Observational Evidence for the Ekman Layer Lecture by Steve Lentz
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Ekman Layer at the Sea Surface • Ekman Mass Transport • Application of Ekman Theory • Langmuir Circulation • Important Concepts
Principle of Oceanography Gholamreza Mashayekhinia 2013_2014 Response of the Upper Ocean to Winds Contents • Inertial Motion • Ekman Layer at the Sea Surface • Ekman Mass Transport • Application of Ekman Theory • Langmuir Circulation • Important Concepts Inertial Motion The response of the ocean to an impulse that sets the water in motion. For example, the impulse can be a strong wind blowing for a few hours. The water then moves under the influence of coriolis force and gravity. No other forces act on the water. In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. This low pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force. Such motion is said to be inertial. The mass of water continues to move due to its inertia. If the water were in space, it would move in a straight line according to Newton's second law. But on a rotating Earth, the motion is much different. The equations of motion for a frictionless ocean are: 푑푢 1 휕푝 = − + 2Ω푣 푠푖푛휑 (1a) 푑푡 휌 휕푥 푑푣 1 휕푝 = − − 2Ω푢 푠푖푛휑 (1b) 푑푡 휌 휕푦 푑휔 1 휕푝 = − + 2Ω푢 푐표푠휑 − 푔 (1c) 푑푡 휌 휕푥 Where p is pressure, Ω = 2 π/(sidereal day) = 7.292 × 10-5 rad/s is the rotation of the Earth in fixed coordinates, and φ is latitude. We have also used Fi = 0 because the fluid is frictionless. Let's now look for simple solutions to these equations. To do this we must simplify the momentum equations. -
Intro to Tidal Theory
Introduction to Tidal Theory Ruth Farre (BSc. Cert. Nat. Sci.) South African Navy Hydrographic Office, Private Bag X1, Tokai, 7966 1. INTRODUCTION Tides: The periodic vertical movement of water on the Earth’s Surface (Admiralty Manual of Navigation) Tides are very often neglected or taken for granted, “they are just the sea advancing and retreating once or twice a day.” The Ancient Greeks and Romans weren’t particularly concerned with the tides at all, since in the Mediterranean they are almost imperceptible. It was this ignorance of tides that led to the loss of Caesar’s war galleys on the English shores, he failed to pull them up high enough to avoid the returning tide. In the beginning tides were explained by all sorts of legends. One ascribed the tides to the breathing cycle of a giant whale. In the late 10 th century, the Arabs had already begun to relate the timing of the tides to the cycles of the moon. However a scientific explanation for the tidal phenomenon had to wait for Sir Isaac Newton and his universal theory of gravitation which was published in 1687. He described in his “ Principia Mathematica ” how the tides arose from the gravitational attraction of the moon and the sun on the earth. He also showed why there are two tides for each lunar transit, the reason why spring and neap tides occurred, why diurnal tides are largest when the moon was furthest from the plane of the equator and why the equinoxial tides are larger in general than those at the solstices. -
Chapter 5 Frictional Boundary Layers
Chapter 5 Frictional boundary layers 5.1 The Ekman layer problem over a solid surface In this chapter we will take up the important question of the role of friction, especially in the case when the friction is relatively small (and we will have to find an objective measure of what we mean by small). As we noted in the last chapter, the no-slip boundary condition has to be satisfied no matter how small friction is but ignoring friction lowers the spatial order of the Navier Stokes equations and makes the satisfaction of the boundary condition impossible. What is the resolution of this fundamental perplexity? At the same time, the examination of this basic fluid mechanical question allows us to investigate a physical phenomenon of great importance to both meteorology and oceanography, the frictional boundary layer in a rotating fluid, called the Ekman Layer. The historical background of this development is very interesting, partly because of the fascinating people involved. Ekman (1874-1954) was a student of the great Norwegian meteorologist, Vilhelm Bjerknes, (himself the father of Jacques Bjerknes who did so much to understand the nature of the Southern Oscillation). Vilhelm Bjerknes, who was the first to seriously attempt to formulate meteorology as a problem in fluid mechanics, was a student of his own father Christian Bjerknes, the physicist who in turn worked with Hertz who was the first to demonstrate the correctness of Maxwell’s formulation of electrodynamics. So, we are part of a joined sequence of scientists going back to the great days of classical physics. -
