Helly metric: Difference between revisions

Latest revision as of 11:23, 8 June 2013

In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953.^[1]

The Ursell number is derived from the Stokes wave expansion, a perturbation series for nonlinear periodic waves, in the long-wave limit of shallow water — when the wavelength is much larger than the water depth. Then the Ursell number U is defined as:

U\,=\,{\frac {H}{h}}\left({\frac {\lambda }{h}}\right)^{2}\,=\,{\frac {H\,\lambda ^{2}}{h^{3}}},

which is, apart from a constant 3 / (32 π²), the ratio of the amplitudes of the second-order to the first-order term in the free surface elevation.^[2] The used parameters are:

H : the wave height, i.e. the difference between the elevations of the wave crest and trough,
h : the mean water depth, and
λ : the wavelength, which has to be large compared to the depth, λ ≫ h.

So the Ursell parameter U is the relative wave height H / h times the relative wavelength λ / h squared.

For long waves (λ ≫ h) with small Ursell number, U ≪ 32 π² / 3 ≈ 100,^[3] linear wave theory is applicable. Otherwise (and most often) a non-linear theory for fairly long waves (λ > 7 h)^[4] — like the Korteweg–de Vries equation or Boussinesq equations — has to be used. The parameter, with different normalisation, was already introduced by George Gabriel Stokes in his historical paper on surface gravity waves of 1847.^[5]

Notes

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My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 In 2 parts, 967 pages.
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 722 pages.

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↑ Dingemans (1997), Part 1, §2.8.1, pp. 182–184.
↑ This factor is due to the neglected constant in the amplitude ratio of the second-order to first-order terms in the Stokes' wave expansion. See Dingemans (1997), p. 179 & 182.
↑ Dingemans (1997), Part 2, pp. 473 & 516.
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Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[2] Dingemans (1997), Part 1, §2.8.1, pp. 182–184.

[3] This factor is due to the neglected constant in the amplitude ratio of the second-order to first-order terms in the Stokes' wave expansion. See Dingemans (1997), p. 179 & 182.

[4] Dingemans (1997), Part 2, pp. 473 & 516.

[Stokes1847-5] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
Reprinted in: 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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+[[File:Sine wave amplitude.svg|right|thumb|Wave characteristics.]]
+In [[fluid dynamics]], the '''Ursell number''' indicates the [[nonlinearity]] of long [[ocean surface wave|surface gravity waves]] on a [[fluid]] layer. This [[dimensionless]] parameter is named after [[Fritz Ursell]], who discussed its significance in 1953.<ref>{{cite journal | first=F | last=Ursell | title=The long-wave paradox in the theory of gravity waves | journal=Proceedings of the Cambridge Philosophical Society | pages=685–694 | issue=4 | volume=49 | doi=10.1017/S0305004100028887 | year=1953|bibcode = 1953PCPS...49..685U }}</ref>
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+The Ursell number is derived from the [[Stokes wave|Stokes wave expansion]], a [[perturbation theory|perturbation series]] for nonlinear [[periodic function|periodic]] waves, in the long-wave [[limit (mathematics)|limit]] of [[waves and shallow water|shallow water]] — when the [[wavelength]] is much larger than the water depth. Then the Ursell number ''U'' is defined as:
+:<math>U\, =\, \frac{H}{h} \left(\frac{\lambda}{h}\right)^2\, =\, \frac{H\, \lambda^2}{h^3},</math>
+which is, apart from a constant 3 / (32 π<sup>2</sup>), the ratio of the [[amplitude]]s of the second-order to the first-order term in the [[free surface]] elevation.<ref>Dingemans (1997), Part 1, §2.8.1, pp. 182–184.</ref>
+The used parameters are:
+* ''H'' : the [[wave height]], ''i.e.'' the difference between the elevations of the wave [[crest (physics)|crest]] and [[trough (physics)|trough]],
+* ''h'' : the mean water depth, and
+* ''λ'' : the wavelength, which has to be large compared to the depth, ''λ'' ≫ ''h''.
+So the Ursell parameter ''U'' is the relative wave height ''H'' / ''h'' times the relative wavelength ''λ'' / ''h'' squared.
+For long waves (''λ'' ≫ ''h'') with small Ursell number, ''U'' ≪ 32 π<sup>2</sup> / 3 ≈ 100,<ref>This factor is due to the neglected constant in the amplitude ratio of the second-order to first-order terms in the Stokes' wave expansion. See Dingemans (1997), p. 179 & 182.</ref> linear wave theory is applicable. Otherwise (and most often) a non-linear theory for fairly long waves (''λ''&nbsp;>&nbsp;7&nbsp;''h'')<ref>Dingemans (1997), Part 2, pp. 473 & 516.</ref> — like the [[Korteweg–de Vries equation]] or [[Boussinesq approximation (water waves)|Boussinesq equations]] — has to be used.
+The parameter, with different normalisation, was already introduced by [[George Gabriel Stokes]] in his historical paper on surface gravity waves of 1847.<ref name=Stokes1847>{{cite journal | first= G. G. | last=Stokes | year= 1847 | title= On the theory of oscillatory waves | journal= Transactions of the Cambridge Philosophical Society | volume= 8 | pages= 441–455 }}<br>Reprinted in: {{cite book | first= G. G. | last=Stokes | year= 1880 | title= Mathematical and Physical Papers, Volume I | publisher= Cambridge University Press | pages= 197–229 | url= http://www.archive.org/details/mathphyspapers01stokrich }}</ref>
+== Notes ==
+{{reflist}}
+== References ==
+* {{cite book | title=Water wave propagation over uneven bottoms | first=M. W. | last=Dingemans | year=1997 | series=Advanced Series on Ocean Engineering | volume=13 | publisher=World Scientific | location=Singapore | isbn=981-02-0427-2 }} In 2 parts, 967 pages.
+* {{cite book | title=Introduction to nearshore hydrodynamics | first=I. A. | last=Svendsen | year=2006 | series=Advanced Series on Ocean Engineering | volume=24 | publisher=World Scientific | location=Singapore | isbn=981-256-142-0 }} 722 pages.
+{{NonDimFluMech}}
+[[Category:Dimensionless numbers of fluid mechanics]]
+[[Category:Fluid dynamics]]
+[[Category:Water waves]]

Helly metric: Difference between revisions

Latest revision as of 11:23, 8 June 2013

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