Length is normalized by the approximate natural wavelength. What is the relationship between ekman transport and ekman. Near western boundaries the dynamics are governed by the western boundary. In light of the universitys newly released policy regarding covid19 recommending the community minimize social contact we encourage students to utilize virtual options when seeking support or information from the earth systems program. Ekman transport is the integrated horizontal flow in the boundary layer resulting from the balance between frictional forces at the surface or bottom and coriolis.
The momentum equations will be taken in the form du dt. Approximate solutions for the ekman transport for flows with small rossby number, but arbitrary geometry, are also given. Note that the ekman transport is independent of the vertical structure and even the. Chapter 4 ekman layer transports, ekman pumping, and the. The ekman spiral we consider now an elegant method of describing the wind in the boundary layer, due originally to v. Ekman transport, the horizontal mass transport associated with a windstress applied on the ocean surface, is modified by the vorticity of ocean currents, leading to what has been termed the. Ekman transport on the left side of the jet is u a and on the right side, u b. This is the volume transport multiplied by density. We would like to show you a description here but the site wont allow us. The ekman number is the ratio of the eddy viscosity the rotation rate and scale depth squared. The details of the eddy viscosity profile have no influence on this result, and the calculation is very robust. The horizontal volume transport integrated over the depth of the ekman layer is independent of the vertical eddy viscosity.
These are important limitations both because the effects of relative vorticity on ekman dynamics scale with the rossby number and because the horizontal ekman transport is itself of in. The role of ekman ocean heat transport in the northern. Ekman layer derivation and mathematical formulation. Cold dark deep ocean where plenty supplies ofcold, dark, deep ocean where plenty supplies of nutrients and carbon exist.
This net transport of water due to coupling between wind and surface waters is known as ekman transport. The magnitude of the ekman layer transport me is given by. The crossisober mass transport through a column of unit width extending through the entire pbl is the vertical integral of. Assume that the coriolis force and friction force are the dominant terms in the horizontal component equations of motion. Along most eastern boundaries box e the wind stress is directed equatorward. E is related to the convergence of the ekman transport. Our estimate agreed with that predicted by ekman theory from wind.
Separating ekman currents and background pressure gradient driven flow long time averages to overcome noise to signal ratio time dependance close to inertial frequencies yes. The second one is ekman pumping, which is the result of a cyclonic wind. The ekman layer scale is set at the depth to give an ekman number 1 note that a factor of the square root of two may be present, depending on the derivation. The role of ekman ocean heat transport in the northern hemisphere response to enso michael a. Ekman ekman transport net water transport the sum of layer movement due to the ekman spiral. Introductory dynamical oceanography, pond and pickard principles of ocean physics, apel sverdrup transport the vorticity equation below the ekman layer so we can ignore the direct effects of wind stress is v v f v t. Feb 2011 abstract a series of schemes designed to include various representationof the ekmandrivenheat. Exact analytical solutions for the ekman transport in a circular vortex are provided and can be used to calculate the vertical ekman pumping velocity to a higher order of accuracy in.
The ekman spiral and ekman transport are named for swedish scientist v. The coriolis force appears in equation of motion as the coriolis term in a rotating frame of reference and causes the coriolis effect. Coriolis effect the coriolis effect is due to an inertial force that is important in a rotating frame of reference. Energetics of bottom ekman layers during buoyancy arrest. Alexander noaaearth system research laboratory, boulder, colorado james d. Relationship between mass transport and wind stress is. Introductory dynamical oceanography, pond and pickard. The ekman spiral is a structure of currents or winds near a horizontal boundary in which the flow direction rotates as one moves away from the boundary. Winds are the main source of energy for ocean circulation, and ekman transport is a component of winddriven ocean current.
Lecture 12 ekman layers university of california, san diego. Submitted to the journal of climate december 2007 corresponding author. Started with a quick recap of the mass transport in the ekman layer, and provided an armwaving description of the velocity structure with depth within the ekman layer. A bulk formula relates the net wind stress to the wind speed. Abstractthe classical ekman spiral is generated by surface wind stress. Ekman transport is part of ekman motion theory, first investigated in 1902 by vagn walfrid ekman. Ekman transport water in the ocean can be divided roughly into three regions based on density. The movement of water in response to these forces is called ekman transport the first observations of ekman type processes were made in the arctic ocean by fridtjof nansen nansen observed that sea ice floating on the ocean surface drifted n a direction 2030. The pycnocline also called the thermocline or halocline. The sverdrup balance, or sverdrup relation, is a theoretical relationship between the wind stress exerted on the surface of the open ocean and the vertically integrated meridional northsouth transport of. The ekman spiral, named after swedish scientist vagn walfrid ekman 18741954 who first theorized it in 1902, is a consequence of the coriolis effect. For ocean water we have viscosity 102 m2 s1 and rotation rate 104 s1, yielding an ekman layer 10 m. Meanwhile, ekman pumping is a vertical motion at the base of the boundary layer resulting from the curl of the wind.
