DOCSLIB.ORG

1.4 Wind Stress Vector Over Sea Waves

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1.4 Wind Stress Vector Over Sea Waves 1.4 WIND STRESS VECTOR OVER SEA WAVES A. A. Grachev * University of Colorado CIRES / NOAA Environmental Technology Laboratory, Boulder, Colorado C. W. Fairall NOAA Environmental Technology Laboratory, Boulder, Colorado J. E. Hare University of Colorado CIRES / NOAA Environmental Technology Laboratory, Boulder, Colorado J. B. Edson Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 1. INTRODUCTION Thus, the term in (1) - (2) is ignored assuming that it is unimportant or insignificant with respect to Determination of the wind stress over oceans is a fundamental problem of air-sea interaction. The stress . Standard Monin - Obukhov similarity theory vector, , is the tangential force per unit area exerted by (MOST) is based on the assumption that stress and wind the wind on the surface. In practice the stress is usually vectors are aligned in the same direction, and measured by a sonic anemometer at level of order 10 m = 0 by definition. With the exception of several papers, above the sea surface. The stress vector at some level there has been a general lack of investigation concerning well above the viscous sublayer may be represented the stress vector direction relative to the mean wind and directly by the following relation (eddy-correlation surface waves direction. method): Based on field measurements Smith (1980), and Geernaert (1988) reported high values of the crosswind (1) component and angle in (2). Geernaert et al. (1993) observed that when swell propagates at an oblique where and represent the longitudinal ( x - axis) and direction with respect to the local wind direction, the stress lateral ( y - axis) unit vectors, < > is a time or/and spatial vector has a direction which is in general a blend between averaging operator, u, v or w are the longitudinal, lateral, the wind direction and the swell direction. Rieder et al. and vertical velocity components, respectively, and (1994) considered further the influence of the surface waves on wind stress direction. They provided statistically denotes fluctuations about a mean value. It is a common significant evidence that the wind stress lies between the practice to align the x - axis with wind direction at a mean wind direction and direction of the long waves. reference height, z. Thus is the The Geernaert (1988), Geernaert et al. (1993), and Rieder et al. (1994) studies restricted their analysis to downstream stress, and is the cross- moderate to high wind speeds. In the light wind speed wind stress. The following sign conversion for stress is regime, the influence of the surface waves on wind stress used, > 0 if the longitudinal stress component is facing direction is more dramatic. It is common place that in calm weather conditions the wind and stress vectors are not in the wind direction and vice versa, is positive aligned, and often the wind and stress directions are (negative) if the lateral stress component is directed to the nearly opposite (Drennan et al. 1999). right (left) of the wind vector. The purpose of this study is to extend these prior The magnitude of the stress vector, , is analyses by including additional experimental evidence of numerically equal to the magnitude of the momentum flux, the influence of surface waves direction on the stress . For this reason there is a common practice to do not vector direction. differentiate between stress and momentum flux. 2. BASIC APPROACH The angle between the stress and wind vectors is calculated according to Over the sea, the total stress, , can be expressed as vector sum of the viscous stress, , turbulent shear (2) stress, , and wave-induced stress (normal or form where positive angles of correspond to the stress stress), , (e.g. Hare et al., 1997): vector oriented to the right of the wind direction. In most analyses to date, the direction of the stress (3) vector is generally assumed to be aligned with the wind. In a general case all constituents in (3) depends on a reference height, z. However, under certain conditions (the wind and wave fields are stationary in time and * Corresponding author address: Andrey Grachev, space), it is assumed that on the left side of (3) is NOAA/Environmental Technology Laboratory, R/ET7, constant with height, i.e. The amplitude of 325 Broadway, Boulder CO 80305-3328; e-mail: wave-induced pressure perturbations falls off [email protected] approximately exponentionally with z, and therefore, well stress may also reverse sign to negative, < 0. The away from the surface, tends to zero. Assuming that case > 0 is associated with strong winds is invariant with height (constant flux layer), changes of traveling in the same direction as swell or with