DOCSLIB.ORG

Hydrodynamics V

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. Differences between large am- internal wave propagation. An interesting point plitude surface and internal solitary waves are ad- to make is that the including strong nonlinear- dressed. ity does not simply add new nonlinear terms but change dispersive characters, from linear to non- 1 Introduction linear. Despite of recent progress, the two-layer sys- Two fundamental physical mechanisms, nonlin- tem is often too simplified to be useful for prac- earity and dispersion, play important roles in tical applications. For instance, the two-layer the evolution of long internal gravity waves com- model has not only its limited despcription of monly observed in the ocean, more generally in smoothly stratified ocean but also the lack of any stratified fluids. Under the assumption of higher-order baroclinic wave modes. Therefore weakly nonlinear and weakly dispersive, the bal- the theory needs be extended to the more general ance between these two effects leads to a re- situation relevant for real oceanic applications. markable phenomenon of solitons, very localized Here we will study a continuously stratified fluid disturbances propagating without any change in approximated by a stack ofseveral homogeneous form. However there have been a number of layers. observations of large amplitude internal waves for which the weakly nonlinear assumption is far from being realistic. For example, in the north- 2 Governing Equations western coastal area of the Unites States, Stan- For an inviscid and incompressible fluid of den- ton & Ostrovsky (1998) observed the train of sily pi, the velocity components in Cartesian tidally-generated internal waves in the form of coordinates (ut,wt) and the pressure pt (i : solitary waves depressing the 7m deep pycnocline 1,' . N) satisfy the continuity equation and up to 30m. Evidently the weakly nonlinear mod- , the Euler equations: els like the Korteweg-de Vries (KdV) equation commonly used in the community of geophysi- ui, wi" (1) cal fluid dynamics are completely irrelevant in * 0, such cases and new models need to be devel- u6 * uiu6* * wiui" -pi.rlpi, (2) oped. The theory to be desired is of course one u61luiwi**w6w4" -ptr/pt-9, (3) where .L is a typical wavelength' For finite- amplitude waves' we also assume that u;lus: OG;'lh): O(1)' (10) : where LIs is a characteristic speed chosen as [/g scalings in (9)-(10), we Gh)t|". Based on the non-dimensionalize all physical variables as n : Lr*, z : hz*, 1: (LlUs)t., ) (tl) Ci: hei, pi: biu&)pi, l ui : Uout, wi : eUowi' ) and assume that all variables with asterisks are O(1) in e. by integrating (i)-(2) across the i-th laver Figure 1: A multi-laYer sYstem the boundary con- ?lt+r < z < rli) and imposing ditions (4)-(6)' we obtain the layer-mean equa- acceleration and sub- where g is the gravitational tions (Wu J.981): scripts with respect to space and time represent For a stable stratiflcation' (12) puriiul difierentiation. uu+ (Hrtr),:0, Ht:nt- Tr+t, pi < pi+\ is assumed . The boundary condi- the i- -HIFG, (13) iions at the upper and lower interfaces of (Hfia)t+ (ntun;),: th layer require the continuity of normal velocity is defined as and pressure: where the layer-mean quantity / 2:r1i@'t)' (4) nit+ucrlir:wi, at (r,z,t)dz, (14) !(n,t1: ; I::.,f : at 2 : r1aa1(t't)' (5) \t+t1l uirli+lr ui, and we have dropped the asterisks for simplic- pi = pi-r at 7 : r1i(x',t) (6) ity. The quantities ufi and p1r prevent closure the location In (4)-(6), nt@,t) (d : 1,''' , N) is oi the .yste* of layer-mean equations (12)-(13)' given by of ttr" tpp"t interface of the i-th layer The following analysis will therefore focus on ex- pressing these quantities in terms of 14 and ul to nr: et-'i n,, (7) close the sYstem. j=t The vertical momentum equation (3) for the be written as i-th i-th layer can where h1 is the undisturbed thickness of the interfacial displacement' Iayer and (1(r,t) is the : -L - "l*0, * u'iwir r wi'wi"f' (15) be Pt, TLe position of the bottom, nv+t(n,t) can written as Hence, we can seek an asymptotic expansion of e2, N f : (ua,wi,pt) in Powersof : (n+r -Dni: (r+r - h, (8) ?N+1 (16) j=1 !