Ekman transport the details of the ekman spiral velocity profile as a function of depth are more of theoretical interest that practical importance. Scott cires, university of colorado, and noaaearth system research laboratory, boulder, colorado. If the wind blows along the coast, then ekman transport is perpendicular to the coast, so there must be either downwelling or upwelling at the coast to feed the ekman. What is the relationship between ekman transport and ekman pumping. Ekman layer transports, ekman pumping, and the sverdrup. Walfrid ekman who first described the spiral in 1905. Ekman transport in balanced currents with curvature. One consequence of a sloping ocean surface is the generation of horizontal differences gradients in water pressure. The crossisober mass transport per unit area in the planetary boundary layer pbl is just. These components of the ekman transport describe depth integrated flow in m 2 s1 velocity times depth that is 90 0 to the right left of the wind stress in the northern southern hemisphere. Next, integrate the continuity equation through the pbl. Pdf radar imaging of intense nonlinear ekman divergence. The ekman transport relation predicts a transport at right angles to the wind stress, in direct proportion to the wind and inversely proportional to the coriolis parameter.
With the first two assumptions, here are the relevant horizontal equations of motion. Current profiles closely resembling the theoretical result are seldom, if ever, observed. Particles move perpendicular to the applied force, to the right in the northern hemisphere, to the left in the southern hemisphere 2. The details of the spiral profile depend on the assumed eddy viscosity, and a v constant is not a particularly good assumption. Traditional ekman heat transport implicitly assume that viscosity decays with depth. Numerical solution of unsteady ekman equation modified by. For steady, horizontally homogeneous, incompressible flow the momentum equations for the atmospheric boundary layer may be. Section 2 introduces the basic equations and boundary. Because the real ocean does not match the idealized conditions of the ekman spiral, windinduced water movements often differ appreciably from theoretical predictions. This can be derived from the ekman equations that can be rewritten as.
For large scale winds and ocean currents, the coriolis effect is an important consideration because it changes the net direction of heat transport. Coastal upwelling occurs where ekman transport moves surface waters away from the coast. Ekman transport is directed offshore but cannot come out of the coast again, upwelling. Scott cires, university of colorado, and noaa earth system research laboratory, boulder, colorado. Seasonal variability of the ekman transport and pumping in. The coastline is the other place where ekman transport divergence or convergence can occur, and it is not included in eq. Energetics of bottom ekman layers during buoyancy arrest lars umlauf leibnizinstitute for baltic sea research, warnemunde, germany william d. Wind driven ekman layers university of california, san diego.
Ekman transport is directed offshore but cannot come out of the coast again, upwelling must occur. Alexander noaaearth system research laboratory, boulder, colorado, usa james d. This dimensionless quantity can be obtained in the same way the rossby number is obtained. Radar imaging of intense nonlinear ekman divergence. Where ekman transport moves surface waters toward the coast, the water piles up and sinks in the process known as downwelling. Ekman heat transport for slab oceans francis codron received. Although, the traditional boundary layer has no particular thickness and grows either downstream or with time, the existence of the depth scale d in rotating. Ekman transport occurs when ocean surface waters are influenced by the friction force acting on them via the wind. It derives its name from the swedish oceanographer vagn walfrid ekman. One of the objective of this paper is to analyze and evaluate shipboard wind data and calculate the ekman volume transport using indirect methods since it is difficult to measure perturbations in the vertical momentum flux in equation 5. Ekman spiral in a horizontally inhomogeneous ocean with.
The deflection of surface currents was first noticed by the norwegian oceanographer fridtjof nansen during the fram expedition 18931896 and the effect was first. Particles do not move steadily but oscillate with an inertial frequency. To help him make a mathematical model of these movements, ekman used the observations that fridtjof nansen made while frozen into the arctic sea ice. Geostrophic, ekman and adcp volume transports through. Pdf ekman transport in balanced currents with curvature. Ekman transport piles up surface water in some areas of the ocean and removes water from other areas, producing variations in the height of the sea surface, causing it to slope gradually. In this coordinate system, after dropping primes for. Trivially derived the continuity equation using the reynolds transport theorem. We consider now an elegant method of describing the wind. The theory cannot be applied at the equator where f 0. Winddriven lateral circulation in a stratified estuary.