Coastal Upwelling Revisited: Ekman, Bakun, and Improved 10.1029/2018JC014187 Upwelling Indices for the U.S
Journal of Geophysical Research: Oceans RESEARCH ARTICLE Coastal Upwelling Revisited: Ekman, Bakun, and Improved 10.1029/2018JC014187 Upwelling Indices for the U.S. West Coast Key Points: Michael G. Jacox1,2 , Christopher A. Edwards3 , Elliott L. Hazen1 , and Steven J. Bograd1 • New upwelling indices are presented – for the U.S. West Coast (31 47°N) to 1NOAA Southwest Fisheries Science Center, Monterey, CA, USA, 2NOAA Earth System Research Laboratory, Boulder, CO, address shortcomings in historical 3 indices USA, University of California, Santa Cruz, CA, USA • The Coastal Upwelling Transport Index (CUTI) estimates vertical volume transport (i.e., Abstract Coastal upwelling is responsible for thriving marine ecosystems and fisheries that are upwelling/downwelling) disproportionately productive relative to their surface area, particularly in the world’s major eastern • The Biologically Effective Upwelling ’ Transport Index (BEUTI) estimates boundary upwelling systems. Along oceanic eastern boundaries, equatorward wind stress and the Earth s vertical nitrate flux rotation combine to drive a near-surface layer of water offshore, a process called Ekman transport. Similarly, positive wind stress curl drives divergence in the surface Ekman layer and consequently upwelling from Supporting Information: below, a process known as Ekman suction. In both cases, displaced water is replaced by upwelling of relatively • Supporting Information S1 nutrient-rich water from below, which stimulates the growth of microscopic phytoplankton that form the base of the marine food web. Ekman theory is foundational and underlies the calculation of upwelling indices Correspondence to: such as the “Bakun Index” that are ubiquitous in eastern boundary upwelling system studies. While generally M. G. Jacox, fi [email protected] valuable rst-order descriptions, these indices and their underlying theory provide an incomplete picture of coastal upwelling. -
Oceanography 200, Spring 2008 Armbrust/Strickland Study Guide Exam 1
Oceanography 200, Spring 2008 Armbrust/Strickland Study Guide Exam 1 Geography of Earth & Oceans Latitude & longitude Properties of Water Structure of water molecule: polarity, hydrogen bonds, effects on water as a solvent and on freezing Latent heat of fusion & vaporization & physical explanation Effects of latent heat on heat transport between ocean & atmosphere & within atmosphere Definition of density, density of ice vs. water Physical meaning of temperature & heat Heat capacity of water & why water requires a lot of heat gain or loss to change temperature Effects of heating & cooling on density of water, and physical explanation Difference in albedo of ice/snow vs. water, and effects on Earth temperature Properties of Seawater Definitions of salinity, conservative & non-conservative seawater constituents, density (sigma-t) Average ocean salinity & how it is measured 3 technology systems for monitoring ocean salinity and other properties 6 most abundant constituents of seawater & Principle of Constant Proportions Effects of freezing on seawater Effects of temperature & salinity on density, T-S diagram Processes that increase & decrease salinity & temperature and where they occur Generalized depth profiles of temperature, salinity, density & ocean stratification & stability Generalized depth profiles of O2 & CO2 and processes determining these profiles Forms of dissolved inorganic carbon in seawater and their buffering effect on pH of seawater Water Properties and Climate Change 2 main causes of global sea level rise, 2 main causes of local sea level rise Physical properties of water that affect sea level rise Icebergs & sea ice: Differences in sources, and effects of freezing & melting on sea level How heat content of upper ocean & Arctic sea ice extent have changed since about 1970s Invasion of fossil fuel CO2 in the oceans and effects on pH The Sea Floor & Plate Tectonics General differences in rock type & density of oceanic vs. -
