Characteristics of Global Oceanic Rossby Wave and Mesoscale Eddies Propagation from Multiple Datasets Analysis
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Internal Gravity Waves: from Instabilities to Turbulence Chantal Staquet, Joël Sommeria
Internal gravity waves: from instabilities to turbulence Chantal Staquet, Joël Sommeria To cite this version: Chantal Staquet, Joël Sommeria. Internal gravity waves: from instabilities to turbulence. Annual Review of Fluid Mechanics, Annual Reviews, 2002, 34, pp.559-593. 10.1146/an- nurev.fluid.34.090601.130953. hal-00264617 HAL Id: hal-00264617 https://hal.archives-ouvertes.fr/hal-00264617 Submitted on 4 Feb 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License INTERNAL GRAVITY WAVES: From Instabilities to Turbulence C. Staquet and J. Sommeria Laboratoire des Ecoulements Geophysiques´ et Industriels, BP 53, 38041 Grenoble Cedex 9, France; e-mail: [email protected], [email protected] Key Words geophysical fluid dynamics, stratified fluids, wave interactions, wave breaking Abstract We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steep- ening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. -
Baroclinic Instability, Lecture 19
19. Baroclinic Instability In two-dimensional barotropic flow, there is an exact relationship between mass 2 streamfunction ψ and the conserved quantity, vorticity (η)given by η = ∇ ψ.The evolution of the conserved variable η in turn depends only on the spatial distribution of η andonthe flow, whichisd erivable fromψ and thus, by inverting the elliptic relation, from η itself. This strongly constrains the flow evolution and allows one to think about the flow by following η around and inverting its distribution to get the flow. In three-dimensional flow, the vorticity is a vector and is not in general con served. The appropriate conserved variable is the potential vorticity, but this is not in general invertible to find the flow, unless other constraints are provided. One such constraint is geostrophy, and a simple starting point is the set of quasi-geostrophic equations which yield the conserved and invertible quantity qp, the pseudo-potential vorticity. The same dynamical processes that yield stable and unstable Rossby waves in two-dimensional flow are responsible for waves and instability in three-dimensional baroclinic flow, though unlike the barotropic 2-D case, the three-dimensional dy namics depends on at least an approximate balance between the mass and flow fields. 97 Figure 19.1 a. The Eady model Perhaps the simplest example of an instability arising from the interaction of Rossby waves in a baroclinic flow is provided by the Eady Model, named after the British mathematician Eric Eady, who published his results in 1949. The equilibrium flow in Eady’s idealization is illustrated in Figure 19.1. -
Internal Waves Study on a Narrow Steep Shelf of the Black Sea Using the Spatial Antenna of Line Temperature Sensors
Journal of Marine Science and Engineering Article Internal Waves Study on a Narrow Steep Shelf of the Black Sea Using the Spatial Antenna of Line Temperature Sensors Andrey Serebryany 1,2,* , Elizaveta Khimchenko 1 , Oleg Popov 3, Dmitriy Denisov 2 and Genrikh Kenigsberger 4 1 Shirshov Institute of Oceanology, Russian Academy of Sciences, 117997 Moscow, Russia; [email protected] 2 Andreyev Acoustics Institute, 117036 Moscow, Russia; [email protected] 3 Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia; [email protected] 4 Institute of Ecology of the Academy of Sciences of Abkhazia, Sukhum 384900, Abkhazia; [email protected] * Correspondence: [email protected] Received: 4 August 2020; Accepted: 19 October 2020; Published: 22 October 2020 Abstract: The results of investigations into internal waves on a narrow steep shelf of the northeastern coast of the Black Sea are presented here. To measure the parameters of internal waves, the spatial antenna of three autonomous line temperature sensors were equipped in the depth range of 17 to 27 m. In observations that lasted for 10 days, near-inertial internal waves with a period close to 17 h and short-period internal waves with periods of 2–8 min, regularly approaching the coast, were revealed. The wave amplitudes were 4–8 m for inertial waves and 0.5–4 m for short-period internal waves. It was determined that most of the short-period internal waves approached from the southeast direction, from Cape Kodor. A large number of short waves reflected from the coast were also recorded. The intensification of short-period waves with inertial periodicity and the belonging of trains of short waves to crests of inertial waves were identified. -
ATMS 310 Rossby Waves Properties of Waves in the Atmosphere Waves
