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[[File:Mitch 01.jpg|right|300px|thumb|Model forecast of [[Hurricane Mitch]] created by the [[Geophysical Fluid Dynamics Laboratory]]. The arrows are wind vectors and the grey shading indicates an [[equivalent potential temperature]] surface that highlights the surface inflow layer and [[eye (cyclone)|eyewall]] region.]] | |||
'''Geophysical fluid dynamics''' is the study of naturally occurring, large-scale flows on [[Earth]] and other [[planet]]s. It is applied to the motion of [[fluid]]s in the [[ocean]] and [[outer core]], and to [[gases]] in the [[atmosphere]] of Earth and other planets. Two features that are common to many of the phenomena studied in geophysical fluid dynamics are [[Rotating reference frame|rotation of the fluid]] due to the planetary rotation and stratification (layering). The applications of geophysical fluid dynamics do not generally include the circulation of the [[mantle (geology)|mantle]], which is the subject of [[geodynamics]], or fluid phenomena in the [[magnetosphere]]. Smaller scale flow features (those negligibly influenced by the rotation of the Earth) are the province of fields such as [[hydrology]], [[physical oceanography]] and [[meteorology]].<ref>{{harvnb|Pedlosky|1987|loc=pages 1-2}}</ref> | |||
== Fundamentals == | |||
To describe the flow of geophysical fluids, equations are needed for [[Momentum#Conservation|conservation of momentum]] (or [[Newton's second law]]) and [[conservation of energy]]. The former leads to the [[Navier-Stokes equations]]. Further approximations are generally made. First, the fluid is assumed to be [[incompressible flow|incompressible]]. Remarkably, this works well even for a highly compressible fluid like air as long as [[sound]] and [[shock wave]]s can be ignored. Second, the fluid is assumed to be a [[Newtonian fluid]], meaning that there is a linear relation between the [[shear stress]] {{math|<var>τ</var>}} and the [[Deformation (mechanics)#Strain|strain]] {{math|''u''}}, for example | |||
:<math> \tau = \mu \frac{d u}{d x},</math> | |||
where {{math|<var>μ</var>}} is the [[viscosity]]. Under these assumptions the Navier-Stokes equations are | |||
:<math> | |||
\overbrace{\rho \Big( | |||
\underbrace{\frac{\partial \mathbf{v}}{\partial t}}_{ | |||
\begin{smallmatrix} | |||
\text{Eulerian}\\ | |||
\text{acceleration} | |||
\end{smallmatrix}} + | |||
\underbrace{\mathbf{v} \cdot \nabla \mathbf{v}}_{ | |||
\begin{smallmatrix} | |||
\text{Advection} | |||
\end{smallmatrix}}\Big)}^{\text{Inertia (per volume)}} = | |||
\overbrace{\underbrace{-\nabla p}_{ | |||
\begin{smallmatrix} | |||
\text{Pressure} \\ | |||
\text{gradient} | |||
\end{smallmatrix}} + | |||
\underbrace{\mu \nabla^2 \mathbf{v}}_{\text{Viscosity}}}^{\text{Divergence of stress}} + | |||
\underbrace{\mathbf{f}}_{ | |||
\begin{smallmatrix} | |||
\text{Other} \\ | |||
\text{body} \\ | |||
\text{forces} | |||
\end{smallmatrix}}. | |||
</math> | |||
The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (a [[Lagrangian and Eulerian specification of the flow field|Lagrangian frame of reference]]). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity and [[advection]], a measure of the rate of flow in or out of a small region.<ref name=Tritton>{{harvnb|Tritton|1990}}</ref> | |||
The equation for energy conservation is essentially an equation for heat flow. If heat is transported by [[Thermal conduction|conduction]], the heat flow is governed by a [[diffusion]] equation. If there are also [[buoyancy]] effects, for example hot air rising, then [[natural convection]] can occur. | |||
== Buoyancy and stratification == | |||
Fluid that is less dense than its surroundings tends to rise until it has the same density as its surroundings. If there is not much energy input to the system, it will tend to become [[Stratigraphy|stratified]]. On a large scale, Earth's atmosphere is [[Atmosphere of Earth#Principal layers|divided into a series of layers]]. Going upwards from the ground, these are the [[troposphere]], [[stratosphere]], [[mesosphere]], [[thermosphere]], and [[exosphere]]. | |||
The density of air is mainly determined by temperature and [[water vapor]] content, the density of [[seawater|sea water]] by temperature and [[salinity]], and the density of lake water by temperature. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a [[pycnocline]] (density), [[thermocline]] (temperature), [[halocline]] (salinity), or [[chemocline]] (chemistry, including oxygenation). | |||
The same buoyancy that gives rise to stratification also drives [[gravity wave]]s. If the gravity waves occur within the fluid, they are called [[internal wave]]s. | |||
