A Topographic Drag Closure Built on an Analytical Base Flux

2005 ◽  
Vol 62 (7) ◽  
pp. 2302-2315 ◽  
Author(s):  
Stephen T. Garner
Keyword(s):  
Dimensional Analysis ◽  
Wave Train ◽  
Average Height ◽  
Height Distribution ◽  
Ocean Tides ◽  
Linear Solution ◽  
Flow Over Topography ◽  
Linear Drag ◽  
The Vertical Distribution ◽  
State Assumption

Abstract Topographic drag schemes depend on grid-scale representations of the average height, width, and orientation of the subgrid topography. Until now, these representations have been based on a combination of statistics and dimensional analysis. However, under certain physical assumptions, linear analysis provides the exact amplitude and orientation of the drag for arbitrary topography. The author proposes a computationally practical closure based on this analysis. Also proposed is a nonlinear correction for nonpropagating base flux. This is patterned after existing schemes but is better constrained to match the linear solution because it assumes a correlation between mountain height and width. When the correction is interpreted as a formula for the transition to saturation in the wave train, it also provides a way of estimating the vertical distribution of the momentum forcing. The explicit subgrid height distribution causes a natural broadening of the layers experiencing the forcing. Linear drag due to simple oscillating flow over topography, which is relevant to ocean tides, has almost the same form as for the stationary atmospheric problem. However, dimensional analysis suggests that the nonpropagating drag in this situation is mostly due to topographic length scales that are small enough to keep the steady-state assumption satisfied.

Dependence of Shape Parameter of Weibull Distribution on Wave Spectral Width and Nonlinearity

2008 ◽  
Author(s):  
Changliang Li ◽  
Bingchen Liang ◽  
Lin Zhao
Keyword(s):  
Weibull Distribution ◽  
Wave Height ◽  
Shape Parameter ◽  
Wave Train ◽  
Spectral Width ◽  
Rayleigh Distribution ◽  
Height Distribution ◽  
Irregular Wave ◽  
Wave Height Distribution ◽  
Ocean Environment

In practice, the wave height distribution associated with an irregular wave train is always mathematically modeled as a Rayleigh distribution. However, the realistic ocean wave height distribution might deviate from a Rayleigh distribution. The present study demonstrates that a better mathematical model for wave height distribution under realistic ocean environment is a Weibull distribution. In comparison with a Rayleigh distribution, a Weibull distribution has the flexibility on choosing its “shape parameter”. According to the nonlinear Monte Carlo simulations, this study investigates the nonlinearity and spectral width effects on the shape parameter for the Weibull wave height distribution. A new empirical formula for calculating the shape parameter is proposed, which can be used easily in application.

scholarly journals The vertical distribution of atmospheric ozone in high latitudes

1935 ◽  
Vol 148 (865) ◽  
pp. 598-603 ◽  
Keyword(s):  
Vertical Distribution ◽  
Ultra Violet ◽  
Early Summer ◽  
Thin Layers ◽  
Ozone Content ◽  
Average Height ◽  
The Sun ◽  
Lower Height ◽  
The Vertical Distribution ◽  
Very High

In conjunction with Dr. Götz we have recently given an account of a new method of finding the vertical distribution of ozone in the atmosphere, and have used this method to determine the distribution above Arosa, Switzerland. It was found that the average height of the ozone in the atmosphere was much lower than had previously been thought, and these results have since been confirmed by Professor Regener who has obtained ultra-violet spectra from small balloons up to a height of 30 km. So far the vertical distribution of ozone has not been found anywhere except in Switzerland and in view of the connection between the variations in amount of ozone and atmospheric pressure distribution, and with polar and equatorial air currents, it was of interest to know the distribution in high and low latitudes also. By the kindness of Professor Vegard and the Norwegian Committee for Geophysics arrangements were made to take one of the special photoelectric spectro-photometers for measuring ozone to Tromsø (latitude 69° 40' N., 18° 57' E.) where observations were carried out at the Nordlysobservatorium during May and June, 1934. It had been hoped that by taking observations in the early summer some days with very high that by taking observations in the early summer some days with very high ozone content would have been found; unfortunately this did not occur and the ozone content only ranged from 0·230 cm to 0·294 cm, 13 good days' observations being obtained in all. The method of deducing the distribution of ozone which was used was similar to that employed in the Swiss observations (Method B) to which reference should be made for all details. Suffice it to say that for purposes of calculation both air and ozone are assumed to be concentrated into a number of thin layers. Owing to our better knowledge of the distribution gained through the Arosa work it was decided to recalculate the results for the assumed fundamental distribution, the effect of the lower height of Tromsø also being allowed for. Since the sun never set during part of the time, it was impossible to get observations when the sun was on, or below, the horizon; hence the "sunset theory" used at Arosa, which gives the amount of ozone in the highest layer, could not be employed and we have assumed that the ozone content of the atmosphere above 40 km is the same as that found at Arosa. Further, it was decided that there would be a gain in general accuracy if it were assumed that the amount of ozone in the lowest layer was equal to that in the next higher layer, since this reduced the number of variables.