ATMS 310 Rossby Waves Properties of Waves in the Atmosphere Waves – Oscillations in field variables that propagate in space and time. There are several aspects of waves that we can use to characterize their nature: 1) Period – The amount of time it takes to complete one oscillation of the wave\ 2) Wavelength (λ) – Distance between two peaks of troughs 3) Amplitude – The distance between the peak and the trough of the wave 4) Phase – Where the wave is in a cycle of amplitude change For a 1-D wave moving in the x-direction, the phase is defined by: φ ),( = −υtkxtx − α (1) 2π where φ is the phase, k is the wave number = , υ = frequency of oscillation (s-1), and λ α = constant determined by the initial conditions. If the observer is moving at the phase υ speed of the wave ( c ≡ ), then the phase of the wave is constant. k For simplification purposes, we will only deal with linear sinusoidal wave motions. Dispersive vs. Non-dispersive Waves When describing the velocity of waves, a distinction must be made between the group velocity and the phase speed. The group velocity is the velocity at which the observable disturbance (energy of the wave) moves with time. The phase speed of the wave (as given above) is how fast the constant phase portion of the wave moves. A dispersive wave is one in which the pattern of the wave changes with time. In dispersive waves, the group velocity is usually different than the phase speed. A non- dispersive wave is one in which the patterns of the wave do not change with time as the wave propagates (“rigid” wave). -
TTL Upwelling Driven by Equatorial Waves
TTL Upwelling driven by Equatorial Waves L09804 LIUWhat drives the annual cycle in TTL upwelling? ET AL.: START OF WATER VAPOR AND CO TAPE RECORDERS L09804 Liu et al. (2007) Ortland, D. and M. J. Alexander, The residual mean circula8on in the TTL driven by tropical waves, JAS, (in review), 2013. Figure 1. (a) Seasonal variation of 10°N–10°S mean EOS MLS water vapor after dividing by the mean value at each level. (b) Seasonal variation of 10°N–10°S EOS MLS CO after dividing by the mean value at each level. represented in two principal ways. The first is by the area of [8]ConcentrationsofwatervaporandCOnearthe clouds with low infrared brightness temperatures [Gettelman tropical tropopause are available from retrievals of EOS et al.,2002;Massie et al.,2002;Liu et al.,2007].Thesecond MLS measurements [Livesey et al.,2005,2006].Monthly is by the area of radar echoes reaching the tropopause mean water vapor and CO mixing ratios at 146 hPa and [Alcala and Dessler,2002;Liu and Zipser, 2005]. In this 100 hPa in the 10°N–10°Sand10° longitude boxes are study, we examine the areas of clouds that have TRMM calculated from one full year (2005) of version 1.5 MLS Visible and Infrared Scanner (VIRS) 10.8 mmbrightness retrievals. In this work, all MLS data are processed with temperatures colder than 210 K, and the area of 20 dBZ requirements described by Livesey et al. [2005]. Tropopause echoes at 14 km measured by the TRMM Precipitation temperature is averaged from the 2.5° resolution NCEP Radar (PR). -
Internal Wave Generation in a Non-Hydrostatic Wave Model
water Article Internal Wave Generation in a Non-Hydrostatic Wave Model Panagiotis Vasarmidis 1,* , Vasiliki Stratigaki 1 , Tomohiro Suzuki 2,3 , Marcel Zijlema 3 and Peter Troch 1 1 Department of Civil Engineering, Ghent University, Technologiepark 60, 9052 Ghent, Belgium; [email protected] (V.S.); [email protected] (P.T.) 2 Flanders Hydraulics Research, Berchemlei 115, 2140 Antwerp, Belgium; [email protected] 3 Department of Hydraulic Engineering, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands; [email protected] * Correspondence: [email protected]; Tel.: +32-9-264-54-89 Received: 18 April 2019; Accepted: 7 May 2019; Published: 10 May 2019 Abstract: In this work, internal wave generation techniques are developed in an open source non-hydrostatic wave model (Simulating WAves till SHore, SWASH) for accurate generation of regular and irregular long-crested waves. Two different internal wave generation techniques are examined: a source term addition method where additional surface elevation is added to the calculated surface elevation in a specific location in the domain and a spatially distributed source function where a spatially distributed mass is added in the continuity equation. These internal wave generation techniques in combination with numerical wave absorbing sponge layers are proposed as an alternative to the weakly reflective wave generation boundary to avoid re-reflections in case of dispersive and directional waves. The implemented techniques are validated against analytical solutions and experimental data including water surface elevations, orbital velocities, frequency spectra and wave heights. The numerical results show a very good agreement with the analytical solution and the experimental data indicating that SWASH with the addition of the proposed internal wave generation technique can be used to study coastal areas and wave energy converter (WEC) farms even under highly dispersive and directional waves without any spurious reflection from the wave generator. -
Leaky Slope Waves and Sea Level: Unusual Consequences of the Beta Effect Along Western Boundaries with Bottom Topography and Dissipation
