Geophysical Fluid Dynamics, Nonautonomous Dynamical Systems, and the Climate Sciences
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Rossby Number Similarity of Atmospheric RANS Using Limited
https://doi.org/10.5194/wes-2019-74 Preprint. Discussion started: 21 October 2019 c Author(s) 2019. CC BY 4.0 License. Rossby number similarity of atmospheric RANS using limited length scale turbulence closures extended to unstable stratification Maarten Paul van der Laan1, Mark Kelly1, Rogier Floors1, and Alfredo Peña1 1Technical University of Denmark, DTU Wind Energy, Risø Campus, Frederiksborgvej 399, 4000 Roskilde, Denmark Correspondence: Maarten Paul van der Laan ([email protected]) Abstract. The design of wind turbines and wind farms can be improved by increasing the accuracy of the inflow models repre- senting the atmospheric boundary layer. In this work we employ one-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations of the idealized atmospheric boundary layer (ABL), using turbulence closures with a length scale limiter. These models can represent the mean effects of surface roughness, Coriolis force, limited ABL depth, and neutral and stable atmo- 5 spheric conditions using four input parameters: the roughness length, the Coriolis parameter, a maximum turbulence length, and the geostrophic wind speed. We find a new model-based Rossby similarity, which reduces the four input parameters to two Rossby numbers with different length scales. In addition, we extend the limited length scale turbulence models to treat the mean effect of unstable stratification in steady-state simulations. The original and extended turbulence models are compared with historical measurements of meteorological quantities and profiles of the atmospheric boundary layer for different atmospheric 10 stabilities. 1 Introduction Wind turbines operate in the turbulent atmospheric boundary layer (ABL) but are designed with simplified inflow conditions that represent analytic wind profiles of the atmospheric surface layer (ASL). -
The Decadal Mean Ocean Circulation and Sverdrup Balance
Journal of Marine Research, 69, 417–434, 2011 The decadal mean ocean circulation and Sverdrup balance by Carl Wunsch1 ABSTRACT Elementary Sverdrup balance is tested in the context of the time-average of a 16-year duration time-varying ocean circulation estimate employing the great majority of global-scale data available between 1992 and 2007. The time-average circulation exhibits all of the conventional major features as depicted both through its absolute surface topography and vertically integrated transport stream function. Important small-scale features of the time average only become apparent, however, in the time-average vertical velocity, whether near the surface or in the abyss. In testing Sverdrup balance, the requirement is made that there should be a mid-water column depth where the magnitude of the vertical velocity is less than 10−8 m/s (about 0.3 m/year displacement). The requirement is not met in the Southern Ocean or high northern latitudes. Over much of the subtropical and lower latitude ocean, Sverdrup balance appears to provide a quantitatively useful estimate of the meridional transport (about 40% of the oceanic area). Application to computing the zonal component, by integration from the eastern boundary is, however, precluded in many places by failure of the local balances close to the coasts. Failure of Sverdrup balance at high northern latitudes is consistent with the expected much longer time to achieve dynamic equilibrium there, and the action of other forces, and has important consequences for ongoing ocean monitoring efforts. 1. Introduction The very elegant and powerful theories of the time-mean ocean circulation, treated as a laminar flow, remain of intense interest, despite the widespread recognition that the oceanic kinetic energy is dominated by the time variability. -
Role of Regional Ocean Dynamics in Dynamic Sea Level Projections by the End of the 21St Century Over Southeast Asia
EGU21-8618, updated on 25 Sep 2021 https://doi.org/10.5194/egusphere-egu21-8618 EGU General Assembly 2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. Role of Regional Ocean Dynamics in Dynamic Sea Level Projections by the end of the 21st Century over Southeast Asia Dhrubajyoti Samanta1, Svetlana Jevrejeva2, Hindumathi K. Palanisamy2, Kristopher B. Karnauskas3, Nathalie F. Goodkin1,4, and Benjamin P. Horton1 1Nanyang Technological University, Singapore ([email protected]) 2Centre for Climate Research Singapore, Singapore 3University of Colorado Boulder, USA 4American Museum of Natural History, USA Southeast Asia is especially vulnerable to the impacts of sea-level rise due to the presence of many low-lying small islands and highly populated coastal cities. However, our current understanding of sea-level projections and changes in upper-ocean dynamics over this region currently rely on relatively coarse resolution (~100 km) global climate model (GCM) simulations and is therefore limited over the coastal regions. Here using GCM simulations from the High-Resolution Model Intercomparison Project (HighResMIP) of the Coupled Model Intercomparison Project Phase 6 (CMIP6) to (1) examine the improvement of mean-state biases in the tropical Pacific and dynamic sea-level (DSL) over Southeast Asia; (2) generate projection on DSL over Southeast Asia under shared socioeconomic pathways phase-5 (SSP5-585); and (3) diagnose the role of changes in regional ocean dynamics under SSP5-585. We select HighResMIP models that included a historical period and shared socioeconomic pathways (SSP) 5-8.5 future scenario for the same ensemble and estimate the projected changes relative to the 1993-2014 period. -