In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using the [[Boussinesq approximation (buoyancy)|Boussinesq approximation]]. This ignores variations in density except where they are multiplied by the [[gravitational acceleration]] {{math|''g''}}. | |||
If the pressure depends only on density and vice versa, the fluid dynamics are called [[Barotropic fluid|barotropic]]. In the atmosphere, this corresponds to a lack of fronts, as in the [[tropics]]. If there are fronts, the flow is [[Baroclinity|baroclinic]], and instabilities such as [[cyclone]]s can occur.<ref name=Haby>{{harvnb|Haby|2011}}</ref> | |||
=== Barotropic waves === | |||
*[[Kelvin wave]] | |||
*[[Rossby wave]] | |||
== Rotation == | |||
*[[Coriolis effect]] | |||
*[[Circulation (fluid dynamics)|Circulation]] | |||
*[[Kelvin's circulation theorem]] | |||
*[[Vorticity equation]] | |||
*[[Thermal wind]] | |||
*[[Geostrophic current]] | |||
*[[Geostrophic wind]] | |||
*[[Taylor–Proudman theorem]] | |||
*[[Hydrostatic equilibrium]] | |||
*[[Ekman spiral]] | |||
*[[Ekman layer]] | |||
== General circulation == | |||
*[[Atmospheric circulation]] | |||
*[[Ocean current]] | |||
*[[Ocean dynamics]] | |||
*[[Thermohaline circulation]] | |||
*[[Boundary current]] | |||
*[[Sverdrup balance]] | |||
*[[Subsurface currents]] | |||
== Notes == | |||
{{Reflist}} | |||
== See also == | |||
*[[Geophysical Fluid Dynamics Laboratory]] | |||
== References == | |||
*{{cite book | |||
|last = Cushman-Roisin | |||
|first = Benoit | |||
|last2 = Beckers | |||
|first2 = Jean-Marie | |||
|title = Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects | |||
|edition = Second | |||
|publisher = [[Academic Press]] | |||
|date = October 2011 | |||
|isbn = 978-0-12-088759-0 | |||
|url = http://www.elsevierdirect.com/product.jsp?isbn=9780120887590 | |||
|ref = harvnb | |||
|accessdate = October 14, 2010 | |||
}} | |||
* Gill, A.E. (1982). ''Atmosphere-Ocean Dynamics''. Academic Press. | |||
*{{cite web | |||
|last1=Haby | |||
|first1=Jeff | |||
|title=Barotropic and baroclinic defined | |||
|url=http://www.theweatherprediction.com/habyhints/49/ | |||
|work=Haby's weather forecasting hints | |||
|accessdate=September 2011 | |||
|ref=harvnb | |||
}} | |||
* McWilliams, J. (2006). ''Fundamentals of Geophysical Fluid Dynamics''. Cambridge University Press. | |||
* Monin, A.S. (1990). ''Theoretical Geophysical Fluid Dynamics.'' Kluwer. | |||
*{{cite book | |||
|last = Pedlosky | |||
|first = Joseph | |||
|title = Geophysical Fluid Dynamics | |||
|edition = Second | |||
|publisher = [[Springer-Verlag]] | |||
|year = 1987 | |||
|isbn = 0-387-96387-1 | |||
|ref = harvnb | |||
}} | |||
* Salmon, R. (1998). ''Lectures on Geophysical Fluid Dynamics''. Oxford University Press. | |||
*{{cite book | |||
|last=Tritton | |||
|first=D. J. | |||
|title = Physical Fluid Dynamics | |||
|edition = Second | |||
|year = 1990 | |||
|publisher = [[Oxford University Press]] | |||
|isbn = 0-19-854489-8 | |||
|ref = harvnb | |||
}} | |||
* Vallis, G.K. (2006). ''Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation''. Cambridge University Press. | |||
== External links == | |||
*[http://www.whoi.edu/page.do?pid=7937 Geophysical Fluid Dynamics Program ([[Woods Hole Oceanographic Institution]])] | |||
*[http://www.ocean.washington.edu/research/gfd/index.html Geophysical Fluid Dynamics Laboratory ([[University of Washington]])] | |||
{{Geophysics navbox}} | |||
{{physical oceanography}} | |||
[[Category:Atmospheric dynamics]] | |||
[[Category:Geophysics]] | |||
[[Category:Fluid dynamics]] | |||
[[Category:Physical oceanography]] |
Latest revision as of 16:54, 21 March 2013
Geophysical fluid dynamics is the study of naturally occurring, large-scale flows on Earth and other planets. It is applied to the motion of fluids in the ocean and outer core, and to gases in the atmosphere of Earth and other planets. Two features that are common to many of the phenomena studied in geophysical fluid dynamics are rotation of the fluid due to the planetary rotation and stratification (layering). The applications of geophysical fluid dynamics do not generally include the circulation of the mantle, which is the subject of geodynamics, or fluid phenomena in the magnetosphere. Smaller scale flow features (those negligibly influenced by the rotation of the Earth) are the province of fields such as hydrology, physical oceanography and meteorology.[1]
Fundamentals