JANUARY 2020 W I S E E T A L . 217 Leaky Slope Waves and Sea Level: Unusual Consequences of the Beta Effect along Western Boundaries with Bottom Topography and Dissipation ANTHONY WISE National Oceanography Centre, and Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, United Kingdom CHRIS W. HUGHES Department of Earth, Ocean and Ecological Sciences, University of Liverpool, and National Oceanography Centre, Liverpool, United Kingdom JEFF A. POLTON AND JOHN M. HUTHNANCE National Oceanography Centre, Liverpool, United Kingdom (Manuscript received 5 April 2019, in final form 29 October 2019) ABSTRACT Coastal trapped waves (CTWs) carry the ocean’s response to changes in forcing along boundaries and are important mechanisms in the context of coastal sea level and the meridional overturning circulation. Motivated by the western boundary response to high-latitude and open-ocean variability, we use a linear, barotropic model to investigate how the latitude dependence of the Coriolis parameter (b effect), bottom topography, and bottom friction modify the evolution of western boundary CTWs and sea level. For annual and longer period waves, the boundary response is characterized by modified shelf waves and a new class of leaky slope waves that propagate alongshore, typically at an order slower than shelf waves, and radiate short Rossby waves into the interior. Energy is not only transmitted equatorward along the slope, but also eastward into the interior, leading to the dissipation of energy locally and offshore. The b effectandfrictionresultinshelfandslope waves that decay alongshore in the direction of the equator, decreasing the extent to which high-latitude variability affects lower latitudes and increasing the penetration of open-ocean variability onto the shelf—narrower conti- nental shelves and larger friction coefficients increase this penetration. -
Hydrodynamics V
PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON ITYDRODYNAMICS / YOKOHAMA / 7-9 SEPTEMBER 2OOO HYDRODYNAMICSV Theory andApplications Edited by Y.Goda, M.Ikehata& K.Suzuki Yoko ham a Nat i onal Univers ity OFFPRINT IAHR1- S=== @ a' AIRH ICHD2000Local OrganizingCommittee lYokohama I 2000 Modeling of Strongly Nonlinear Internal Gravity Waves WooyoungChoi Theoretical Division and Center for Nonlinear Studies Los Alamos National Laboratory, Los Alamos, NM 87545,USA Abstract being able to account for full nonlinearity of the problem but this simple idea has never been suc- We consider strongly nonlinear internal gravity cessfully realized. Recently Choi and Camassa waves in a multilayer fluid and propose a math- (1996, 1999) have derived various new models for ematical model to describe the time evolution of strongly nonlinear dispersive waves in a simple large amplitude internal waves. Model equations two-layer system, using a systematic asymptotic follow from the original Euler equations under expansion method for a natural small parame- the sole assumption that the waves are long com- ter in the ocean, that is the aspect ratio between pared to the undisturbed thickness of one of the vertical and horizontal length scales. Analytic fluid layers. No small amplitude assumption is and numerical solutions of the new models de- made. Both analytic and numerical solutions of scribe strongly nonlinear phenomena which have the new model exhibit all essential features of been observed but not been explained by using large amplitude internal waves, observed in the any weakly nonlinear models. This indicates the ocean but not captured by the existing weakly importance of strongly nonlinear aspects in the nonlinear models. -
Internal Waves in the Ocean: a Review
REVIEWSOF GEOPHYSICSAND SPACEPHYSICS, VOL. 21, NO. 5, PAGES1206-1216, JUNE 1983 U.S. NATIONAL REPORTTO INTERNATIONAL UNION OF GEODESYAND GEOPHYSICS 1979-1982 INTERNAL WAVES IN THE OCEAN: A REVIEW Murray D. Levine School of Oceanography, Oregon State University, Corvallis, OR 97331 Introduction dispersion relation. A major advance in describing the internal wave field has been the This review documents the advances in our empirical model of Garrett and Munk (Garrett and knowledge of the oceanic internal wave field Munk, 1972, 1975; hereafter referred to as GM). during the past quadrennium. Emphasis is placed The GM model organizes many diverse observations on studies that deal most directly with the from the deep ocean into a fairly consistent measurement and modeling of internal waves as statistical representation by assuming that the they exist in the ocean. Progress has come by internal wave field is composed of a sum of realizing that specific physical processes might weakly interacting waves of random phase. behave differently when embedded in the complex, Once a kinematic description of the wave field omnipresent sea of internal waves. To understand is determined, it may be possible to assess . fully the dynamics of the internal wave field quantitatively the dynamical processes requires knowledge of the simultaneous responsible for maintaining the observed internal interactions of the internal waves with other waves. The concept of a weakly interacting oceanic phenomena as well as with themselves. system has been exploited in formulating the This report is not meant to be a comprehensive energy balance of the internal wave field (e.g., overview of internal waves. -
