DOCSLIB.ORG

The Structure and Dynamics of Atmospheric Bores and Solitons As Determined from Remote Sensing and Modeling Experiments During Ihop

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Structure and Dynamics of Atmospheric Bores and Solitons As Determined from Remote Sensing and Modeling Experiments During Ihop JP6J.4 THE STRUCTURE AND DYNAMICS OF ATMOSPHERIC BORES AND SOLITONS AS DETERMINED FROM REMOTE SENSING AND MODELING EXPERIMENTS DURING IHOP Steven E. Koch, Mariusz Pagowski1,2, James W. Wilson3, Frederic Fabry4, Cyrille Flamant5, Wayne Feltz6, Geary Schwemmer7, and Bart Geerts8 1 NOAA Research – Forecast Systems Laboratory, Boulder, Colorado 2 Cooperative Institute for Research in the Atmosphere, Colorado State University 3 National Center for Atmospheric Research 4 Radar Observatory, McGill University 5 Institut Pierre-Simon Laplace, Paris, France 6 Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin 7 NASA Goddard Space Flight Center 8 Department of Atmospheric Sciences, University of Wyoming 1. Introduction 2. Background material on bores Solitary waves are a class of gravity waves The presence of low-level stratification favors consisting of a single elevation of finite amplitude the ordered evolution of gravity currents into that, owing to a balance between nonlinearity and turbulent bores, bores, solitons, and finally solitary dispersion, propagates without change of form. A waves (Christie et al. 1979; Simpson 1987). One family of solitary waves, which is termed a characteristic of gravity currents is a “feeder flow” “soliton”, forms as the natural consequence of the of air directed from behind the head of the gravity evolution of a bore – a type of gravity wave current toward its leading edge in a current-relative (hydraulic jump) generated as a density current framework. Passage of gravity currents at a (such as cold air from a thunderstorm) intrudes ground site is usually identifiable by an abrupt into a fluid of lesser density, which in the case of pressure jump hydrostatically related to the mean the atmosphere, occurs beneath a low-level cooling throughout the depth of the current, a inversion. These phenomena were observed sharp wind shift caused by the horizontal gradient repeatedly by a multitude of ground-based and of the pressure perturbation field, and increased airborne remote sensing systems during the six- gustiness due to strong vertical mixing in the head. week field phase of the International H20 Project (IHOP), even though bores were not one of the An internal bore in the atmosphere is a type of primary IHOP objectives (Weckwerth et al. 2004). gravity wave disturbance that propagates on a These observing systems together produced the low-level inversion ahead of gravity currents. most extensive set of observations ever collected Bores typically are generated as a gravity current of the evolving structure of bores, solitons, and intrudes into a stably-stratified boundary layer solitary waves. In spite of this, a more complete (SBL) of sufficient depth near the ground, resulting understanding of the dynamics of these in a sustained elevation of the inversion layer. phenomena and their interactions required use of Amplitude-ordered solitary waves (a train of which very high-resolution numerical weather prediction is referred to as a soliton) can evolve from bores in models initialized with IHOP data. These some instances. Because the speed of a solitary observations and the numerical modeling together wave is proportional to the wave amplitude, a offer the opportunity for an unprecedented study of dispersive family of waves evolves from the initial the evolving structure of bores, solitons, and bore with amplitudes inversely related to their solitary waves. widths. The number of waves increases continuously with time to a finite value, though the Corresponding author address: Steven E. Koch, NOAA/OAR/FSL, R/FS1, 325 Broadway, Boulder, CO number of waves is highly dependent upon the 80305-3328; e-mail < [email protected]> turbulent dissipation. According to the hydraulic theory of Rottman defined solitary waves may propagate ahead of and Simpson (1989), hereafter RS89, bore the gravity current. propagation speed depends upon its depth (db), the SBL inversion depth (h0), and the speed of a This prediction for the strength of a bore may be long gravity wave (Cgw) as follows: compared to another one based upon hydraulic theory and the laboratory work of RS89, which 1 2 does not require knowledge of the inflow velocity, C C = !0.5 d h 1+ d h # . (1) bore gw " ( b 0 )( b 0 )$ but instead