counter- with height must be compensated by variations of swell. The last leads to enhancement of the total stress (e.g. Drennan et al. 1999). Unlike the wave-induced and . The layer where the influence of cannot stress, the shear stress is always positive, i.e. > 0. be neglected is known as the wave boundary layer (WBL). It is generally believed that above WBL, but within the Note that the direction of wind waves is frequently surface layer, standard MOST is applicable for description close to the wind direction, and therefore the vectors of the momentum transfer. and are about co-linear. Substituting of The wave-induced stress is associated with the and into (4) gives atmospheric pressure distribution across the front and rear faces of the waves. In the case of a pure unimodal wave field is aligned with the direction of the wave (5) propagation. The fundamental difference between airflow Eq. (5) shows that the total stress tends to be governed over land and sea derives from mobility of the water by two vectors aligned with wind and swell direction surface. Traditionally this phenomenon is described in respectively. Thus, rather than a decomposition of in a terms of wave age. Based on wave age, the sea state is classified into young (or developing) sea and mature fixed rectangular Cartesian reference frame associated (decaying) sea. Wave-induced stress components in the with the wind alone and used in (1), consider a marine surface layer show strong dependence on wave decomposition in a fixed non-rectangular reference frame age, and range from positive to negative values. For associated with the wind and swell directions (5). Fig. 1 young seas the longitudinal component of wave-induced shows decomposition of the stress vector. stress is positive, i.e. > 0 (respectively to wind According to the above discussion, the vector direction, x axis). With increasing wave age, may face in to the wind direction ( > 0), as well as in decreases, reaches zero, and reverses sign in the case of the opposite direction ( < 0). Similarly, may be the old seas, < 0. The fact that the wave-induced faced in the swell direction ( > 0), and in the counter- stress can be positive as well as negative is a key point in swell direction ( < 0). Combinations of these cases the understanding of the stress vector orientation over ocean waves. gives all possible situations associated with the wind It is generally assumed that surface gravity waves stress directions. Some of these situations are prohibited, can be separated into pure wind sea and swell waves. e.g. in counter swell can be only negative. Wind surface waves are short waves and travel much Strictly speaking the conceptual scheme discussed more slowly than the wind, while swell are long and fast above is derived for the values at the wavy surface, traveling ocean waves. Generally wind waves and swell although the vector balance in Eqs. (4) - (5) is valid at any propagate in different directions. Swell has a period and wavelength that is not associated with local winds. In the majority of cases the wave energy of swell is contained in a narrow range around the peak frequency in the wave τ spectrum, and it is separated from the wave energy of x wind dominant waves. Thus, it makes sense to split τ into two parts, , where and 1 are due to pure wind waves and swell respectively. τ Combining this assumption and Eq. (3) yields: (4) θ τ where . 2 2 It the case of mixed wind sea and swell it is thought τ that and in (4) are governed by their own y wave age (two peaks in the wave spectra are expected). Since the swell usually travels faster and short waves more slowly than the wind, in the majority of cases > 0 and < 0. However, reverse signs are also possible in transient conditions. The case Figure 1. Decomposition of the stress vector, , into and < 0 is associated with decaying wind conditions, in a wind-associated coordinate system, and into and in a e.g. after the passage of a storm or gale, when the total wind-swell coordinate system. height. However, the extrapolation of the surface stress to 360 n o the elevated measurements is not a trivial problem. This i 270 t c is because both and generally are e r i 180 d not described by a simple exponentially decaying profiles d Following swell n i 90 Counter swell and have a more complicated nonmonotonic structure. W a Among other things, it was found that the wave-induced 0 stress may reverse sign with height several times (e.g. 0 2 4 6 8 10 12 e 90 l Hare et al. 1997). Thus, different constituents in the right g n a side of (5) vary with height in different ways and the vector 0 d n balance shown in Fig. 1 will be changed with height, i w -90 f f including cases when the stress vector will lie in different o s -180 sectors created by wind-swell directions.