Nonlinear Wave Interaction with Vertical Cylinder of Large Diameter

1977 ◽  
Vol 21 (02) ◽  
pp. 120-124
Author(s):  
H. Raman ◽  
N. Jothi Shankar ◽  
P. Venkatanarasaiah
Keyword(s):  
Nonlinear Wave ◽  
Large Diameter ◽  
Vertical Cylinder ◽  
Wave Interaction ◽  
Diffraction Theory ◽  
Second Order ◽  
Wave Forces ◽  
Height Distribution ◽  
Linear Solution ◽  
Nonlinear Diffraction

A nonlinear diffraction theory for interaction of waves with a vertical cylinder of large diameter is presented. The nonlinear second-order solution is examined in comparison with a linear solution and other existing second-order solutions. The computed nonlinear wave forces are found to compare very well with the experimental results. The effect of nonlinearity on the crest height distribution around the cylinder is also studied. It is found that as the ratio of wave height to water depth decreases the nonlinear solution approaches the linear solution.

scholarly journals Local average height distribution of fluctuating interfaces

2017 ◽  
Vol 95 (1) ◽  
Author(s):  
Naftali R. Smith ◽  
Baruch Meerson ◽  
Pavel V. Sasorov
Keyword(s):  
Average Height ◽  
Height Distribution ◽  
Fluctuating Interfaces ◽  
Local Average

scholarly journals Growth Delay and Height-Age: Alternative Indicators of Population Health Based on Child Height Distributions

2020 ◽  
Vol 4 (Supplement_2) ◽  
pp. 865-865
Author(s):  
Liina Mansukoski ◽  
Huma Qamar ◽  
Ashley Aimone ◽  
Nandita Perumal ◽  
Diego Bassani ◽  
...  
Keyword(s):  
Chronological Age ◽  
Growth Delay ◽  
Demographic And Health Surveys ◽  
Average Height ◽  
Height Distribution ◽  
Population Mean ◽  
Child Height ◽  
Population Average ◽  
Z Scores ◽  
Height For Age

Abstract Objectives Alternative indicators may enrich the description of population height distributions alongside age- and sex-standardised height-for-age Z-scores (HAZ) and prevalence of under-5 stunting. We propose two indicators of linear growth that account for the partial biological dependency of child height on growth tempo: height-age, which is the age at which the observed height distribution would be normal; and, population ‘growth delay’, which is the difference between height-age and chronological age. Methods Using data from 145 Demographic and Health Surveys from 64 countries (2000–2018), population-average height ages were estimated by transforming child heights (in cm) into WHO Growth Standard (WHO-GS) HAZ-values. Population mean HAZ at a given age was estimated using predictions from linear spline models, where HAZ was regressed on age for each survey. Mean HAZ values were back-transformed to heights using WHO-GS-LMS parameters to identify the age at which the observed population mean height was closest to WHO-GS-median height (referred to as the height-age). Growth delay was computed by subtracting height-age from chronological age. Primary analyses were based on height-age at 5 years (60 months) chronological age. For comparison, mean height-for-age differences (HAD) and under 5-stunting prevalence (in %) were calculated. Results In the most recent surveys for each country (N = 64), height-age at 60 months chronological age ranged from 40.9–58.1 months, such that growth delay ranged from 1.9–19.1 months. Mean HAZ ranged from −2.32 to −0.22 Z-scores, and under-5 stunting prevalence from 7.1–56.0%. A comparison of growth delay at 5-years, under-5 stunting prevalence and mean HAZ at 5-years showed that countries were similarly ranked by all indicators. Country case studies showed some differences in the trajectories of growth delay by age, versus mean HAZ or HAD by age. Conclusions Population-average height-age and growth delay, derived from anthropometric surveys, are biologically consistent and interpretable indicators of child health and nutritional status. These indicators may be preferred over mean HAZ or stunting prevalence for conveying the critical role of growth tempo and later catch-up potential in height. Funding Sources SickKids Child Growth and Development Fellowship.