depends upon: Koch and Clark (1999) have applied other Cgc Cgc Cgc predictive equations for bore speed to account for Fr = = 1 = C 2 N h such factors as finite fluid depth, vanishingly small gw (g !" h0 "vw ) 0 depth of the stable layer, and energy loss and (3) restricted to the neutral layer above the SBL d waveguide (Klemp et al. 1997). In general, the H = gc SBL must be sufficiently deep and intense to h0 support a bore of a given strength. The modeling work of Haase and Smith (1989b), hereafter HS89, where Fr is the Froude number, H is a measure of and Jin et al. (1996) sheds light on this issue. the depth of the gravity current to the inversion HS89 suggest that two parameters govern depth, and the potential temperature change whether an undular bore will be generated from an across the inversion is given by !" . It is of some intrusive gravity current: interest to note that the Froude number used in RS89 is proportional to the inverse of the µ (U ! Cgc ) (U ! Cgc ) F = = parameter used in HS89, i.e., the critical value C* g "# dgc #vw µ >0.7 equates in the RS89 nomenclature to: and (2) Cgc 2 C0 2N h0 $ 0.91 . (4) µ = = < = N h0 !µc Cgc Cgc The presence of the gravity current is no The first parameter F is the ratio of the front- longer critical to the evolution of the undular bore relative “inflow velocity” of the cold air (U - C ) to gc and solitary waves once the bore has been the densimetric speed of a gravity current (C*), the generated (Christie 1989). In the simplest case, latter being a function of the gravity current depth the bore is generated on top of a surface-based, d and temperature contrast ( ). The second gc µ pre-frontal stable layer of sufficient depth as the parameter is the ratio of the long gravity wave gravity current intrudes into the SBL. In the real phase speed C0 to the gravity current speed (Cgc). atmosphere, complex stratification, vertical wind Note that C0 depends upon the inversion layer shear, elevated inversions, and unsteady and/or strength (N) and depth (h0). The parameter µ multiple gravity currents may complicate matters. determines whether an undular bore (or solitary In addition, the PBL must be sufficiently deep and wave) will form and propagate ahead of the gravity intense to support a bore of a given strength current as required. When µ <0.7 (the (Rottman and Simpson 1989). If a mechanism is “supercritical regime”), the gravity current not present to trap the vertical propagation of wave propagates faster than any gravity waves and a energy, the bore will quickly diminish (Crook 1988; well-defined feeder flow is present. When the Koch et al. 1991; Koch and Clark 1999). Wave value of µ increases to near 0.7, but still within trapping ability is typically measured by the Scorer parameter defined as: this supercritical regime, undular bores may form. Bores and solitary waves are spawned when 2 2 2 >0.7 (the “subcritical regime”) as the gravity 2 Nm " U "z 2 µ m = ! ! k , (5) 2 U C wave propagates considerably faster than the (U ! Cbore ) ( ! bore ) gravity current. For large values of F, several well- where k and m are the horizontal and vertical windshift into the direction of movement of the wavenumbers, Nm is the moist Brunt-Väisälä disturbance associated with a sudden pressure frequency, U is the background wind in the jump, and a net cooling in the lower troposphere. direction of bore propagation, and Cbore is the bore The degree of cooling should be hydrostatically propagation speed. A rapid decrease of m with consistent with the sustained surface pressure height supports wave trapping. Of particular increase that follows an initial abrupt pressure relevance to bores is the low-level jet mechanism, jump, as recorded in sensitive surface which seems to be quite prevalent in bore case microbarograph data. Cooling associated with studies (Koch et al.1991), since it gives rise to gravity currents is due primarily to horizontal strong trapping related to curvature in the velocity advection of the denser air, whereas adiabatic profile (the second term in the Scorer equation). ascent is the cause of cooling in the case of a bore. Thus, pronounced surface cooling is not Koch and Clark (1999) provide a methodology characteristic of bores; in fact, weak warming (and for determining whether observed phenomena are drying) may occur as the result of turbulent gravity currents, bores, or solitary waves. The downward mixing of warmer (and typically drier) minimum requirements that must be satisfied to air from above the inversion into the SBL. support the hypothesis that a phenomenon is