Load more

Recommended publications
  • A Global Ocean Wind Stress Climatology Based on Ecmwf Analyses
    NCAR/TN-338+STR NCAR TECHNICAL NOTE - August 1989 A GLOBAL OCEAN WIND STRESS CLIMATOLOGY BASED ON ECMWF ANALYSES KEVIN E. TRENBERTH JERRY G. OLSON WILLIAM G. LARGE T (ANNUAL) 90N 60N 30N 0 30S 60S 90S- 0 30E 60E 90E 120E 150E 180 150 120N 90 6W 30W 0 CLIMATE AND GLOBAL DYNAMICS DIVISION I NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER. COLORADO I Table of Contents Preface . v Acknowledgments . .. v 1. Introduction . 1 2. D ata . .. 6 3. The drag coefficient . .... 8 4. Mean annual cycle . 13 4.1 Monthly mean wind stress . .13 4.2 Monthly mean wind stress curl . 18 4.3 Sverdrup transports . 23 4.4 Results in tropics . 30 5. Comparisons with Hellerman and Rosenstein . 34 5.1 Differences in wind stress . 34 5.2 Changes in the atmospheric circulation . 47 6. Interannual variations . 55 7. Conclusions ....................... 68 References . 70 Appendix I ECMWF surface winds .... 75 Appendix II Curl of the wind stress . 81 Appendix III Stability fields . 83 iii Preface Computations of the surface wind stress over the global oceans have been made using surface winds from the European Centre for Medium Range Weather Forecasts (ECMWF) for seven years. The drag coefficient is a function of wind speed and atmospheric stability, and the density is computed for each observation. Seven year climatologies of wind stress, wind stress curl and Sverdrup transport are computed and compared with those of other studies. The interannual variability of these quantities over the seven years is presented. Results for the long term and individual monthly means are archived and available at NCAR.
    [Show full text]
  • Ocean and Climate
    Ocean currents II Wind-water interaction and drag forces Ekman transport, circular and geostrophic flow General ocean flow pattern Wind-Water surface interaction Water motion at the surface of the ocean (mixed layer) is driven by wind effects. Friction causes drag effects on the water, transferring momentum from the atmospheric winds to the ocean surface water. The drag force Wind generates vertical and horizontal motion in the water, triggering convective motion, causing turbulent mixing down to about 100m depth, which defines the isothermal mixed layer. The drag force FD on the water depends on wind velocity v: 2 FD CD Aa v CD drag coefficient dimensionless factor for wind water interaction CD 0.002, A cross sectional area depending on surface roughness, and particularly the emergence of waves! Katsushika Hokusai: The Great Wave off Kanagawa The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0.514 m/s = 1.85 km/h)! For land and city people Bft 6 Bft 7 Bft 8 Bft 9 Bft 10 Bft 11 Bft 12 m Conversion from scale to wind velocity: v 0.836 B3/ 2 s A strong breeze of B=6 corresponds to wind speed of v=39 to 49 km/h at which long waves begin to form and white foam crests become frequent. The drag force can be calculated to: kg km m F C A v2 1200 v 45 12.5 C 0.001 D D a a m3 h s D 2 kg 2 m 2 FD 0.0011200 Am 12.5 187.5 A N or FD A 187.5 N m m3 s For a strong gale (B=12), v=35 m/s, the drag stress on the water will be: 2 kg m 2 FD / A 0.00251200 35 3675 N m m3 s kg m 1200 v 35 C 0.0025 a m3 s D Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u, is balanced by the Coriolis force, but drag decreases with depth z.
    [Show full text]
  • Arxiv:1809.01376V1 [Astro-Ph.EP] 5 Sep 2018
    Draft version March 9, 2021 Typeset using LATEX preprint2 style in AASTeX61 IDEALIZED WIND-DRIVEN OCEAN CIRCULATIONS ON EXOPLANETS Weiwen Ji,1 Ru Chen,2 and Jun Yang1 1Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, 100871, Beijing, China 2University of California, 92521, Los Angeles, USA ABSTRACT Motivated by the important role of the ocean in the Earth climate system, here we investigate possible scenarios of ocean circulations on exoplanets using a one-layer shallow water ocean model. Specifically, we investigate how planetary rotation rate, wind stress, fluid eddy viscosity and land structure (a closed basin vs. a reentrant channel) influence the pattern and strength of wind-driven ocean circulations. The meridional variation of the Coriolis force, arising from planetary rotation and the spheric shape of the planets, induces the western intensification of ocean circulations. Our simulations confirm that in a closed basin, changes of other factors contribute to only enhancing or weakening the ocean circulations (e.g., as wind stress decreases or fluid eddy viscosity increases, the ocean circulations weaken, and vice versa). In a reentrant channel, just as the Southern Ocean region on the Earth, the ocean pattern is characterized by zonal flows. In the quasi-linear case, the sensitivity of ocean circulations characteristics to these parameters is also interpreted using simple analytical models. This study is the preliminary step for exploring the possible ocean circulations on exoplanets, future work with multi-layer ocean models and fully coupled ocean-atmosphere models are required for studying exoplanetary climates. Keywords: astrobiology | planets and satellites: oceans | planets and satellites: terrestrial planets arXiv:1809.01376v1 [astro-ph.EP] 5 Sep 2018 Corresponding author: Jun Yang [email protected] 2 Ji, Chen and Yang 1.