To describe the flow of geophysical fluids, equations are needed for conservation of momentum (or Newton's second law) and conservation of energy. The former leads to the Navier-Stokes equations. Further approximations are generally made. First, the fluid is assumed to be incompressible. Remarkably, this works well even for a highly compressible fluid like air as long as sound and shock waves can be ignored. Second, the fluid is assumed to be a Newtonian fluid, meaning that there is a linear relation between the shear stress Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.
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Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.
There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity
This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.
A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.
If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.
Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer., for example
where Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.
Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.
There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity
This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.
A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.
If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.
Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. is the viscosity. Under these assumptions the Navier-Stokes equations are
The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (a Lagrangian frame of reference). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity and advection, a measure of the rate of flow in or out of a small region.[2]
The equation for energy conservation is essentially an equation for heat flow. If heat is transported by conduction, the heat flow is governed by a diffusion equation. If there are also buoyancy effects, for example hot air rising, then natural convection can occur.
Buoyancy and stratification
Fluid that is less dense than its surroundings tends to rise until it has the same density as its surroundings. If there is not much energy input to the system, it will tend to become stratified. On a large scale, Earth's atmosphere is divided into a series of layers. Going upwards from the ground, these are the troposphere, stratosphere, mesosphere, thermosphere, and exosphere.
The density of air is mainly determined by temperature and water vapor content, the density of sea water by temperature and salinity, and the density of lake water by temperature. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a pycnocline (density), thermocline (temperature), halocline (salinity), or chemocline (chemistry, including oxygenation).
The same buoyancy that gives rise to stratification also drives gravity waves. If the gravity waves occur within the fluid, they are called internal waves.
In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using the Boussinesq approximation. This ignores variations in density except where they are multiplied by the gravitational acceleration Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.
Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.
There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity
This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.
A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.
If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.
Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer..
If the pressure depends only on density and vice versa, the fluid dynamics are called barotropic. In the atmosphere, this corresponds to a lack of fronts, as in the tropics. If there are fronts, the flow is baroclinic, and instabilities such as cyclones can occur.[3]
Barotropic waves
Rotation
- Coriolis effect
- Circulation
- Kelvin's circulation theorem
- Vorticity equation
- Thermal wind
- Geostrophic current
- Geostrophic wind
- Taylor–Proudman theorem
- Hydrostatic equilibrium
- Ekman spiral
- Ekman layer
General circulation
- Atmospheric circulation
- Ocean current
- Ocean dynamics
- Thermohaline circulation
- Boundary current
- Sverdrup balance
- Subsurface currents
Notes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
See also
References
- 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 - Gill, A.E. (1982). Atmosphere-Ocean Dynamics. Academic Press.
- Template:Cite web
- McWilliams, J. (2006). Fundamentals of Geophysical Fluid Dynamics. Cambridge University Press.
- Monin, A.S. (1990). Theoretical Geophysical Fluid Dynamics. Kluwer.
- 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 - Salmon, R. (1998). Lectures on Geophysical Fluid Dynamics. Oxford University Press.
- 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 - Vallis, G.K. (2006). Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press.