actually a gravity current are that: Gravity currents may generate other kinds of gravity waves besides bores and solitary waves. • Its depth as predicted hydrostatically using Model simulations show that a broad spectrum of gravity current theory agrees with that gravity waves may be produced by gravity measured by the remotely sensed data. currents, including trapped lee-type waves created • Its speed of propagation observed prior to by strong flow over the head of the gravity current deceleration is consistent with that predicted (Jin et al. 1996). Trapped lee waves display no from gravity current theory. vertical tilt and are motionless relative to the • A region of pronounced positive front-relative gravity current head. Lee-wave trapping occurs “feeder flow” is observed behind the leading only under a very special condition in which the edge of the gravity current above the surface Scorer parameter decreases sufficiently rapidly layer (so as to minimize frictional effects).
Load more

Recommended publications
  • Fourth-Order Nonlinear Evolution Equations for Surface Gravity Waves in the Presence of a Thin Thermocline
    J. Austral. Math. Soc. Ser. B 39(1997), 214-229 FOURTH-ORDER NONLINEAR EVOLUTION EQUATIONS FOR SURFACE GRAVITY WAVES IN THE PRESENCE OF A THIN THERMOCLINE SUDEBI BHATTACHARYYA1 and K. P. DAS1 (Received 14 August 1995; revised 21 December 1995) Abstract Two coupled nonlinear evolution equations correct to fourth order in wave steepness are derived for a three-dimensional wave packet in the presence of a thin thermocline. These two coupled equations are reduced to a single equation on the assumption that the space variation of the amplitudes takes place along a line making an arbitrary fixed angle with the direction of propagation of the wave. This single equation is used to study the stability of a uniform wave train. Expressions for maximum growth rate of instability and wave number at marginal stability are obtained. Some of the results are shown graphically. It is found that a thin thermocline has a stabilizing influence and the maximum growth rate of instability decreases with the increase of thermocline depth. 1. Introduction There exist a number of papers on nonlinear interaction between surface gravity waves and internal waves. Most of these are concerned with the mechanism of generation of internal waves through nonlinear interaction of surface gravity waves. Coherent three wave interactions of two surface waves and one internal wave have been investigated by Ball [1], Thorpe [22], Watson, West and Cohen [23] and others. Using the theoretical model of Hasselman [12] for incoherent three-wave interaction, Olber and Hertrich [18] have reported a mechanism of generation of internal waves by coupling with surface waves using a three-layer model of the ocean.
    [Show full text]
  • 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]
  • A Multidiagnostic Investigation of the Mesospheric Bore Phenomenon Steven M
    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A2, 1083, doi:10.1029/2002JA009500, 2003 A multidiagnostic investigation of the mesospheric bore phenomenon Steven M. Smith,1 Michael J. Taylor,2 Gary R. Swenson,3 Chiao-Yao She,4 Wayne Hocking,5 Jeffrey Baumgardner,1 and Michael Mendillo1 Received 24 May 2002; revised 3 September 2002; accepted 5 September 2002; published 20 February 2003. [1] Imaging measurements of a bright wave event in the nighttime mesosphere were made on 14 November 1999 at two sites separated by over 500 km in the southwestern United States. The event was characterized by a sharp onset of a series of extensive wavefronts that propagated across the entire sky. The waves were easily visible to the 1 naked eye, and the entire event was observed for at least 5 2 hours. The event was observed using three wide-angle imaging systems located at the Boston University field station at McDonald Observatory (MDO), Fort Davis, Texas, and the Starfire Optical Range (SOR), Albuquerque, New Mexico. The spaced imaging measurements provided a unique opportunity to estimate the physical extent and time history of the disturbance. Simultaneous radar neutral wind measurements in the 82 to 98 km altitude region were also made at the SOR which indicated that a strong vertical wind shear of 19.5 msÀ1kmÀ1 occurred between 80 and 95 km just prior to the appearance of the disturbance. Simultaneous lidar temperature and density measurements made at Fort Collins, Colorado, 1100 km north of MDO, show the presence of a large (50 K) temperature inversion layer at the time of the wave event.