    [Show full text]
  • 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.
    [Show full text]
  • Shifting Surface Currents in the Northern North Atlantic Ocean Sirpa
    I, Source of Acquisition / NASA Goddard Space mght Center Shifting surface currents in the northern North Atlantic Ocean Sirpa Hakkinen (1) and Peter B. Rhines (2) (1) NASA Goddard Space Flight Center, Code 614.2, Greenbelt, RID 20771 (2) University of Washington, Seattle, PO Box 357940, WA 98195 Analysis of surface drifter tracks in the North Atlantic Ocean from the time period 1990 to 2006 provides the first evidence that the Gulf Stream waters can have direct pathways to the Nordic Seas. Prior to 2000, the drifters entering the channels leading to the Nordic Seas originated in the western and central subpolar region. Since 2001 several paths fiom the western subtropics have been present in the drifter tracks leading to the Rockall Trough through wfuch the most saline North Atlantic Waters pass to the Nordic Seas. Eddy kinetic energy fiom altimetry shows also the increased energy along the same paths as the drifters, These near surface changes have taken effect while the altimetry shows a continual weakening of the subpolar gyre. These findings highlight the changes in the vertical structure of the northern North Atlantic Ocean, its dynamics and exchanges with the higher latitudes, and show how pathways of the thermohaline circulation can open up and maintain or increase its intensity even as the basin-wide circulation spins down. Shifting surface currents in the northern North Atlantic Ocean Sirpa Hakkinen (1) and Peter B. Rhines (2) (1) NASA Goddard Space Flight Center, Code 614.2, Greenbelt, MD 20771 (2) University of Washington, Seattle, PO Box 357940, WA 98195 Inflows to the Nordic seas from the main North Atlantic pass through three routes: through the Rockall Trough to the Faroe-Shetland Channel, through the Iceland basin over the Iceland-Faroe Ridge and via the Irminger Current passing west of Iceland.
    [Show full text]
  • 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.
    [Show full text]
  • On the Coupling of Wind Stress and Sea Surface Temperature
    15 APRIL 2006 SAMELSON ET AL. 1557 On the Coupling of Wind Stress and Sea Surface Temperature R. M. SAMELSON,E.D.SKYLLINGSTAD,D.B.CHELTON,S.K.ESBENSEN,L.W.O’NEILL, AND N. THUM College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon (Manuscript received 25 January 2005, in final form 5 August 2005) ABSTRACT A simple quasi-equilibrium analytical model is used to explore hypotheses related to observed spatial correlations between sea surface temperatures and wind stress on horizontal scales of 50–500 km. It is argued that a plausible contributor to the observed correlations is the approximate linear relationship between the surface wind stress and stress boundary layer depth under conditions in which the stress boundary layer has come into approximate equilibrium with steady free-atmospheric forcing. Warmer sea surface temperature is associated with deeper boundary layers and stronger wind stress, while colder temperature is associated with shallower boundary layers and weaker wind stress. Two interpretations of a previous hypothesis involving the downward mixing of horizontal momentum are discussed, and it is argued that neither is appropriate for the warm-to-cold transition or quasi-equilibrium conditions, while one may be appropriate for the cold-to-warm transition. Solutions of a turbulent large-eddy simulation numerical ␥ model illustrate some of the processes represented in the analytical model. A dimensionless ratio ␶A is introduced to measure the relative influence of lateral momentum advection and local surface stress on the ␥ Ͻ boundary layer wind profile. It is argued that when ␶A 1, and under conditions in which the thermo- dynamically induced lateral pressure gradients are small, the boundary layer depth effect will dominate lateral advection and control the surface stress.