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Vol. 62 Bollettino Vol. 62 - SUPPLEMENT 1 pp. 327 di Geofisica An International teorica ed applicata Journal of Earth Sciences IMDIS 2021 International Conference on Marine Data and Information Systems 12-14 April, 2021 Online Book of Abstracts SUPPLEMENT 1 Guest Editors: Michèle Fichaut, Vanessa Tosello, Alessandra Giorgetti BOLLETTINO DI GEOFISICA teorica ed applicata 210109 - OGS.Supp.Vol62.cover_08dorso19.indd 3 03/05/21 10:54 EDITOR-IN-CHIEF D. Slejko; Trieste, Italy EDITORIAL COUNCIL SUBSCRIPTIONS 2021 A. Camerlenghi, N. Casagli, F. Coren, P. Del Negro, F. Ferraccioli, S. Parolai, G. Rossi, C. Solidoro; Trieste, Italy ASSOCIATE EDITORS A. SOLID EaRTH GeOPHYsICs N. Abu-Zeid; Ferrara, Italy J. Ba; Nanjing, China R. Barzaghi; Milano, Italy J. Boaga; Padova, Italy C. Braitenberg; Trieste, Italy A. Casas; Barcelona, Spain G. Cassiani; Padova, Italy F. Cavallini; Trieste, Italy A. Del Ben; Trieste, Italy P. dell’Aversana; San Donato Milanese, Italy C. Doglioni; Roma, Italy F. Ferrucci, Vibo Valentia, Italy E. Forte; Trieste, Italy M.-J. Jimenez; Madrid, Spain C. Layland-Bachmann, Berkeley, U.S.A. Bollettino di Geofisica Teorica ed Applicata G. Li; Zhoushan, China c/o Istituto Nazionale di Oceanografia P. Paganini; Trieste, Italy e di Geofisica Sperimentale V. Paoletti, Naples, Italy Borgo Grotta Gigante, 42/c E. Papadimitriou; Thessaloniki, Greece 34010 Sgonico, Trieste, Italy R. Petrini; Pisa, Italy e-mail: [email protected] M. Pipan; Trieste, Italy G. Seriani; Trieste, Italy http-server: bgta.eu A. Shogenova; Tallin, Estonia E. Stucchi; Milano, Italy S. Trevisani; Venezia, Italy M. Vellico; Trieste, Italy A. Vesnaver; Trieste, Italy V. Volpi; Trieste, Italy A. -
Rotating Fluids
26 Rotating fluids The conductor of a carousel knows about fictitious forces. Moving from horse to horse while collecting tickets, he not only has to fight the centrifugal force trying to kick him off, but also has to deal with the dizzying sideways Coriolis force. On a typical carousel with a five meter radius and turning once every six seconds, the centrifugal force is strongest at the rim where it amounts to about 50% of gravity. Walking across the carousel at a normal speed of one meter per second, the conductor experiences a Coriolis force of about 20% of gravity. Provided the carousel turns anticlockwise seen from above, as most carousels seem to do, the Coriolis force always pulls the conductor off his course to the right. The conductor seems to prefer to move from horse to horse against the rotation, and this is quite understandable, since the Coriolis force then counteracts the centrifugal force. The whole world is a carousel, and not only in the metaphorical sense. The centrifugal force on Earth acts like a cylindrical antigravity field, reducing gravity at the equator by 0.3%. This is hardly a worry, unless you have to adjust Olympic records for geographic latitude. The Coriolis force is even less noticeable at Olympic speeds. You have to move as fast as a jet aircraft for it to amount to 0.3% of a percent of gravity. Weather systems and sea currents are so huge and move so slowly compared to Earth’s local rotation speed that the weak Coriolis force can become a major player in their dynamics. -
Atmosphere-Ocean Dynamics
1 80 o N o E 75 o N 30 o o E 70 N 20 o 65 N o a) E 10 oN 30o o 60 o o W 20 W 10 W 0 Atmosphere-Ocean Dynamics J. H. LaCasce Dept. of Geosciences University of Oslo LAST REVISED August 28, 2018 2 Contents 1 Equations 9 1.1 Derivatives ................................. 9 1.2 Continuityequation............................. 11 1.3 Momentumequations............................ 13 1.4 Equationsofstate.............................. 21 1.5 Thermodynamic equations . 22 1.6 Exercises .................................. 30 2 Basic balances 33 2.1 Hydrostaticbalance............................. 33 2.2 Horizontal momentum balances . 39 2.2.1 Geostrophicflow .......................... 41 2.2.2 Cyclostrophic flow . 44 2.2.3 Inertialflow............................. 46 2.2.4 Gradientwind............................ 47 2.3 The f-plane and β-plane approximations . 50 2.4 Incompressibility .............................. 52 2.4.1 The Boussinesq approximation . 52 2.4.2 Pressurecoordinates . 53 2.5 Thermalwind................................ 