Microcontinuity

In oceanography, Ekman velocity – also referred as a kind of the residual ageostropic velocity as it derivates from geostrophy – is part of the total horizontal velocity (u) in the upper layer of water of the open ocean. This velocity, caused by winds blowing over the surface of the ocean, is such that the Coriolis force on this layer is balanced by the force of the wind.

Typically, it takes about two days for the Ekman velocity before it is directed at right angles to the wind. The Ekman velocity is named after the Swedish oceanographer Vagn Walfrid Ekman (1874–1954).

Theory

Through vertical eddy viscosity, winds act directly and frictionally on the Ekman layer, which typically is the upper 50–100m in the ocean. The frictional surface flow (u) is at an angle to the right of the wind (45 degrees if viscosity is uniform in the vertical z-direction). This surface flow then modifies the flow slightly beneath it, which then is slightly more to the right, and finally the exponentially-weaker-with-depth flow vectors get weaker with depth (exponentially weaker), die down at around 50–100 meters, and finally form a spiral, called the Ekman spiral. The angle of each successive layer as we move downward through the spiral depends on the strength and vertical distribution of the vertical eddy viscosity.

When the contributions from all the vertical layers are added up – the integration of the velocity over depth, from the bottom to the top of the Ekman layer – the total "Ekman transport" is exactly 90 degrees to the right of the wind direction in the Northern Hemisphere and left in the Southern Hemisphere.

Mathematical formulation

Suppose geostrophic balance is achieved in the Ekman layer, and wind stress is applied at the water surface:

$f{\hat {\boldsymbol {z}}}\times {\boldsymbol {u}}=-\nabla \phi +{\frac {\partial {\boldsymbol {\tau }}}{\partial z}},$ (1)

where $\phi =p/\rho _{0},\,$ ${\boldsymbol {\tau }}$ is the applied stress divided by $\rho _{0}\,$ (the mean density of water in the Ekman layer)；${\hat {\boldsymbol {z}}}$ is the unit vector in the vertical direction (opposing the direction of gravity).

The definition of Ekman velocity is the difference between the total horizontal velocity (${\boldsymbol {u}}$) and the geostrophic velocity (${\boldsymbol {u}}_{g}$):

${\boldsymbol {u}}_{e}={\boldsymbol {u}}-{\boldsymbol {u}}_{g}.$ (2)

As the geostropic velocity (${\boldsymbol {u}}_{g}$) is defined as

${\boldsymbol {u}}_{g}={\frac {1}{f}}{\hat {\boldsymbol {z}}}\times \nabla \phi ,$ (3)

therefore

$f{\hat {\boldsymbol {z}}}\times {\boldsymbol {u}}_{e}={\frac {\partial {\boldsymbol {\tau }}}{\partial z}}$ (4)

or

${\boldsymbol {u}}_{e}=-{\hat {\boldsymbol {z}}}\times {\Big (}{\frac {1}{f}}{\frac {\partial {\boldsymbol {\tau }}}{\partial z}}{\Big )}.$ (5)

Next, the Ekman transport is obtained by integrating the Ekman velocity from the bottom level ($z=z_{b}\,$) – at which the Ekman velocity vanishes – to the surface ($z=z_{t}\,$).

${\boldsymbol {U}}_{e}=\int _{z_{b}}^{z_{t}}{\boldsymbol {u}}_{e}\;dz=-{\hat {\boldsymbol {z}}}\times {\Big (}{\frac {{\boldsymbol {\tau }}_{t}-{\boldsymbol {\tau }}_{b}}{f}}{\Big )}.$ (6)

The SI unit of Ekman transport is: m²·s⁻¹, which is the horizontal velocity integrated in the vertical direction.

Usage

Based on Ekman theory and geostrophic dynamics, the analysis of near-surface currents, i.e. tropical Pacific near-surface currents, can be generated by using high resolution data of wind and altimeter sea level. The surface velocity is defined as the motion of a standard World Ocean Circulation Experiment/Tropical Ocean-Global Atmosphere (WOCE/TOGA) 15m drogue drifter. Near-surface Ekman velocity can be estimated with variables which best represent the ageostrophic motion of the WOCE/TOGA 15m drogue drifters relative to the surface wind stress. Geostrophic velocities are calculated with sea level gradients which are derived from TOPEX/Poseidon sea surface height analyses (TOPEX/Poseidon altimeter sea level anomalies from along-track data is used here, interpolated to 1°X1°grid, spanning the domain of 25°N-25°S,90°E-290°E, during Oct1992-Sep1998). Geostrophic and Ekman velocity are assumed to satisfy the lowest-order dynamics of the surface velocity, and they can be obtained independently from surface height and wind stress data. Standard f plan satisfies geostrophic balance, the lowest-order balance for quasi-steady circulation at higher latitudes. However, coriolis parameter f is close to zero near the equator, the geostropic balance is not satisfied as the velocity is proportional to the height gradiant divided by the coriolis parameter f. It has been shown in many studies that beta plane geostrophic approximation involving the second derivative of surface height is in good agreement with the observed velocities in the equatorial undercurrent, as a result, geostrophic currents which are near equator are obtained with a weighted blend of the equatorial beta-plane and conventional f-plane geostrophic equations.

A negative sea surface temperature (SST) anomaly prevails in the eastern equatorial Pacific from October to January. A zone of strong easterly Ekman flow propagates westward into the central Pacific basin near the date line during December–February. Relaxation of trade winds in the eastern coincided with the eastward propagation of the geostrophic flow east of 240°E (particularly in February), while westward currents dominated in the central and western equatorial region, which then reversal in the east, with weak local trade winds and weak upwelling along the coast, coincided with the onset of warm SST anomaly.(This anomaly first appeared off South America in March and April). Geostrophic current anomaly, like a Kelvin wave signature propagating eastward to South America between December and April can be easily discerned, and this arrival to South America also coincided with the above-mentioned SST anomaly onset. The geostrophic reversed in April to a strong eastward jet spanning the whole equatorial Pacific. As the El Niño SST anomaly developed during May and June, this eastward geostropic flow persisted.

See also

• Ekman layer
• Ekman spiral
• Ekman transport
• Ekman number

Footnotes

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.

References

• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
• Fu, L., E. J. Christensen, C. A. Yamarone, M. Lefebvfe, Y. Menard, M. Dorer, and P. Escudier, 1994: TOPEX/POSEIDON mission overview, J. Geophys. Res., 99, 24,369-24,382，doi:10.1029/94JC01761
• Pedlosky,J., Geophysical Fluid Dynamics, 624 pp., Springer-Verlag,New York, 1979.
• Lukas, R., and E. Firing, 1984：The geostrophic balance of the Pacific Equatorial Undercurrent, Deep Sea Res., Part A, 31, 61-66. doi:10.1016/0198-0149(84)90072-4
• Picaut, J., S. P. Hayes, and M. J. McPhaden, 1989：Use of the geostrophic approximation to estimate time-varying zonal currents at the equator, J. Geophys Res., 94, 3228-323. doi:10.1029/JC094iC03p03228

External links

• SIO 210: Introduction to Physical Oceanography – Dynamics IV: rotation and wind stress (Ekman layers) and other mixed layer topics
• Chapter 9 – Response of the Upper Ocean to Winds – Ekman Mass Transports
• Ocean Dynamics – Spring 2005
• El Nino Tropical Pacific Currents