    [Show full text]
  • Evaluation of Subtropical North Atlantic Ocean Circulation in CMIP5 Models Against the Observational Array at 26.5°N and Its Changes Under Continued Warming
    1DECEMBER 2018 B E A D L I N G E T A L . 9697 Evaluation of Subtropical North Atlantic Ocean Circulation in CMIP5 Models against the Observational Array at 26.5°N and Its Changes under Continued Warming R. L. BEADLING,J.L.RUSSELL,R.J.STOUFFER, AND P. J. GOODMAN Department of Geosciences, The University of Arizona, Tucson, Arizona (Manuscript received 12 December 2017, in final form 16 September 2018) ABSTRACT Observationally based metrics derived from the Rapid Climate Change (RAPID) array are used to assess the large-scale ocean circulation in the subtropical North Atlantic simulated in a suite of fully coupled climate models that contributed to phase 5 of the Coupled Model Intercomparison Project (CMIP5). The modeled circulation at 26.58N is decomposed into four components similar to those RAPID observes to estimate the Atlantic meridional overturning circulation (AMOC): the northward-flowing western boundary current (WBC), the southward transport in the upper midocean, the near-surface Ekman transport, and the south- ward deep ocean transport. The decadal-mean AMOC and the transports associated with its flow are captured well by CMIP5 models at the start of the twenty-first century. By the end of the century, under representative concentration pathway 8.5 (RCP8.5), averaged across models, the northward transport of waters in the upper 2 WBC is projected to weaken by 7.6 Sv (1 Sv [ 106 m3 s 1; 221%). This reduced northward flow is a combined result of a reduction in the subtropical gyre return flow in the upper ocean (22.9 Sv; 212%) and a weakened net southward transport in the deep ocean (24.4 Sv; 228%) corresponding to the weakened AMOC.
    [Show full text]
  • Modification of the Charnock Wind Stress Formula to Include the Effects of Free Convection and Swell
    3 Modification of the Charnock Wind Stress Formula to Include the Effects of Free Convection and Swell C.H. Huang U.S. Department of the Interior, Bureau of Ocean Energy Management, Regulation, and Enforcement, USA 1. Introduction The estimate of the surface fluxes of momentum, sensible heat, and water vapor over the ocean is important in numerical modeling for weather forecasting, air quality modeling, environmental impact assessment, and climate modeling, which, in particular, requires more accurate flux calculations. The accuracy of flux calculations depends on an important parameter: the surface roughness length. More than five decades ago Charnock (1955) formulated the surface roughness length over the ocean, relating the sea-surface roughness to wind stress on the basis of dimensional argument. Even now the Charnock wind stress formula is widely used. However, in the free convection limit, the horizontal mean wind speed and the wind stress approach zero, therefore the friction velocity also approaches zero; in this condition, the Charnock wind stress formula is no longer applicable and the Monin-Obukhov similarity theory (MOST) has a singularity; MOST relies on the dimensional analysis of relevant key parameters that characterize the flow behavior and the structure of turbulence in the atmospheric surface layer. Thus, in the conditions of free convection, the traditional MOST is no longer valid, because the surface roughness length also approaches zero. In numerical modeling, the surface fluxes, wind, and temperature in the surface layer are important, because they are used as lower boundary conditions. In the Charnock formulation of surface roughness, two important physical processes were not considered: one is the free convection and the other is the swell.
    [Show full text]
  • ATM 241, Spring 2020 Lecture 9B the Wind-Driven Circulation (Part 2)
    ATM 241, Spring 2020 Lecture 9b The Wind-Driven Circulation (Part 2) Paul A. Ullrich [email protected] Marshall & Plumb Ch. 10 Paul Ullrich The Wind-Driven Circulation Spring 2020 In this section… Questions • What is the relationship between wind stress and Ekman pumping / suction? • What is responsible for strong western boundary currents? • How does wind stress drive the equatorial counter-current? Paul Ullrich The Wind-Driven Circulation Spring 2020 Ekman Pumping and Suction Paul Ullrich The Wind-Driven Circulation Spring 2020 Ekman Pumping and Suction Recall that the continuity equation in the ocean is given by u =0 r · @w Expand: u + =0 rh · h @z @w Use zero horizontal divergence of geostrophic motion: u + =0 rh · ag @z And that the ageostrophic winds are associated with friction in the Ekman layer: 1 @⌧ 1 @⌧ fk uag = uag = k ⇥ ⇢ref @z −f⇢ref ⇥ @z 1 ⌧wind And so: wek = k ⇢ · r⇥ f ref ✓ ◆ Paul Ullrich The Wind-Driven Circulation Spring 2020 Ekman Pumping and Suction 1 ⌧ w = k wind Anticyclonic Cyclonic ek ⇢ · r⇥ f ref ✓ ◆ applied stress applied stress Rotation in the wind stress then drives vertical motion. In particular, an (anticyclonic) cyclonic applied stress leads to (downwelling) upwelling. convergence and divergence and downwelling upwelling Anticyclonic stress: Ekman pumping (negative wek) Figure: Similar to the atmosphere, vortical wind stresses are responsible for driving Cyclonic stress: horizontally divergent motion, which in turn Ekman suction (positive wek) drive upwelling and downwelling. Paul Ullrich The Wind-Driven Circulation Spring 2020 Ekman Pumping and Suction westerlies easterlies Ekman pumping Figure: A schematic showing midlatitude westerlies (eastward wind stress) and tropical easterlies (westward wind stress).