57 2.6 Summary of synoptic scale balances . 63 2.7 Exercises .................................. 64 3 Shallow water flows 67 3.1 Fundamentals ................................ 67 3.1.1 Assumptions ............................ 67 3.1.2 Shallow water equations . 70 3.2 Materialconservedquantities. 72 3.2.1 Volume ............................... 72 3.2.2 Vorticity............................... 73 3.2.3 Kelvin’s theorem . 75 3.2.4 Potential vorticity . 76 3.3 Integral conserved quantities . 77 3.3.1 Mass ................................ 77 3 4 CONTENTS 3.3.2 Circulation ............................. 78 3.3.3 Energy ............................... 79 3.4 Linearshallowwaterequations . 80 3.5 Gravitywaves................................ 82 3.6 Gravity waves with rotation . 87 3.7 Steadyflow ................................. 91 3.8 Geostrophicadjustment. 91 3.9 Kelvinwaves ................................ 95 3.10 EquatorialKelvinwaves . -
(Potential) Vorticity: the Swirling Motion of Geophysical Fluids
(Potential) vorticity: the swirling motion of geophysical fluids Vortices occur abundantly in both atmosphere and oceans and on all scales. The leaves, chasing each other in autumn, are driven by vortices. The wake of boats and brides form strings of vortices in the water. On the global scale we all know the rotating nature of tropical cyclones and depressions in the atmosphere, and the gyres constituting the large-scale wind driven ocean circulation. To understand the role of vortices in geophysical fluids, vorticity and, in particular, potential vorticity are key quantities of the flow. In a 3D flow, vorticity is a 3D vector field with as complicated dynamics as the flow itself. In this lecture, we focus on 2D flow, so that vorticity reduces to a scalar field. More importantly, after including Earth rotation a fairly simple equation for planar geostrophic fluids arises which can explain many characteristics of the atmosphere and ocean circulation. In the lecture, we first will derive the vorticity equation and discuss the various terms. Next, we define the various vorticity related quantities: relative, planetary, absolute and potential vorticity. Using the shallow water equations, we derive the potential vorticity equation. In the final part of the lecture we discuss several applications of this equation of geophysical vortices and geophysical flow. The preparation material includes - Lecture slides - Chapter 12 of Stewart (http://www.colorado.edu/oclab/sites/default/files/attached- files/stewart_textbook.pdf), of which only sections 12.1-12.3 are discussed today. Willem Jan van de Berg Chapter 12 Vorticity in the Ocean Most of the fluid flows with which we are familiar, from bathtubs to swimming pools, are not rotating, or they are rotating so slowly that rotation is not im- portant except maybe at the drain of a bathtub as water is let out. -
Shallow Water Waves and Solitary Waves Article Outline Glossary
Shallow Water Waves and Solitary Waves Willy Hereman Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, USA Article Outline Glossary I. Definition of the Subject II. Introduction{Historical Perspective III. Completely Integrable Shallow Water Wave Equations IV. Shallow Water Wave Equations of Geophysical Fluid Dynamics V. Computation of Solitary Wave Solutions VI. Water Wave Experiments and Observations VII. Future Directions VIII. Bibliography Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a fluid. The maximum velocity and maximum amplitude occur within the fluid or at an internal boundary (interface). Internal waves depend on the density-stratification of the fluid. Shallow water A surface wave is said to be in shallow water if its wavelength is much larger than the local water depth. Shallow water waves Shallow water waves correspond to the flow at the free surface of a body of shallow water under the force of gravity, or to the flow below a horizontal pressure surface in a fluid. Shallow water wave equations Shallow water wave equations are a set of partial differential equations that describe shallow water waves. 1 Solitary wave A solitary wave is a localized gravity wave that maintains its coherence and, hence, its visi- bility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and propagate with constant speed and constant shape. Soliton Solitons are solitary waves that have an elastic scattering property: they retain their shape and speed after colliding with each other. -
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. -
Mesoscale and Submesoscale Physical-Biological Interactions
