DOCSLIB.ORG

Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography fluids Article Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography Ikha Magdalena * , Nadhira Karima and Hany Qoshirotur Rif’atin Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung 40132, Indonesia; [email protected] (N.K.); [email protected] (H.Q.R.) * Correspondence: [email protected] Abstract: Seiches and resonances are two closely related phenomena that can cause damage to coastal areas. Seiches that occur in a basin at a distinct period named the resonant period may generate resonance when a wave induced by external forces enters the basin and has the same period as the seiches. Studying this period has become essential if we want to understand the resonance better. Thus, in this paper, we derive the resonant period in various shapes of semi-closed basin using the shallow water equations. The equations are then solved analytically using the separation of variables method and numerically using the finite volume method on staggered grid to discover the resonant period for each basin. To validate the numerical scheme, we compare its results against the analytical resonant periods, resulting in a very small error for each basin, suggesting that the numerical model is quite reliable in the estimation of the analytical resonant period. Further, resonant wave profiles are also observed. It is revealed that, in the coupled rectangular basin, the maximum wave elevation is disproportionate to the ratio of the length of the basin, while, in the trapezoidal basin, the ratio of the depth of the basin has no significant impact on the maximum wave elevation. Keywords: resonant period; seiches; shallow water equations; finite volume method Citation: Magdalena, I.; Karima, N.; Rif’atin, H.Q. Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography. Fluids 1. Introduction 2021, 6, 181. https://doi.org/ Seiches are standing waves that arise in a closed basin (e.g., lake, pool, and reservoir) 10.3390/fluids6050181 or semi-closed basin (e.g., bay, port, and harbor) with a unique period. Many theories sur- rounding seiches originate from Forel’s remarkable publications, which began in 1892 [1]. Academic Editor: Alberto Alberello Seiches may be initiated by a number of exciting forces, such as seismic and atmospheric pressure disturbances, wind, or internal and surface gravity waves [2,3]. These oscillations Received: 29 March 2021 occur at a particular period commonly called the natural (resonant) period, which strongly Accepted: 29 April 2021 Published: 9 May 2021 depends on the length and depth of the basin in which the seiches occur. The major issue is considered when an external wave enters the basin and has a period that matches the natu- Publisher’s Note: MDPI stays neutral ral period, and therefore resonance happens. Such an occurrence is potentially destructive, with regard to jurisdictional claims in as it can destroy moored ships and infrastructures in a port, disrupt coastal activities, and published maps and institutional affil- harm the structure located near lakes, reservoirs, or coastlines. The worst consequence iations. that we might encounter is a tsunami wave accompanied by a resonance that ultimately leads to a hazard in the coastal region. Several researchers have documented tsunami cases that are associated with resonance, such as Munger and Cheung [4], Roeber et al. [5], and Yamazaki and Cheung [6], who confirmed the 2006 Kuril, 2009 Samoa, and 2010 Chilean tsunamis over the insular shelves and slopes of Hawaii, American Samoa, and Chile that Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. triggered long oscillations in coastal waters. This article is an open access article In consideration of the negative impacts of tsunami waves on coastlines, we need to distributed under the terms and find an appropriate way to avoid resonance phenomena. One of the strategies to prevent conditions of the Creative Commons resonance is to understand the characteristics of seiches over a certain type of basin, particu- Attribution (CC BY) license (https:// larly its resonant period. Numerous studies have analytically examined the resonant period creativecommons.org/licenses/by/ in the simpler geometric form of basin, which is a rectangular type [7–11]. In addition, 4.0/). many other researchers have discovered the resonant period of the triangular (isosceles) Fluids 2021, 6, 181. https://doi.org/10.3390/fluids6050181 https://www.mdpi.com/journal/fluids Fluids 2021, 6, 181 2 of 15 and parabolic shaped basin [9,11]. Magdalena, et. al [12] have extended these studies by involving bottom friction in the derivation of wave resonant period. More complicated bottom topographies, such as semi-closed quartic, triangular (right-angled), trapezoidal, and coupled rectangular type, are rarely studied analytically due to the complexities of the basin depth formula. One of the rare studies that have investigated the quartic basin using an analytical approach was published by Chrystal [1] and Magdalena et al. [13]. However, they only provided the resonant period for closed quartic basin. Meanwhile, for triangular (right-angled), trapezoidal, and coupled rectangular form, e.g., Wilson [14], Rabinovich [15], and Dean and Dalrymple [16] derived analytical solutions from potential theory to approximate the resonant period of seiches in closed basins of those types, while the subject analysis for semi-closed basins has not yet been published, experimentally, analytically, or computationally. Thus, the analytical and numerical solution presented in this paper are new approaches in calculating the resonant period for semi-closed quartic, triangular (right-angled), trapezoidal, and