ◽  
Vol 87 (2) ◽  
pp. 305-319 ◽  
Author(s):  
Cha-Mei Tang ◽  
Steven A. Orszag
Keyword(s):  
Energy Transfer ◽  
Spectral Methods ◽  
Large Scale ◽  
Spherical Geometry ◽  
Numerical Results ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Constants Of Motion ◽  
Cartesian Geometry ◽  
Back Transfer

Large-scale atmospheric flow shares certain attributes with two-dimensional turbulence. In this paper, we study the effect of spherical geometry on two-dimensional turbulence.Energy transfer is multi-component in spherical geometry in contrast to energy transfer among triads of wave vectors in Cartesian geometry. It follows that energy transfer is more local in spherical than in Cartesian geometry. Enstrophy transfer to higher wavenumbers in spherical geometry is less than enstrophy transfer to higher wavenumbers in Cartesian geometry. Since both energy and enstrophy are inviscid constants of motion, the back transfer of energy is also less in spherical than in Cartesian geometry. Therefore, with a finite viscosity, enstrophy decays more slowly in spherical geometry than in Cartesian geometry. Here these conjectures are tested numerically by spectral methods. The numerical results agree well with the conjectures.

scholarly journals Turbulent separation upstream of a forward-facing step

2013 ◽  
Vol 724 ◽  
pp. 284-304 ◽  
Author(s):  
D. S. Pearson ◽  
P. J. Goulart ◽  
B. Ganapathisubramani
Keyword(s):  
Boundary Layer ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Steady Increase ◽  
Separation Region ◽  
Two Dimensional ◽  
Low Velocity ◽  
Time Resolved ◽  
Displacement Thickness ◽  
Forward Facing Step

AbstractThe turbulent flow over a forward-facing step is studied using two-dimensional time-resolved particle image velocimetry. The structure and behaviour of the separation region in front of the step is investigated using conditional averages based on the area of reverse flow present. The relation between the position of the upstream separation and the two-dimensional shape of the separation region is presented. It is shown that when of ‘closed’ form, the separation region can become unstable resulting in the ejection of fluid over the corner of the step. The separation region is shown to grow simultaneously in both the wall-normal and streamwise directions, to a point where the maximum extent of the upstream position of separation is limited by the accompanying transfer of mass over the step corner. The conditional averages are traced backwards in time to identify the average behaviour of the boundary-layer displacement thickness leading up to such events. It is shown that these ejections are preceded by the convection of low-velocity regions from upstream, resulting in a three-dimensional interaction within the separation region. The size of the low-velocity regions, and the time scale at which the separation region fluctuates, is shown to be consistent with the large boundary layer structures observed in the literature. Instances of a highly suppressed separation region are accompanied by a steady increase in velocity in the upstream boundary layer.

scholarly journals Analytic solutions for Long's equation and its generalization

2017 ◽  
Vol 24 (4) ◽  
pp. 727-735
Author(s):  
Mayer Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Flow Over Topography ◽  
Isothermal Flows

Abstract. Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Examination of the flow near the leading edge of attached cavitation. Part 1. Detachment of two-dimensional and axisymmetric cavities

1998 ◽  
Vol 376 ◽  
pp. 61-90 ◽  
Author(s):  
A. TASSIN LEGER ◽  
S. L. CECCIO
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
Two Dimensional ◽  
Cavitating Flows ◽  
Layer Separation ◽  
Measured Flow ◽  
Forward Facing Step ◽  
Axisymmetric Cavities ◽  
Test Objects

The flow near the cavity detachment region of stable attached cavitation was examined using qualitative and quantitative flow visualization. The non-cavitating and cavitating flows around a hydrophilic brass and hydrophobic Teflon sphere and cylinder were examined. The location of non-cavitating boundary layer separation and cavity detachment was related to the free-stream Reynolds and cavitation numbers. The shape of the cavity near the detachment was greatly affected by the material of the cavitating object. The cavity interface on the hydrophilic test objects curved downstream to form a forward facing step. A region of recirculating fluid existed upstream of the cavity interface. The cavity detachment on the hydrophobic test objects was much closer to the location of boundary layer separation. The forward facing step and the recirculating region were nearly absent.The measured flow field near the surface of the brass sphere, cylinder, and hydrofoils under cavitating and non-cavitating conditions was used to calculate the position of two-dimensional laminar boundary layer separation. Thwaites' and Stratford's methods were used to predict the location of boundary layer separation upstream of the cavity detachment. The predictions compared well with the observed position of separation.

scholarly journals Long's equation in terrain following coordinates

2009 ◽  
Vol 16 (4) ◽  
pp. 533-541 ◽  
Author(s):  
M. Humi
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Gravity Wave ◽  
Two Dimensional ◽  
Complex Topography ◽  
Atmospheric Flow ◽  
Wave Patterns ◽  
Terrain Following ◽  
New Formulation

Abstract. Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorporates the terrain as part of the differential equation rather than the geometry of the domain. This new formulation enables us to compute analytically steady state gravity wave patterns over complex topography in some limiting cases of the parameters that appear in this equation.

scholarly journals Analytic Solutions for Long's Equation and its Generalization

2017 ◽  
Author(s):  
Mayer Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Flow Over Topography ◽  
Isothermal Flows

Abstract. Two dimensional, steady state, stratified, isothermal, atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic type solutions in addition to regular gravity waves. These new analytical solutions provide insights about the propagation and amplitude of gravity waves over topography.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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