(r,z,t):1(o) a e27$)*Ot'+'' (1,,11(z,t) is the bottom topography and :0, 1,' ' " where where /(-) : O(1) for m h is the total dePth. Ilom (15)-(16), after imposing the pressure (6)' continuity across the interface given by the 3 Nonlinear DisPersive Model leading-order Pressrue Pr(o) is (o): -e - rt)+ Pi@,t), (17) Under the assumption that the thickness of each p Iayer is much smaller than the characteristic where P;(r, t) : paa(x,r1l,J) is the pressureat wavelength, we have the following scaling relation of the ith layer' For i : 1' from the continuity equation the upper surface betweerrzl arrd wi, p1 : since the upper boundary is free, we impose (1), at' z :4r, instead of (6), where P1 is wtlut : O(hil L) : O(e) 4<I, (9) Py(t,t) the.'knowq,atposphericpressure. By'substit;rting For l ( i ( fl, (27)-(28) determines the evolu- (16)-(17)into (2), one obtains tion of 2-l[-un]nowns, E4 and.q;, while Pais given by the following recursionformula obtainedfrom u[o):ulo)@,t) if urLo):o (17) (26): ,at 1:ou, and - - Notice that condition (18) is automatically sat- Pi+r : Pt,i pr (ono Lon*o" uor,n). (29) isfied if we assumethat the flow is initi{tlly'ino- tational (Choi & Camassa1996). From ({), *e Theseequations have been derived under the sole ca,nnovv obtain the leading-order vertical'velodity assumption that the waves a,re long compa,red ut(o) tutt.*tot the kinematicboundary cbndition wlth the'water depth and we'have imposedno (5) at the interfaceas assumption on wave amplitude. The kinematic equation (27) is exact, while the dyna,rnicequa- .[o) : -1uaf))Q - rto+r,)* D$1r+t, (19) ti6ns (28)-(29) have non-hidioStatic contribu- tioirs coriect up to O(e2). where D; stands for material derivative, Even for rigidJid approximation ((r : 0), the ' Dt: 0t t un(016, (20) system :ot (27\-(28) is still tralid if Pr is regarded as unknown pressureat the top bounda,ry. Fbom (16) and (18), it can be easily shownthat Hru,-U: H;'E'idt+ O(eA), (2L) 4 Hydrostatic Approximation so that the layer-mean horizontal mormentum When we neglectdispersive effects (say ai : bi: equation (13) fn dlmbnsionlessform becomes 0), we recoverthe hydrostatic equationsfor mul- (i : il**Etdu - -P;; + O(ea). (22) tilayersystem L,." , N): At O(e2),from (15)-(16) and (19), the equa- H6+ (HtU),:0, Ht=qa-rli+r, (30) tion for pr(1)is du'41*Tilfra, -l /ort + SL Hj, * grtt+t, puLi) -L.ulo'+ui(o)ui(o) +wn@wn@ll \-r)r i=l rt : aa@,t)(z- \e+i 'f ba(r,t)' (23) = -Prrlh,(31) In equation (23), a; and bl are definedas where (29) has been used. ' a6(x,t):-u;6 *fr;Ttir, - (6tn)' , (24) ba(x,t): -D;2rh+t, (25) 5 One-layer System where we'have used E; : vo(o) + O(e2)' After For the'.case of a honogeneous 'layer (1V - 1), integrating (23) with respect to z and imqosing equations (27)-(28) reduce to the system of equa- the dyna,mic boundary condition in (6), we ob- tions derivedby Green& Naghdi (1976)by using tain pa(1); the director sheet theory. Without any topogra- pressure - - - phy- at the bottom gnd exlernal at the p'(L): t"nl@ nr+t)2(no nn*r)"] &&eesurface (ez : h,: 0), equations(27)-(28) + urlk- q+L).-(a - ru,)] . (zo) possessthe solitary wave solution given by (r(x) : aseeh2(kx), X : n - ct, (32) Fbom'(lD'and (26), we can find ffi;',the right-hand-si{g term of the horizontal moderr- .,.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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].