    [Show full text]
  • The Internal Gravity Wave Spectrum: a New Frontier in Global Ocean Modeling
    The internal gravity wave spectrum: A new frontier in global ocean modeling Brian K. Arbic Department of Earth and Environmental Sciences University of Michigan Supported by funding from: Office of Naval Research (ONR) National Aeronautics and Space Administration (NASA) National Science Foundation (NSF) Brian K. Arbic Internal wave spectrum in global ocean models Collaborators • Naval Research Laboratory Stennis Space Center: Joe Metzger, Jim Richman, Jay Shriver, Alan Wallcraft, Luis Zamudio • University of Southern Mississippi: Maarten Buijsman • University of Michigan: Joseph Ansong, Steve Bassette, Conrad Luecke, Anna Savage • McGill University: David Trossman • Bangor University: Patrick Timko • Norwegian Meteorological Institute: Malte M¨uller • University of Brest and The University of Texas at Austin: Rob Scott • NASA Goddard: Richard Ray • Florida State University: Eric Chassignet • Others including many members of the NSF-funded Climate Process Team led by Jennifer MacKinnon of Scripps Brian K. Arbic Internal wave spectrum in global ocean models Motivation • Breaking internal gravity waves drive most of the mixing in the subsurface ocean. • The internal gravity wave spectrum is just starting to be resolved in global ocean models. • Somewhat analogous to resolution of mesoscale eddies in basin- and global-scale models in 1990s and early 2000s. • Builds on global internal tide modeling, which began with 2004 Arbic et al. and Simmons et al. papers utilizing Hallberg Isopycnal Model (HIM) run with tidal foricng only and employing a horizontally uniform stratification. Brian K. Arbic Internal wave spectrum in global ocean models Motivation continued... • Here we utilize simulations of the HYbrid Coordinate Ocean Model (HYCOM) with both atmospheric and tidal forcing. • Near-inertial waves and tides are put into a model with a realistically varying background stratification.
    [Show full text]
  • Gravity Waves Are Just Waves As Pressure He Was Observing
    FLIGHTOPS Nearly impossible to predict and difficult to detect, this weather phenomenon presents Gravitya hidden risk, especially close to the ground. regory Bean, an experienced pi- National Weather Service observer re- around and land back at Burlington. lot and flight instructor, says he ferred to this as a “gravity wave.” Neither The wind had now swung around to wasn’t expecting any problems the controller nor Bean knew what the 270 degrees at 25 kt. At this point, he while preparing for his flight weather observer was talking about. recalled, his rate of descent became fromG Burlington, Vermont, to Platts- Deciding he could deal with the “alarming.” The VSI now pegged at the burgh, New York, U.S. His Piper Seneca wind, Bean was cleared for takeoff. The bottom of the scale. Despite the control checked out fine. The weather that April takeoff and initial climb were normal difficulty, he landed the aircraft without evening seemed benign. While waiting but he soon encountered turbulence “as further incident. Bean may not have for clearance, he was taken aback by a rough as I have ever encountered.” He known what a gravity wave was, but report of winds gusting to 35 kt from wanted to climb to 2,600 ft. With the he now knew what it could do to an 140 degrees. The air traffic control- vertical speed indicator (VSI) “pegged,” airplane.1 ler commented on rapid changes in he shot up to 3,600 ft. Finally control- Gravity waves are just waves as pressure he was observing. He said the ling the airplane, Bean opted to turn most people normally think of them.