coupled rectangular basin. Moreover, these shapes are more realistic in approximating the structure of a waterbody (e.g., continental shelf, inlet, and gulf) than the simpler geometries mentioned above. Therefore, in this paper, we propose a mathematical model to simulate seiches, along with corresponding resonance phenomena, in various types of basin, in particular semi- closed quartic, triangular (right-angled), trapezoidal, and coupled rectangular type, in which configurations are modification from Wilson [14]. To focus the study, we only examine the phenomena in semi-closed basins with constant width and no friction force is involved. The main objectives of this paper are to determine the fundamental resonant period of the seiches in each type of basin and analyze the wave profile as a result of the resonance phenomenon. Linear shallow water equations (LSWE) are used, which are to be solved analytically and numerically in order to obtain the resonant period. Separation of the variables method is applied to derive the periods analytically, while the finite volume method on the staggered grid is implemented to formulate a scheme to simulate the model and to acquire the periods numerically. The LSWE model have already been validated previously against the available experimental resonant periods for rectangular, triangular (isosceles), and parabolic cases [9,11]. However, in this work, because we use different basin configurations from the mentioned studies, the analytical approaches in those works are not applicable for our cases. Hence, we need to develop a new analytical procedure in finding the resonant period. The numerical scheme used in this paper has been tested and validated [17–20] to emulate various fluid phenomena. In this paper, we apply the same numerical method to simulate the wave resonance phenomenon and obtain the natural period. We also confirm our numerical model, particularly on approximating the resonant period of quar- tic, triangular (right-angled), trapezoidal, and coupled rectangular semi-closed basin, by comparing the simulations results against the analytical solutions. The accuracy of the numerical method is tested along with the rate of convergence, which has not been provided yet by other works. Further, the profile of the resonant wave is also evalu- ated to understand the behavior of the wave produced by the resonance phenomenon, depending on the type of basin. From this paper, we expect that the developed model and computational scheme can be conveniently used to extend the topic of the resonant period in the future, so that we can examine seiches, resonance, and their periods in other types of basin that have not been discovered before without the need for a costly experimental model. The paper is organized into six main sections. Section1 provides a concise explanation of seiches, resonances, and why those events are dangerous and need to be investigated. Then, the LSWE model used to solve the problem stated in the previous section is intro- duced in Section2. The model is then solved analytically in Section3 and numerically in Section4. Further, Section5 presents the simulation results and discussion on the accu- racy of our model. Finally, the conclusions of the findings of this study are addressed in Section6. Fluids 2021, 6, 181 3 of 15 2. Mathematical Model In this section, we introduce the governing equations that are used to model the prop- agation of seiches in a semi-closed basin with arbitrary bottom topography. It is presumed that the seiches oscillating within the basin follow the shallow water condition where the wavelength is much greater than the maximum depth of the basin (depth < l/20). Another assumption considered in this model is that the surface elevation, denoted by h(x, t) (see Figure1), is relatively small compared to the total water depth h = h + d, where d(x) is the depth of the basin measured at z = 0. Therefore, we can claim that h ≈ d. Thus, it is appropriate to apply the well-known linear shallow water equations (LSWE) as the governing equations of this model. The LSWE are illustrated in Figure1 and consist of the two equations below. ht + (hu)x = 0, (1) ut + ghx = 0, (2) Figure 1. Description of the shallow water equations model in a semi-closed basin with arbitrary bottom topography. As pictured in Figure1, we assume that the seiches in the semi-closed basin are initiated by waves entering the open boundary at the right end of the basin.
Load more

Recommended publications
  • Well-Balanced Schemes for the Shallow Water Equations with Coriolis Forces
    Well-balanced schemes for the shallow water equations with Coriolis forces Alina Chertock, Michael Dudzinski, Alexander Kurganov & Mária Lukáčová- Medvid’ová Numerische Mathematik ISSN 0029-599X Volume 138 Number 4 Numer. Math. (2018) 138:939-973 DOI 10.1007/s00211-017-0928-0 1 23 Your article is protected by copyright and all rights are held exclusively by Springer- Verlag GmbH Germany, part of Springer Nature. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”. 1 23 Author's personal copy Numer. Math. (2018) 138:939–973 Numerische https://doi.org/10.1007/s00211-017-0928-0 Mathematik Well-balanced schemes for the shallow water equations with Coriolis forces Alina Chertock1 · Michael Dudzinski2 · Alexander Kurganov3,4 · Mária Lukáˇcová-Medvid’ová5 Received: 28 April 2014 / Revised: 19 September 2017 / Published online: 2 December 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract In the present paper we study shallow water equations with bottom topog- raphy and Coriolis forces. The latter yield non-local potential operators that need to be taken into account in order to derive a well-balanced numerical scheme.