    [Show full text]
  • On the Modifications of Near-Inertial Waves at Fronts
    Noname manuscript No. (will be inserted by the editor) On the modifications of near-inertial waves at fronts: Implications for energy transfer across scales Leif N. Thomas Received: date / Accepted: date Abstract In the ocean, wind-generated kinetic energy (KE) manifests itself primarily in balanced currents and near-inertial waves. The dynamics of these flows is strongly constrained by the Earth's rotation, causing the KE in bal- anced currents to follow an inverse cascade but also preventing wave-wave interactions from fluxing energy in the near-inertial band to lower frequencies and higher vertical wavenumbers. How wind-generated KE is transferred to small-scale turbulence and dissipated is thus a non-trivial problem. This article presents a review of recent theoretical calculations and numerical simulations that demonstrate how some surprising modifications to internal wave physics by the lateral density gradients present at ocean fronts allow for strong in- teractions between balanced currents and near-inertial waves that ultimately result in energy loss for both types of motion. Keywords fronts · internal waves · wave-mean flow interactions 1 Introduction Winds blowing over the ocean generate currents with a range of frequencies. The bulk of the kinetic energy (KE) in these flows is contained in mesoscale currents and eddies with low frequencies, which are strongly constrained by the Earth's rotation to follow the geostrophic balance. Winds also generate near-inertial waves (NIWs), which are oscillatory, unbalanced motions with frequencies close to the inertial frequency f = 2Ω sin φ (Ω is the Earth's angular velocity and φ latitude). The dissimilar temporal scales of the bal- anced, mesoscale currents and the NIWs suggest that the two types of motion should not interact very effectively, and that the fast waves should simply pass Leif N.
    [Show full text]
  • Relaxation Processes for Internal Waves in Mesoscale Flow (Transport Phenomena/Rossby Waves) KENNETH M
    Proc. NatL Acad. Sci. USA Vol. 80, pp. 1144-1146, February 1983 Applied Physical Sciences Relaxation processes for internal waves in mesoscale flow (transport phenomena/Rossby waves) KENNETH M. WATSON University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego, California 92152 Contributed by Kenneth M. Watson, October 12, 1982 ABSTRACT A dynamical "test-wave" model has been devel- Here kh is the projection of the wave number k in the horizontal oped to study transport phenomena within oceanic internal wave plane, wkis the angularfrequency of alinearwave ofwave num- fields. This model is extended here to describe effects of a me- ber k, and c.c. stands for complex conjugate. In the absence of soscale flow field on internal wave transport. Previous work with nonlinear interactions among the waves, the Fourier coeffi- weak-interaction perturbation theory has suggested a substantial cients bk are constant. enhancement due to mesoscale currents. Extension to the strong- In the induced diffusion limit [3], the wave field is separated interaction regime in the present paper suggests a relatively small into large-scale waves, designated here with wave number 1, and effect due to mesoscale interactions. small-scale waves, designated here by wave numbers k and m. Systems of nonlinearly interacting waves have various appli- I shall refer to the large-scale waves as the "ambient field. " This cations in plasma physics, geophysics, and solid-state physics. will consist of internal wave (IW) and Rossby wave (RW) com- A "test-wave" model for triad, or three-wave, interactions has ponents.
    [Show full text]
  • Mysterious Underwater Waves
    FEATURE | PROF. LEO MAAS, NIOZ ROYAL NETHERLANDS INSTITUTE FOR SEA RESEARCH, THE NETHERLANDS Uncharted Reality? Mysterious Underwater Waves In addition to surface waves generated by wind, tidal forces or, in case of tsunamis, seismic events, there exists a less well-known class of bigger waves under water. These underwater waves (internal waves) are generated by the same forces, but owe their existence to the ocean’s non-uniform density distribution. This paper introduces various underwater waves that appear on interfaces or in continuous density stratification. In uniformly-stratified seas, these waves differ from surface waves in nearly every conceivable aspect, creating underwater ‘storms’ at certain hotspots, which may possibly impact natural and man-made structures, and which may transport heat and material vertically. The ocean’s salt and heat content, which its boundary. While ocean and atmosphere approximately a factor thousand, the ratio of determines its density, vary with depth. are dynamically quite similar, we never see the cross-thermocline density difference to This stable stratification supports underwater such waves in the ocean though, because mean density. Therefore, interfacial waves waves. Due to slight differences in density, the ocean is opaque. Light penetrates a mere attain larger amplitudes (up to hundreds of these waves easily displace fluid parcels hundred metres, leaving the remainder of metres), have longer periods (longer than vertically over hundreds of metres. the ocean literally and figuratively in the dark. 10 minutes, say) and have wavelengths (up Depending on the local rate with which But oceanographic instruments ‘visualise to kilometres) that are short compared to density increases with depth, they propagate the invisible’.