    [Show full text]
  • Gravity Wave and Tidal Influences On
    Ann. Geophys., 26, 3235–3252, 2008 www.ann-geophys.net/26/3235/2008/ Annales © European Geosciences Union 2008 Geophysicae Gravity wave and tidal influences on equatorial spread F based on observations during the Spread F Experiment (SpreadFEx) D. C. Fritts1, S. L. Vadas1, D. M. Riggin1, M. A. Abdu2, I. S. Batista2, H. Takahashi2, A. Medeiros3, F. Kamalabadi4, H.-L. Liu5, B. G. Fejer6, and M. J. Taylor6 1NorthWest Research Associates, CoRA Division, Boulder, CO, USA 2Instituto Nacional de Pesquisas Espaciais (INPE), San Jose dos Campos, Brazil 3Universidade Federal de Campina Grande. Campina Grande. Paraiba. Brazil 4University of Illinois, Champaign, IL, USA 5National Center for Atmospheric research, Boulder, CO, USA 6Utah State University, Logan, UT, USA Received: 15 April 2008 – Revised: 7 August 2008 – Accepted: 7 August 2008 – Published: 21 October 2008 Abstract. The Spread F Experiment, or SpreadFEx, was per- Keywords. Ionosphere (Equatorial ionosphere; Ionosphere- formed from September to November 2005 to define the po- atmosphere interactions; Plasma convection) – Meteorology tential role of neutral atmosphere dynamics, primarily grav- and atmospheric dynamics (Middle atmosphere dynamics; ity waves propagating upward from the lower atmosphere, in Thermospheric dynamics; Waves and tides) seeding equatorial spread F (ESF) and plasma bubbles ex- tending to higher altitudes. A description of the SpreadFEx campaign motivations, goals, instrumentation, and structure, 1 Introduction and an overview of the results presented in this special issue, are provided by Fritts et al. (2008a). The various analyses of The primary goal of the Spread F Experiment (SpreadFEx) neutral atmosphere and ionosphere dynamics and structure was to test the theory that gravity waves (GWs) play a key described in this special issue provide enticing evidence of role in the seeding of equatorial spread F (ESF), Rayleigh- gravity waves arising from deep convection in plasma bub- Taylor instability (RTI), and plasma bubbles extending to ble seeding at the bottomside F layer.
    [Show full text]
  • Inertia-Gravity Wave Generation: a WKB Approach
    Inertia-gravity wave generation: a WKB approach Jonathan Maclean Aspden Doctor of Philosophy University of Edinburgh 2010 Declaration I declare that this thesis was composed by myself and that the work contained therein is my own, except where explicitly stated otherwise in the text. (Jonathan Maclean Aspden) iii iv Abstract The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance for the circulation of the atmosphere and oceans, mainly because of the momentum and energy they transport and because of the mixing they create upon breaking. So far the study of inertia-gravity waves has answered a number of questions about their propagation and dissipation, but many aspects of their generation remain poorly understood. The interactions that take place between the slow motion, termed balanced or vortical motion, and the fast inertia-gravity wave modes provide mechanisms for inertia-gravity wave generation. One of these is the instability of balanced flows to gravity-wave-like perturbations; another is the so-called spontaneous generation in which a slowly evolving solution has a small gravity-wave component intrinsically coupled to it. In this thesis, we derive and study a simple model of inertia-gravity wave generation which considers the evolution of a small-scale, small amplitude perturbation superimposed on a large-scale, possibly time-dependent flow. The assumed spatial-scale separation makes it possible to apply a WKB approach which models the perturbation to the flow as a wavepacket.