Small-Scale Processes in the Coastal Ocean
or collective redistirbution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of The Oceanography Society. Send all correspondence to: [email protected] ofor Th e The to: [email protected] Oceanography approval Oceanography correspondence PO all portionthe Send Society. ofwith any permitted articleonly photocopy by Society, is of machine, reposting, this means or collective or other redistirbution article has This been published in SPECIAL ISSUE ON CoasTal Ocean PRocesses TuRBulence, TRansFER, anD EXCHanGE Oceanography BY JAMes N. MouM, JonaTHan D. NasH, , Volume 21, Number 4, a quarterly journal of The Oceanography Society. Copyright 2008 by The Oceanography Society. All rights reserved. Permission is granted to copy this article for use in teaching and research. research. for this and teaching article copy to use in reserved.by The 2008 rights is granted journal ofCopyright OceanographyAll The Permission 21, NumberOceanography 4, a quarterly Society. Society. , Volume anD JODY M. KLYMak Small-Scale Processes in the Coastal Ocean 20 depth (m) 40 B ox 1931, ox R ockville, R epublication, systemmatic reproduction, reproduction, systemmatic epublication, MD 20849-1931, USA. -200 -100 0 100 distance along ship track (m) 22 Oceanography Vol.21, No.4 ABSTRACT. Varied observations over Oregon’s continental shelf illustrate the beauty and complexity of geophysical flows in coastal waters. Rapid, creative, and sometimes fortuitous sampling from ships and moorings has allowed detailed looks at boundary layer processes, internal waves (some extremely nonlinear), and coastal currents, including how they interact. These processes drive turbulence and mixing in shallow coastal waters and encourage rapid biological responses, yet are poorly understood and parameterized. -
Oceanography Lecture 12
Because, OF ALL THE ICE!!! Oceanography Lecture 12 How do you know there’s an Ice Age? i. The Ocean/Atmosphere coupling ii.Surface Ocean Circulation Global Circulation Patterns: Atmosphere-Ocean “coupling” 3) Atmosphere-Ocean “coupling” Atmosphere – Transfer of moisture to the Low latitudes: Oceans atmosphere (heat released in higher latitudes High latitudes: Atmosphere as water condenses!) Atmosphere-Ocean “coupling” In summary Latitudinal Differences in Energy Atmosphere – Transfer of moisture to the atmosphere: Hurricanes! www.weather.com Amount of solar radiation received annually at the Earth’s surface Latitudinal Differences in Salinity Latitudinal Differences in Density Structure of the Oceans Heavy Light T has a much greater impact than S on Density! Atmospheric – Wind patterns Atmospheric – Wind patterns January January Westerlies Easterlies Easterlies Westerlies High/Low Pressure systems: Heat capacity! High/Low Pressure systems: Wind generation Wind drag Zonal Wind Flow Wind is moving air Air molecules drag water molecules across sea surface (remember waves generation?): frictional drag Westerlies If winds are prolonged, the frictional drag generates a current Easterlies Only a small fraction of the wind energy is transferred to Easterlies the water surface Westerlies Any wind blowing in a regular pattern? High/Low Pressure systems: Wind generation by flow from High to Low pressure systems (+ Coriolis effect) 1) Ekman Spiral 1) Ekman Spiral Once the surface film of water molecules is set in motion, they exert a Spiraling current in which speed and direction change with frictional drag on the water molecules immediately beneath them, depth: getting these to move as well. Net transport (average of all transport) is 90° to right Motion is transferred downward into the water column (North Hemisphere) or left (Southern Hemisphere) of the ! Speed diminishes with depth (friction) generating wind. -
A Laboratory Model of Thermocline Depth and Exchange Fluxes Across Circumpolar Fronts*