Chapter 4. MESOSCALE AND SUBMESOSCALE PHYSICAL–BIOLOGICAL INTERACTIONS GLENN FLIERL Massachusetts Institute of Technology DENNIS J. MCGILLICUDDY Woods Hole Oceanographic Institution Contents 1. Introduction 2. Eulerian versus Lagrangian Models 3. Biological Dynamics 4. Review of Eddy Dynamics 5. Rossby Waves and Biological Dynamics 6. Isolated Vortices 7. Eddy Transport, Stirring, and Mixing 8. Instabilities and Generation of Eddies 9. Near-Surface/ Deep-Ocean Interaction 10. Concluding Remarks References 1. Introduction In the 1960s and 1970s, physical oceanographers realized that mesoscale eddy flows were an order of magnitude stronger than the mean currents, that such variability is ubiquitous, and that the transport of momentum and heat by transient motions signif- icantly altered the general circulation of the ocean (see Robinson, 1983). Evidence that eddies can also profoundly alter the distributions and the dynamics of the biota began to accumulate during the latter part of this period (e.g., Angel and Fasham, 1983). As biological measurement technologies continue to improve and interdisci- plinary field studies to progress, we are developing a clearer picture of the spatial and temporal structure of biological variability and its association with the mesoscale and submesoscale band (corresponding to length scales of ten to hundreds of kilometers The Sea, Volume 12, edited by Allan R. Robinson, James J. McCarthy, and Brian J. Rothschild ISBN 0-471-18901-4 2002 John Wiley & Sons, Inc., New York 113 114 GLENN FLIERL AND DENNIS J. MCGILLICUDDY and time scales of days to years). In addition, biophysical modelling now provides a valuable tool for examining the ways in which populations react to these flows. -
Atmospheric Circulation of Terrestrial Exoplanets
Atmospheric Circulation of Terrestrial Exoplanets Adam P. Showman University of Arizona Robin D. Wordsworth University of Chicago Timothy M. Merlis Princeton University Yohai Kaspi Weizmann Institute of Science The investigation of planets around other stars began with the study of gas giants, but is now extending to the discovery and characterization of super-Earths and terrestrial planets. Motivated by this observational tide, we survey the basic dynamical principles governing the atmospheric circulation of terrestrial exoplanets, and discuss the interaction of their circulation with the hydrological cycle and global-scale climate feedbacks. Terrestrial exoplanets occupy a wide range of physical and dynamical conditions, only a small fraction of which have yet been explored in detail. Our approach is to lay out the fundamental dynamical principles governing the atmospheric circulation on terrestrial planets—broadly defined—and show how they can provide a foundation for understanding the atmospheric behavior of these worlds. We first sur- vey basic atmospheric dynamics, including the role of geostrophy, baroclinic instabilities, and jets in the strongly rotating regime (the “extratropics”) and the role of the Hadley circulation, wave adjustment of the thermal structure, and the tendency toward equatorial superrotation in the slowly rotating regime (the “tropics”). We then survey key elements of the hydrological cycle, including the factors that control precipitation, humidity, and cloudiness. Next, we summarize key mechanisms by which the circulation affects the global-mean climate, and hence planetary habitability. In particular, we discuss the runaway greenhouse, transitions to snowball states, atmospheric collapse, and the links between atmospheric circulation and CO2 weathering rates. We finish by summarizing the key questions and challenges for this emerging field in the future. -
An Unconditionally Stable Scheme for the Shallow Water Equations*
810 MONTHLY WEATHER REVIEW VOLUME 128 An Unconditionally Stable Scheme for the Shallow Water Equations* MOSHE ISRAELI Computer Science Department, Technion, Haifa, Israel NAOMI H. NAIK AND MARK A. CANE Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York (Manuscript received 24 September 1998, in ®nal form 1 March 1999) ABSTRACT A ®nite-difference scheme for solving the linear shallow water equations in a bounded domain is described. Its time step is not restricted by a Courant±Friedrichs±Levy (CFL) condition. The scheme, known as Israeli± Naik±Cane (INC), is the offspring of semi-Lagrangian (SL) schemes and the Cane±Patton (CP) algorithm. In common with the latter it treats the shallow water equations implicitly in y and with attention to wave propagation in x. Unlike CP, it uses an SL-like approach to the zonal variations, which allows the scheme to apply to the full primitive equations. The great advantage, even in problems where quasigeostrophic dynamics are appropriate in the interior, is that the INC scheme accommodates complete boundary conditions. 1. Introduction is easy to code and boundary conditions for the discre- The two-dimensional linearized shallow water equa- tized equations are fairly natural to impose. At the other tions represent the evolution of small perturbations in end of the spectrum, the CP algorithm is speci®cally the ¯ow ®eld of a shallow basin on a rotating sphere. designed with the characteristics of the physics of the Our interest in these model equations arises from our equatorial ocean dynamics in mind. By separating the interest in solving for the motions in a linear beta-plane free modes into the eastward propagating Kelvin mode deep ocean.