Strati Ed Ekman Layers
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Lecture 7. More on BL Wind Profiles and Turbulent Eddy Structures in This
Atm S 547 Boundary Layer Meteorology Bretherton Lecture 7. More on BL wind profiles and turbulent eddy structures In this lecture… • Stability and baroclinicity effects on PBL wind and temperature profiles • Large-eddy structures and entrainment in shear-driven and convective BLs. Stability effects on overall boundary layer structure Above the surface layer, the wind profile is also affected by stability. As we mentioned previously, unstable BLs tend to have much more well-mixed wind profiles than stable BLs. Fig. 1 shows observations from the Wangara experiment on how the velocity defects and temperature profile are altered by BL stability (as measured by H/L). Within stability classes, the velocity profiles collapse when scaled with a velocity scale u* and the observed BL depth H, but there is a large difference between the stability classes. Baroclinicity We would expect baroclinicity (vertical shear of geostrophic wind) to also affect the observed wind profile. This is most easily seen for a laminar steady-state Ekman layer in a geostrophic wind with constant vertical shear ug(z) = (G + Mz, Nz), where M = -(g/fT0)∂T/∂y, N = (g/fT0)∂T/∂x. The momentum equations and BCs are: -f(v - Nz) = ν d2u/dz2 f(u - G - Mz) = ν d2v/dz2 u(0) = 0, u(z) ~ G + Mz as z → ∞. v(0) = 0, v(z) ~ Nz as z → ∞. The resultant BL velocity profile is the classical Ekman layer with the thermal wind added onto it. u(z) = G(1 - e-ζ cos ζ) + Mz, (7.1) 1/2 v(z) = G e- ζ sin ζ + Nz. -
In Classical Fluid Dynamics, a Boundary Layer Is the Layer I
Atm S 547 Boundary Layer Meteorology Bretherton Lecture 1 Scope of Boundary Layer (BL) Meteorology (Garratt, Ch. 1) In classical fluid dynamics, a boundary layer is the layer in a nearly inviscid fluid next to a surface in which frictional drag associated with that surface is significant (term introduced by Prandtl, 1905). Such boundary layers can be laminar or turbulent, and are often only mm thick. In atmospheric science, a similar definition is useful. The atmospheric boundary layer (ABL, sometimes called P[lanetary] BL) is the layer of fluid directly above the Earth’s surface in which significant fluxes of momentum, heat and/or moisture are carried by turbulent motions whose horizontal and vertical scales are on the order of the boundary layer depth, and whose circulation timescale is a few hours or less (Garratt, p. 1). A similar definition works for the ocean. The complexity of this definition is due to several complications compared to classical aerodynamics. i) Surface heat exchange can lead to thermal convection ii) Moisture and effects on convection iii) Earth’s rotation iv) Complex surface characteristics and topography. BL is assumed to encompass surface-driven dry convection. Most workers (but not all) include shallow cumulus in BL, but deep precipitating cumuli are usually excluded from scope of BLM due to longer time for most air to recirculate back from clouds into contact with surface. Air-surface exchange BLM also traditionally includes the study of fluxes of heat, moisture and momentum between the atmosphere and the underlying surface, and how to characterize surfaces so as to predict these fluxes (roughness, thermal and moisture fluxes, radiative characteristics). -
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. -
ESCI 485 – Air/Sea Interaction Lesson 3 – the Surface Layer References
ESCI 485 – Air/sea Interaction Lesson 3 – The Surface Layer References: Air-sea Interaction: Laws and Mechanisms , Csanady Structure of the Atmospheric Boundary Layer , Sorbjan THE PLANETARY BOUNDARY LAYER The atmospheric planetary boundary layer (PBL) is that region of the atmosphere in which turbulent fluxes are not negligible. Its depth can vary depending on the stability of the atmosphere. ο In deep convection the PBL can be of the same order as the entire troposphere. ο Usually it is of the order of 1 km or so. The PBL can be further broken down into three layers ο The mixed layer – the upper 90% or so of the PBL in which eddies have nearly mixed properties such as potential temperature, momentum, and moisture. ο The surface layer – The lowest 10% or so of the PBL in which the turbulent fluxes dominate all other terms (Coriolis and PGF) in the momentum equations. ο The viscous sub-layer – A