656 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 34 A Laboratory Model of Thermocline Depth and Exchange Fluxes across Circumpolar Fronts* CLAUDIA CENEDESE Physical Oceanography Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts JOHN MARSHALL Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts J. A. WHITEHEAD Physical Oceanography Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts (Manuscript received 6 January 2003, in ®nal form 7 July 2003) ABSTRACT A laboratory experiment has been constructed to investigate the possibility that the equilibrium depth of a circumpolar front is set by a balance between the rate at which potential energy is created by mechanical and buoyancy forcing and the rate at which it is released by eddies. In a rotating cylindrical tank, the combined action of mechanical and buoyancy forcing builds a strati®cation, creating a large-scale front. At equilibrium, the depth of penetration and strength of the current are then determined by the balance between eddy transport and sources and sinks associated with imposed patterns of Ekman pumping and buoyancy ¯uxes. It is found 2 that the depth of penetration and transport of the front scale like Ï[( fwe)/g9]L and weL , respectively, where we is the Ekman pumping, g9 is the reduced gravity across the front, f is the Coriolis parameter, and L is the width scale of the front. Last, the implications of this study for understanding those processes that set the strati®cation and transport of the Antarctic Circumpolar Current (ACC) are discussed. If the laboratory results scale up to the ACC, they suggest a maximum thermocline depth of approximately h 5 2 km, a zonal current velocity of 4.6 cm s21, and a transport T 5 150 Sv (1 Sv [ 106 m3 s 21), not dissimilar to what is observed. -
Tidal and Wind-Driven Currents from Oscr
FEATURE TIDAL AND WIND-DRIVEN CURRENTS FROM OSCR By David Prandle TWO IMPORTANTASPECTS of tidal currents are (1) be seen by comparing calculations of M, tidal vor- their temporal coherence and (2) their constancy ticity distributions <OV/OX- c?U/OY> from OSCR (over centuries). The first rigorous evaluation of an measurements with corresponding model calcula- Ocean Surface Current Radar (OSCR) system ex- tions (Prandle 1987). ploited these characteristics using sequential de- Tidal Residuals ployments of the one available unit with subse- The propagation of tidal energy from the quent combination of radial components to ocean into shelf seas produces an attendant net construct tidal ellipses (Prandle and Ryder 1985). residual current Uo of 0.5(OUD)cos 0 (0, oscil- Specifications for Tidal Mapping lating current amplitude; c, elevation amplitude: The Rayleigh criterion for separation of closely D, water depth: O, phase difference between lJ spaced constituents in tidal analysis suggests ob- and {). In U.K. waters Uo is typically 0-3 cm s ' servational periods exceeding the related beat fre- compared with 0 of 40-100 cm s ', thus conven- • . enhanced reso- quency, this dictates 15 d of observations to sepa- tional current meters often fail to resolve U~,. lution of the instru- rate the two largest constituents M~ and St. For Moreover, numerical models that accurately sim- tidal elevations this criterion is often relaxed: ulate M z may not resolve U,, with the same accu- mentation reveals however, while elevations show a noise:tidal sig- racy. Year-long deployments of OSCR, in the finer scale dynamical nal ratio of 0(0.1-0.2), the same ratio for currents Dover Straits (Prandle et al., 1993) and the North is 0(0.5). -
On the Patterns of Wind-Power Input to the Ocean Circulation
2328 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 41 On the Patterns of Wind-Power Input to the Ocean Circulation FABIEN ROQUET AND CARL WUNSCH Department of Earth, Atmosphere and Planetary Science, Massachusetts Institute of Technology, Cambridge, Massachusetts GURVAN MADEC Laboratoire d’Oce´anographie Dynamique et de Climatologie, Paris, France (Manuscript received 1 February 2011, in final form 12 July 2011) ABSTRACT Pathways of wind-power input into the ocean general circulation are analyzed using Ekman theory. Direct rates of wind work can be calculated through the wind stress acting on the surface geostrophic flow. However, because that energy is transported laterally in the Ekman layer, the injection into the geostrophic interior is actually controlled by Ekman pumping, with a pattern determined by the wind curl rather than the wind itself. Regions of power injection into the geostrophic interior are thus generally shifted poleward compared to regions of direct wind-power input, most notably in the Southern Ocean, where on average energy enters the interior 108 south of the Antarctic Circumpolar Current core. An interpretation of the wind-power input to the interior is proposed, expressed as a downward flux of pressure work. This energy flux is a measure of the work done by the Ekman pumping against the surface elevation pressure, helping to maintain the observed anomaly of sea surface height relative to the global-mean sea level. 1. Introduction or the input to surface gravity waves (601 TW; Wang and Huang 2004b), but they are not directly related to The wind stress, along with the secondary input from the interior flow. -