    [Show full text]
  • Chapter 16: Waves [Version 1216.1.K]
    Contents 16 Waves 1 16.1Overview...................................... 1 16.2 GravityWavesontheSurfaceofaFluid . ..... 2 16.2.1 DeepWaterWaves ............................ 5 16.2.2 ShallowWaterWaves........................... 5 16.2.3 Capillary Waves and Surface Tension . .... 8 16.2.4 Helioseismology . 12 16.3 Nonlinear Shallow-Water Waves and Solitons . ......... 14 16.3.1 Korteweg-deVries(KdV)Equation . ... 14 16.3.2 Physical Effects in the KdV Equation . ... 16 16.3.3 Single-SolitonSolution . ... 18 16.3.4 Two-SolitonSolution . 19 16.3.5 Solitons in Contemporary Physics . .... 20 16.4 RossbyWavesinaRotatingFluid. .... 22 16.5SoundWaves ................................... 25 16.5.1 WaveEnergy ............................... 27 16.5.2 SoundGeneration............................. 28 16.5.3 T2 Radiation Reaction, Runaway Solutions, and Matched Asymp- toticExpansions ............................. 31 0 Chapter 16 Waves Version 1216.1.K, 7 Sep 2012 Please send comments, suggestions, and errata via email to [email protected] or on paper to Kip Thorne, 350-17 Caltech, Pasadena CA 91125 Box 16.1 Reader’s Guide This chapter relies heavily on Chaps. 13 and 14. • Chap. 17 (compressible flows) relies to some extent on Secs. 16.2, 16.3 and 16.5 of • this chapter. The remaining chapters of this book do not rely significantly on this chapter. • 16.1 Overview In the preceding chapters, we have derived the basic equations of fluid dynamics and devel- oped a variety of techniques to describe stationary flows. We have also demonstrated how, even if there exists a rigorous, stationary solution of these equations for a time-steady flow, instabilities may develop and the amplitude of oscillatory disturbances will grow with time. These unstable modes of an unstable flow can usually be thought of as waves that interact strongly with the flow and extract energy from it.
    [Show full text]
  • On the Transport of Energy in Water Waves
    On The Transport Of Energy in Water Waves Marshall P. Tulin Professor Emeritus, UCSB [email protected] Abstract Theory is developed and utilized for the calculation of the separate transport of kinetic, gravity potential, and surface tension energies within sinusoidal surface waves in water of arbitrary depth. In Section 1 it is shown that each of these three types of energy constituting the wave travel at different speeds, and that the group velocity, cg, is the energy weighted average of these speeds, depth and time averaged in the case of the kinetic energy. It is shown that the time averaged kinetic energy travels at every depth horizontally either with (deep water), or faster than the wave itself, and that the propagation of a sinusoidal wave is made possible by the vertical transport of kinetic energy to the free surface, where it provides the oscillating balance in surface energy just necessary to allow the propagation of the wave. The propagation speed along the surface of the gravity potential energy is null, while the surface tension energy travels forward along the wave surface everywhere at twice the wave velocity, c. The flux of kinetic energy when viewed traveling with a wave provides a pattern of steady flux lines which originate and end on the free surface after making vertical excursions into the wave, even to the bottom, and these are calculated. The pictures produced in this way provide immediate insight into the basic mechanisms of wave motion. In Section 2 the modulated gravity wave is considered in deep water and the balance of terms involved in the propagation of the energy in the wave group is determined; it is shown again that vertical transport of kinetic energy to the surface is fundamental in allowing the propagation of the modulation, and in determining the well known speed of the modulation envelope, cg.