very thin layer (order of cm or less) right near the surface where viscous effects may be important. THE SURFACE LAYER In the surface layer the turbulent momentum flux dominates all other terms in the momentum equations. The surface layer extends upwards on the order of 10 m or so. The Reynolds fluxes (stresses) in the surface layer can be assumed constant with height, and have the same magnitude as the interfacial stress (the stress between the air and water). In the surface layer, the eddy length scale is proportional to the height, z, above the surface. Based on the similarity principle , the following dimensionless group is formed from the friction velocity, eddy length scale, and the mean wind shear z dU = B , (1) u* dz where B is a dimensionless constant. -
The Atmospheric Boundary Layer (ABL Or PBL)
The Atmospheric Boundary Layer (ABL or PBL) • The layer of fluid directly above the Earth’s surface in which significant fluxes of momentum, heat and/or moisture are carried by turbulent motions whose horizontal and vertical scales are on the order of the boundary layer depth, and whose circulation timescale is a few hours or less (Garratt, p. 1). A similar definition works for the ocean. • The complexity of this definition is due to several complications compared to classical aerodynamics: i) Surface heat exchange can lead to thermal convection ii) Moisture and effects on convection iii) Earth’s rotation iv) Complex surface characteristics and topography. Atm S 547 Lecture 1, Slide 1 Sublayers of the atmospheric boundary layer Atm S 547 Lecture 1, Slide 2 Applications and Relevance of BLM i) Climate simulation and NWP ii) Air Pollution and Urban Meteorology iii) Agricultural meteorology iv) Aviation v) Remote Sensing vi) Military Atm S 547 Lecture 1, Slide 3 History of Boundary-Layer Meteorology 1900 – 1910 Development of laminar boundary layer theory for aerodynamics, starting with a seminal paper of Prandtl (1904). Ekman (1905,1906) develops his theory of laminar Ekman layer. 1910 – 1940 Taylor develops basic methods for examining and understanding turbulent mixing Mixing length theory, eddy diffusivity - von Karman, Prandtl, Lettau 1940 – 1950 Kolmogorov (1941) similarity theory of turbulence 1950 – 1960 Buoyancy effects on surface layer (Monin and Obuhkov, 1954). Early field experiments (e. g. Great Plains Expt. of 1953) capable of accurate direct turbulent flux measurements 1960 – 1970 The Golden Age of BLM. Accurate observations of a variety of boundary layer types, including convective, stable and trade- cumulus. -
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. -
A Review of Ocean/Sea Subsurface Water Temperature Studies from Remote Sensing and Non-Remote Sensing Methods
water Review A Review of Ocean/Sea Subsurface Water Temperature Studies from Remote Sensing and Non-Remote Sensing Methods Elahe Akbari 1,2, Seyed Kazem Alavipanah 1,*, Mehrdad Jeihouni 1, Mohammad Hajeb 1,3, Dagmar Haase 4,5 and Sadroddin Alavipanah 4 1 Department of Remote Sensing and GIS, Faculty of Geography, University of Tehran, Tehran 1417853933, Iran; [email protected] (E.A.); [email protected] (M.J.); [email protected] (M.H.) 2 Department of Climatology and Geomorphology, Faculty of Geography and Environmental Sciences, Hakim Sabzevari University, Sabzevar 9617976487, Iran 3 Department of Remote Sensing and GIS, Shahid Beheshti University, Tehran 1983963113, Iran 4 Department of Geography, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany; [email protected] (D.H.); [email protected] (S.A.) 5 Department of Computational Landscape Ecology, Helmholtz Centre for Environmental Research UFZ, 04318 Leipzig, Germany * Correspondence: [email protected]; Tel.: +98-21-6111-3536 Received: 3 October 2017; Accepted: 16 November 2017; Published: 14 December 2017 Abstract: Oceans/Seas are important components of Earth that are affected by global warming and climate change. Recent studies have indicated that the deeper oceans are responsible for climate variability by changing the Earth’s ecosystem; therefore, assessing them has become more important. Remote sensing can provide sea surface data at high spatial/temporal resolution and with large spatial coverage, which allows for remarkable discoveries in the ocean sciences. The deep layers of the ocean/sea, however, cannot be directly detected by satellite remote sensors. -
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).