    [Show full text]
  • Propagation of Internal Wave Packets in the Thermocline
    Center for Turbulence Research 119 Proceedings of the Summer Program 2000 Propagation of internal wave packets in the thermocline By G. F. Carnevale† AND P. Orlandi‡ Internal wave packets propagating vertically in the oceanic thermocline are investigated with numerical simulations. For a typical set of environmental and packet parameters, it is shown that linear dispersion will have a significant effect on the spreading and decay in amplitude of these packets. Sufficiently strong packets are shown to generate turbulence that forms a continuous ‘scar’ of small-scale perturbations in their wake. 1. Introduction Internal wave groups or packets play an important role in the dynamics of the oceanic thermocline, the upper few hundred meters of the ocean where the temperature changes from high surface values to the much lower values below. Recent observations (Alford and Pinkel, 2000) show vertically propagating wave packets at depths from 150 to 350 m. These packets have vertical extent of about 50 m with internal vertical wavelengths of about 12 m and are associated with overturning events with vertical scales of about 2 m. Because overturns can lead to small-scale turbulence and mixing, they form a subject of intense investigation. Recent theoretical analysis by Thorpe (1999) provides a criterion for determining whether the small-scale turbulence generated by a packet will be left behind in just small patches or in continuous ‘scars’ much longer than the size of the packet. Stimulated by these developments, we have embarked on a numerical investigation of internal wave packets. Numerical simulations in this area may be of great benefit because the available oceanic data is primarily one-dimensional, and the full three-dimensional structure obtainable through simulation may aid in deciphering observational data.
    [Show full text]
  • The Baroclinic Instability in a Rotating Stratified Fluid
    The Barostrat Instability: the baroclinic instability in a rotating stratified fluid Patrice Le Gal1, Miklos Vincze2, Ion Borcia3, Uwe Harlander3 1IRPHE, CNRS - Aix Marseille University - Centrale Marseille, 49 rue F. Joliot Curie, 13384 Marseille Cedex 13, France. [email protected] 2MTA-ELTE Theoretical Physics Research Group, Pazmany P. stny. 1/a. H-1117, Budapest, Hungary 3Lehrstuhl Aerodynamik und Strmungsmechanik, Brandenburgische Technische Universitt Cottbus-Senftenberg, Siemens-Halske-Ring 14, 03046 Cottbus, Germany Abstract Our project aims to describe the baroclinic instability that destabilizes an initially strat- ified layer of fluid. Classically, this instability is studied using pure fluid. Here, the originality of our experiment comes from the use of a layer of water initially stratified with salt. Before rotation is started, double convection sets in within the stratified layer with a strongly nonhomogeneous pattern consisting of a double diffusive staircase at the bottom of the container in the very dense water layer and a shallow convective cell in the top surface layer. These two layers are separated by a motionless stably stratified zone. As radial motions take place due to the presence of these convective cells, the action of the Coriolis force generates strong zonal flows as soon as rotation is started. Then, above a rotation rate threshold, the baroclinic instability destabilizes the flow in the top shallow convective layer, generating a ring of pancake vortices sitting above the stably stratified layer. Therefore, this laboratory arrangement mimics the presence of a stratosphere above a baroclinic unstable troposphere. Infrared camera images measure the temperature distributions at the water surface and PIV velocity maps describe the wavy flow pattern at different altitudes.
    [Show full text]
  • Internal Waves in a High Latitude Region
    ISSN 00014370, Oceanology, 2010, Vol. 50, No. 5, pp. 668–674. © Pleiades Publishing, Inc., 2010. Original Russian Text © E.G. Morozov, V.T. Paka, 2010, published in Okeanologiya, 2010, Vol. 50, No. 5, pp. 709–715. MARINE PHYSICS Internal Waves in a HighLatitude Region E. G. Morozova and V. T. Pakab a Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia b Atlantic Branch of the Shirshov Institute of Oceanology, Russian Academy of Sciences, pr. Mira 1, Kaliningrad, 236000 Russia Email: [email protected] Received August 26, 2008; in final form, February 15, 2010 Abstract—Internal waves are studied in two highlatitude regions of the Kara Sea. The measurements were carried out with a towed CTD profiler and a distributed temperature sensor on a mooring. The lack of internal waves with an M2 tidal period and the presence of highfrequency waves are demonstrated on the basis of the measurements and numerical modeling. DOI: 10.1134/S0001437010050048 CHARACTERISTICS OF THE INTERNAL nal tides also depends on the geometrical form of the TIDE IN THE ARCTIC REGION underwater topography. The main factors determining It is known that internal tidal waves are generated the generation are the angle of the slope and the height in the ocean when currents of the barotropic tide flow (the proximity to the layer of the maximum Brunt– over irregularities of the bottom topography [2, 4, 9, Väisälä frequency) of the submarine elevation [12]. If 12, 25]. It is likely that the first paper in which the lin the inclination of the slope is close to the characteris ear theory of internal wave generation by tides on a tics of the internal tidal wave determined from equa submarine slope was developed is the one published by tion Rattray [26].
    [Show full text]