    [Show full text]
  • Chlorophyll a Variabliity Due to Large-Scale North Atlantic
    CHLOROPHYLL A VARIABILITY DUE TO LARGE-SCALE NORTH ATLANTIC CIRCULATION CHANGES By Alexis L. Santos A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Science Atmospheric and Oceanic Sciences at the University of Wisconsin – Madison May 2014 i Chlorophyll a Variability Due to Large-Scale North Atlantic Circulation Changes Alexis L. Santos Under the supervision of Dr. Galen A. McKinley ABSTRACT The North Atlantic Ocean is one of the strongest oceanic carbon sinks and is heavily influenced by biological uptake. Satellite-observed chlorophyll concentrations, a proxy for phytoplankton biomass, declined by 14% in the North Atlantic inter-gyre region (defined in this study as 40-60 °N, 20-40 °W) over 1998-2006. This study examines the drivers behind satellite chlorophyll a concentration changes over 1998-2006 in this North Atlantic inter-gyre region using a regional biogeochemical model of the North Atlantic basin. Light impacts phytoplankton growth seasonally, but nitrate concentrations drive chlorophyll concentrations on interannual timescales. A nitrate budget of the inter-gyre region finds that along-isopycnal horizontal mixing dominates on the mean and is also a first-order control of interannual variability from 1998-2000 to 2004-2006. Horizontal advection of nutrients is on the same order of magnitude as vertical nitrate advection, and horizontal advection is dominated by advection of nitrate by the North Atlantic nutrient stream. All nitrate transfer processes weaken over time, which is connected
    [Show full text]
  • A Steady Stratified Purely Azimuthal Flow Representing the Antarctic Circumpolar Current
    A STEADY STRATIFIED PURELY AZIMUTHAL FLOW REPRESENTING THE ANTARCTIC CIRCUMPOLAR CURRENT CALIN IULIAN MARTIN Faculty of Mathematics, University of Vienna, Austria E-mail address: [email protected] RONALD QUIRCHMAYR∗ Department of Mathematics, KTH Royal Institute of Technology, Sweden E-mail address: [email protected] Abstract. We construct an explicit steady stratified purely azimuthal flow for the governing equations of geophysical fluid dynamics. These equations are con- sidered in a setting that applies to the Antarctic Circumpolar Current, accounting for eddy viscosity and forcing terms. Keywords: Antarctic Circumpolar Current, variable density, azimuthal flows, eddy viscosity, geophysical fluid dynamics. Mathematics Subject Classification: Primary: 35Q31, 35Q35. Secondary: 35Q86. 1. Introduction Thorough analytical investigations of exact solutions to the fully nonlinear governing equations of geophysical fluid dynamics (GFD) represent an extensive and active research area, which was initiated by Constantin [1{4] and Constantin and Johnson [5{8]. Following this approach, we construct a unidirectional flow satisfying GFD considered in the so-called f-plane at the 45th parallel south, enhanced with an eddy viscosity term and a forcing term, and equipped with appropriate boundary conditions. We propose this specific flow for representing the gross dynamics of the arXiv:2010.09389v1 [physics.flu-dyn] 19 Oct 2020 Antarctic Circumpolar Current (ACC)|the World's longest and strongest Ocean current. ACC has no continental barriers: it encircles Antarctica along a 23 000 km path around the polar axis towards East at latitudes between 40° to 60°, see Fig. 1. It thereby links the Atlantic, Pacific and Indian Oceans making it the most impor- tant oceanic current in the Earth's climate system.
    [Show full text]