Method of Studying Modulation Effects of Wind and Swell Waves on Tidal and Seiche Oscillations
Journal of Marine Science and Engineering Article Method of Studying Modulation Effects of Wind and Swell Waves on Tidal and Seiche Oscillations Grigory Ivanovich Dolgikh 1,2,* and Sergey Sergeevich Budrin 1,2,* 1 V.I. Il’ichev Pacific Oceanological Institute, Far Eastern Branch Russian Academy of Sciences, 690041 Vladivostok, Russia 2 Institute for Scientific Research of Aerospace Monitoring “AEROCOSMOS”, 105064 Moscow, Russia * Correspondence: [email protected] (G.I.D.); [email protected] (S.S.B.) Abstract: This paper describes a method for identifying modulation effects caused by the interaction of waves with different frequencies based on regression analysis. We present examples of its applica- tion on experimental data obtained using high-precision laser interference instruments. Using this method, we illustrate and describe the nonlinearity of the change in the period of wind waves that are associated with wave processes of lower frequencies—12- and 24-h tides and seiches. Based on data analysis, we present several basic types of modulation that are characteristic of the interaction of wind and swell waves on seiche oscillations, with the help of which we can explain some peculiarities of change in the process spectrum of these waves. Keywords: wind waves; swell; tides; seiches; remote probing; space monitoring; nonlinearity; modulation 1. Introduction Citation: Dolgikh, G.I.; Budrin, S.S. The phenomenon of modulation of short-period waves on long waves is currently Method of Studying Modulation widely used in the field of non-contact methods for sea surface monitoring. These processes Effects of Wind and Swell Waves on are mainly investigated during space monitoring by means of analyzing optical [1,2] and Tidal and Seiche Oscillations. -
1 the Dynamics of Internal Gravity Waves in the Ocean
The dynamics of internal gravity waves in the ocean: theory and applications Vitaly V. Bulatov, Yury V. Vladimirov Institute for Problems in Mechanics Russian Academy of Sciences Pr. Vernadskogo 101 - 1, Moscow, 119526, Russia [email protected] fax: +7-499-739-9531 Abstract. In this paper we consider fundamental processes of the disturbance and propagation of internal gravity waves in the ocean modeled as a vertically stratified, horizontally non- uniform, and non-stationary medium. We develop asymptotic methods for describing the wave dynamics by generalizing the spatiotemporal ray-tracing method (a geometrical optics method). We present analytical and numerical algorithms for calculating the internal gravity wave fields using actual ocean parameters such as physical characteristics of the sea water, topography of its floor, etc. We demonstrate that our mathematical models can realistically describe the internal gravity wave dynamics in the ocean. Our numerical and analytical results show that the internal gravity waves have a significant impact on underwater objects in the ocean. Key words: Stratified ocean, internal gravity waves, asymptotic methods. 1 Introduction. The history of studying the internal gravity waves in the ocean, as is known, originated in the Arctic Region after F. Nansen had described a phenomenon called “Dead Water”. Nansen was the first man to observe the internal gravity waves in the Arctic Ocean. The notion of internal waves involves different oceanic phenomena such as “Dead Water”, internal tidal waves, large scale oceanic circulation, and powerful pulsating internal waves. Such natural phenomena exist in the atmosphere as well; however, the theory of internal waves in the atmosphere was developed at a later time along with progress of the aircraft industry and aviation technology [1, 2]. -
The Counter-Propagating Rossby-Wave Perspective on Baroclinic Instability
Q. J. R. Meteorol. Soc. (2005), 131, pp. 1393–1424 doi: 10.1256/qj.04.22 The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere 1∗ 2 1 3 CORE By J. METHVEN , E. HEIFETZ , B. J. HOSKINS and C. H. BISHOPMetadata, citation and similar papers at core.ac.uk 1 Provided by Central Archive at the University of Reading University of Reading, UK 2Tel-Aviv University, Israel 3Naval Research Laboratories/UCAR, Monterey, USA (Received 16 February 2004; revised 28 September 2004) SUMMARY Baroclinic instability of perturbations described by the linearized primitive equations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamil- tonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’— potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there.