scholarly journals On the Flaring of Thick Discs of Galaxies: Insights from Simulations

2020 ◽  
Author(s):  
Joaquín García de la Cruz ◽  
Marie Martig ◽  
Ivan Minchev ◽  
Philip James
Keyword(s):  
Surface Density ◽  
Milky Way ◽  
Large Fraction ◽  
High Surface ◽  
Scale Height ◽  
The Other ◽  
Height Distribution ◽  
Thick Disc ◽  
Cosmological Context ◽  
The Vertical Distribution

Abstract Using simulated galaxies in their cosmological context, we analyse how the flaring of mono-age populations (MAPs) influences the flaring and the age structure of geometrically-defined thick discs. We also explore under which circumstances the geometric thin and thick discs are meaningfully distinct components, or are part of a single continuous structure as in the Milky Way. We find that flat thick discs are created when MAPs barely flare or have low surface density at the radius where they start flaring. When looking at the vertical distribution of MAPs, these galaxies show a continuous thin/thick structure. They also have radial age gradients and tend to have quiescent merger histories. Those characteristics are consistent with what is observed in the Milky Way. Flared thick discs, on the other hand, are created when the MAPs that flare have a high surface density at the radius where they start flaring. The thick discs’ scale-heights can either be dominated by multiple MAPs or just a few, depending on the mass and scale-height distribution of the MAPs. In a large fraction of these galaxies, thin and thick discs are clearly distinct structures. Finally, flared thick discs have diverse radial age gradients and merger histories, with galaxies that are more massive or that have undergone massive mergers showing flatter age radial gradients in their thick disc.

scholarly journals The height of watermelons with wall - Extended Abstract

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Thomas Feierl
Keyword(s):  
Average Height ◽  
Height Distribution ◽  
Famous Result ◽  
Plane Trees ◽  
International Audience ◽  
De Bruijn

International audience We derive asymptotics for the moments of the height distribution of watermelons with $p$ branches with wall. This generalises a famous result by de Bruijn, Knuth and Rice on the average height of planted plane trees, and a result by Fulmek on the average height of watermelons with two branches.

A Note on the Evaluation of the Wave Resistance of Two-Dimensional Bodies from Measurements of the Downstream Wave Profile

1983 ◽  
Vol 27 (02) ◽  
pp. 90-92
Author(s):  
James H. Duncan
Keyword(s):  
Wave Train ◽  
Wave Theory ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Third Order ◽  
The Subject ◽  
Lord Kelvin ◽  
The Waves ◽  
The Vertical Distribution

As a body moves horizontally at constant speed in the proximity of a free surface it experiences a resistance due to the generation of waves. In two-dimensional cases the determination of this resistance from properties of the wave train has been the subject of several investigations. The linear theory was first presented by Lord Kelvin [1] 2 and later by Havelock [2] and Lamb [8]. Wehausen and Laitone [4] have derived an exact resistance formula in terms of the vertical distribution of velocity in the waves and the downstream surface height profile. This formula was later evaluated by Salvesen and von Kerczek [5] using third-order Stokes wave theory.

In situ investigation of the primary recrystallization of alpha titanium in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 634-635
Author(s):  
S. Naka ◽  
R. Penelle ◽  
R. Valle
Keyword(s):  
Dimensional Analysis ◽  
Texture Evolution ◽  
Cold Work ◽  
Three Dimensional ◽  
Primary Recrystallization ◽  
Thin Foils ◽  
In Situ Investigation ◽  
Grain Growth Model ◽  
Alpha Titanium

The in situ experimentation technique in HVEM seems to be particularly suitable to clarify the processes involved in recrystallization. The material under investigation was unidirectionally cold-rolled titanium of commercial purity. The problem was approached in two different ways. The three-dimensional analysis of textures was used to describe the texture evolution during the primary recrystallization. Observations of bulk-annealed specimens or thin foils annealed in the microscope were also made in order to provide information concerning the mechanisms involved in the formation of new grains. In contrast to the already published work on titanium, this investigation takes into consideration different values of the cold-work ratio, the temperature and the annealing time.Two different models are commonly used to explain the recrystallization textures i.e. the selective grain growth model (Beck) or the oriented nucleation model (Burgers). The three-dimensional analysis of both the rolling and recrystallization textures was performed to identify the mechanismsl involved in the recrystallization of titanium.

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