    [Show full text]
  • The Equilibrium Dynamics and Statistics of Gravity–Capillary Waves
    J. Fluid Mech. (2015), vol. 767, pp. 449–466. c Cambridge University Press 2015 449 doi:10.1017/jfm.2014.740 The equilibrium dynamics and statistics of gravity–capillary waves W. Kendall Melville1, † and Alexey V. Fedorov2 1Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093-0213, USA 2Department of Geology and Geophysics, Yale University, 210 Whitney Avenue, PO Box 208109, New Haven, CT 06520, USA (Received 24 December 2013; revised 8 October 2014; accepted 19 December 2014; first published online 18 February 2015) Recent field observations and modelling of breaking surface gravity waves suggest that air-entraining breaking is not sufficiently dissipative of surface gravity waves to balance the dynamics of wind-wave growth and nonlinear interactions with dissipation for the shorter gravity waves of O.10/ cm wavelength. Theories of parasitic capillary waves that form at the crest and forward face of shorter steep gravity waves have shown that the dissipative effects of these waves may be one to two orders of magnitude greater than the viscous dissipation of the underlying gravity waves. Thus the parasitic capillaries may provide the required dissipation of the short wind-generated gravity waves. This has been the subject of speculation and conjecture in the literature. Using the nonlinear theory of Fedorov & Melville (J. Fluid Mech., vol. 354, 1998, pp. 1–42), we show that the dissipation due to the parasitic capillaries is sufficient to balance the wind input to the short gravity waves over some range of wave ages and wave slopes. The range of gravity wave lengths on which these parasitic capillary waves are dynamically significant approximately corresponds to the range of short gravity waves that Cox & Munk (J.
    [Show full text]
  • Undular Jump, Numerical Model and Sensitivity
    Alma Mater Studiorum - Università di Bologna FACOLTÀ DI SCIENZE MATEMATICHE, FISICHE E NATURALI Corso di Laurea specialistica in Fisica Dipartimento di Fisica UNDULAR JUMP NUMERICAL MODEL AND SENSITIVITY ANALYSIS Tesi di laurea di: Relatore: MICHELE RAMAZZA Prof. RAMBALDI SANDRO Correlatori: Prof. MANSERVISI SANDRO Dott. CERVONE ANTONIO Sessione III Anno Accademico 2007-2008 2 CONTENTS Abstract................................................................................................................................................5 Sommario.............................................................................................................................................5 List of symbol ....................................................................................................................................6 1.Introduction ....................................................................................................................................8 1.1.Open channel flow.................................................................................................................8 1.1.1.Introduction....................................................................................................................8 1.1.2.Classification of open channel flows.........................................................................8 1.1.3.Complexity ....................................................................................................................8 1.2.Bases of open channel hydraulics ...................................................................................10
    [Show full text]
  • An Undular Bore and Gravity Waves Illustrated by Dramatic Time-Lapse Photography
    AUGUST 2010 C O L E M A N E T A L . 1355 An Undular Bore and Gravity Waves Illustrated by Dramatic Time-Lapse Photography TIMOTHY A. COLEMAN AND KEVIN R. KNUPP Department of Atmospheric Science, University of Alabama in Huntsville, Huntsville, Alabama DARYL E. HERZMANN Department of Agronomy, Iowa State University, Ames, Iowa (Manuscript received 24 March 2010, in final form 17 May 2010) ABSTRACT On 6 May 2007, an intense atmospheric undular bore moved over eastern Iowa. A ‘‘Webcam’’ in Tama, Iowa, captured dramatic images of the effects of the bore and associated gravity waves on cloud features, because its viewing angle was almost normal to the propagation direction of the waves. The time lapse of these images has become a well-known illustration of atmospheric gravity waves. The environment was favorable for bore formation, with a wave-reflecting unstable layer above a low-level stable layer. Surface pressure and wind data are correlated for the waves in the bore, and horizontal wind oscillations are also shown by Doppler radar data. Quantitative analysis of the time-lapse photography shows that the sky brightens in wave troughs because of subsidence and darkens in wave ridges because of ascent. 1. Introduction et al. 2010). There is typically an energy imbalance across the bore. The form of the dissipation of the energy is During the morning hours of 6 May 2007, an intense related to the bore strength h /h ,whereh is the initial atmospheric bore, with a pressure perturbation of 4 hPa, 1 0 0 depth of the stable layer and h is its postbore depth.
    [Show full text]