Physical Oceanography - UNAM, Mexico Lecture 3: the Wind-Driven Oceanic Circulation
Physical Oceanography - UNAM, Mexico Lecture 3: The Wind-Driven Oceanic Circulation Robin Waldman October 17th 2018 A first taste... Many large-scale circulation features are wind-forced ! Outline The Ekman currents and Sverdrup balance The western intensification of gyres The Southern Ocean circulation The Tropical circulation Outline The Ekman currents and Sverdrup balance The western intensification of gyres The Southern Ocean circulation The Tropical circulation Ekman currents Introduction : I First quantitative theory relating the winds and ocean circulation. I Can be deduced by applying a dimensional analysis to the horizontal momentum equations within the surface layer. The resulting balance is geostrophic plus Ekman : I geostrophic : Coriolis and pressure force I Ekman : Coriolis and vertical turbulent momentum fluxes modelled as diffusivities. Ekman currents Ekman’s hypotheses : I The ocean is infinitely large and wide, so that interactions with topography can be neglected ; ¶uh I It has reached a steady state, so that the Eulerian derivative ¶t = 0 ; I It is homogeneous horizontally, so that (uh:r)uh = 0, ¶uh rh:(khurh)uh = 0 and by continuity w = 0 hence w ¶z = 0 ; I Its density is constant, which has the same consequence as the Boussinesq hypotheses for the horizontal momentum equations ; I The vertical eddy diffusivity kzu is constant. ¶ 2u f k × u = k E E zu ¶z2 that is : k ¶ 2v u = zu E E f ¶z2 k ¶ 2u v = − zu E E f ¶z2 Ekman currents Ekman balance : k ¶ 2v u = zu E E f ¶z2 k ¶ 2u v = − zu E E f ¶z2 Ekman currents Ekman balance : ¶ 2u f k × u = k E E zu ¶z2 that is : Ekman currents Ekman balance : ¶ 2u f k × u = k E E zu ¶z2 that is : k ¶ 2v u = zu E E f ¶z2 k ¶ 2u v = − zu E E f ¶z2 ¶uh τ = r0kzu ¶z 0 with τ the surface wind stress. -
Lecture 4: OCEANS (Outline)
LectureLecture 44 :: OCEANSOCEANS (Outline)(Outline) Basic Structures and Dynamics Ekman transport Geostrophic currents Surface Ocean Circulation Subtropicl gyre Boundary current Deep Ocean Circulation Thermohaline conveyor belt ESS200A Prof. Jin -Yi Yu BasicBasic OceanOcean StructuresStructures Warm up by sunlight! Upper Ocean (~100 m) Shallow, warm upper layer where light is abundant and where most marine life can be found. Deep Ocean Cold, dark, deep ocean where plenty supplies of nutrients and carbon exist. ESS200A No sunlight! Prof. Jin -Yi Yu BasicBasic OceanOcean CurrentCurrent SystemsSystems Upper Ocean surface circulation Deep Ocean deep ocean circulation ESS200A (from “Is The Temperature Rising?”) Prof. Jin -Yi Yu TheThe StateState ofof OceansOceans Temperature warm on the upper ocean, cold in the deeper ocean. Salinity variations determined by evaporation, precipitation, sea-ice formation and melt, and river runoff. Density small in the upper ocean, large in the deeper ocean. ESS200A Prof. Jin -Yi Yu PotentialPotential TemperatureTemperature Potential temperature is very close to temperature in the ocean. The average temperature of the world ocean is about 3.6°C. ESS200A (from Global Physical Climatology ) Prof. Jin -Yi Yu SalinitySalinity E < P Sea-ice formation and melting E > P Salinity is the mass of dissolved salts in a kilogram of seawater. Unit: ‰ (part per thousand; per mil). The average salinity of the world ocean is 34.7‰. Four major factors that affect salinity: evaporation, precipitation, inflow of river water, and sea-ice formation and melting. (from Global Physical Climatology ) ESS200A Prof. Jin -Yi Yu Low density due to absorption of solar energy near the surface. DensityDensity Seawater is almost incompressible, so the density of seawater is always very close to 1000 kg/m 3.