    [Show full text]
  • Part II-1 Water Wave Mechanics
    Chapter 1 EM 1110-2-1100 WATER WAVE MECHANICS (Part II) 1 August 2008 (Change 2) Table of Contents Page II-1-1. Introduction ............................................................II-1-1 II-1-2. Regular Waves .........................................................II-1-3 a. Introduction ...........................................................II-1-3 b. Definition of wave parameters .............................................II-1-4 c. Linear wave theory ......................................................II-1-5 (1) Introduction .......................................................II-1-5 (2) Wave celerity, length, and period.......................................II-1-6 (3) The sinusoidal wave profile...........................................II-1-9 (4) Some useful functions ...............................................II-1-9 (5) Local fluid velocities and accelerations .................................II-1-12 (6) Water particle displacements .........................................II-1-13 (7) Subsurface pressure ................................................II-1-21 (8) Group velocity ....................................................II-1-22 (9) Wave energy and power.............................................II-1-26 (10)Summary of linear wave theory.......................................II-1-29 d. Nonlinear wave theories .................................................II-1-30 (1) Introduction ......................................................II-1-30 (2) Stokes finite-amplitude wave theory ...................................II-1-32
    [Show full text]
  • Fluid Simulation Using Shallow Water Equation
    Fluid Simulation using Shallow Water Equation Dhruv Kore Itika Gupta Undergraduate Student Graduate Student University of Illinois at Chicago University of Illinois at Chicago [email protected] [email protected] 847-345-9745 312-478-0764 ABSTRACT rivers and channel. As the name suggest, the main In this paper, we present a technique, which shows how characteristic of shallow Water flows is that the vertical waves once generated from a small drop continue to ripple. dimension is much smaller as compared to the horizontal Waves interact with each other and on collision change the dimension. Naïve Stroke Equation defines the motion of form and direction. Once the waves strike the boundary, fluids and from these equations we derive SWE. they return with the same speed and in sometime, depending on the delay, you can see continuous ripples in In Next section we talk about the related works under the the surface. We use shallow water equation to achieve the heading Literature Review. Then we will explain the desired output. framework and other concepts necessary to understand the SWE and wave equation. In the section followed by it, we Author Keywords show the results achieved using our implementation. Then Naïve Stroke Equation; Shallow Water Equation; Fluid finally we talk about conclusion and future work. Simulation; WebGL; Quadratic function. LITERATURE REVIEW INTRODUCTION In [2] author in detail explains the Shallow water equation In early years of fluid simulation, procedural surface with its derivation. Since then a lot of authors has used generation was used to represent waves as presented by SWE to present the formation of waves in water.
    [Show full text]
  • 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.
    [Show full text]
  • Shallow-Water Equations and Related Topics
    CHAPTER 1 Shallow-Water Equations and Related Topics Didier Bresch UMR 5127 CNRS, LAMA, Universite´ de Savoie, 73376 Le Bourget-du-Lac, France Contents 1. Preface .................................................... 3 2. Introduction ................................................. 4 3. A friction shallow-water system ...................................... 5 3.1. Conservation of potential vorticity .................................. 5 3.2. The inviscid shallow-water equations ................................. 7 3.3. LERAY solutions ........................................... 11 3.3.1. A new mathematical entropy: The BD entropy ........................ 12 3.3.2. Weak solutions with drag terms ................................ 16 3.3.3. Forgetting drag terms – Stability ............................... 19 3.3.4. Bounded domains ....................................... 21 3.4. Strong solutions ............................................ 23 3.5. Other viscous terms in the literature ................................. 23 3.6. Low Froude number limits ...................................... 25 3.6.1. The quasi-geostrophic model ................................. 25 3.6.2. The lake equations ...................................... 34 3.7. An interesting open problem: Open sea boundary conditions .................... 41 3.8. Multi-level and multi-layers models ................................. 43 3.9. Friction shallow-water equations derivation ............................. 44 3.9.1. Formal derivation ....................................... 44 3.10.
    [Show full text]
  • Waves in Water from Ripples to Tsunamis and to Rogue Waves
    Waves in Water from ripples to tsunamis and to rogue waves Vera Mikyoung Hur (Mathematics) (Image from Flickr) The motion of a fluid can be very complicated as we know whenever we see waves break on a beach, (Image from the Internet) The motion of a fluid can be very complicated as we know whenever we fly in an airplane, (Image from the Internet) The motion of a fluid can be very complicated as we know whenever we look at a lake on a windy day. (Image from the Internet) Euler in the 1750s proposed a mathematical model of an incompressible fluid. @u + (u · r)u + rP = F, @t r · u = 0. Here, u(x; t) is the velocity of the fluid at the point x and time t, P(x; t) is the pressure, and F(x; t) is an outside force. The Navier-Stokes equations (adding ν∆u) allow the fluid to be viscous. It is concise and captures the essence of fluid behavior. The theory of fluids has provided source and inspiration to many branches of mathematics, e.g. Cauchy's complex function theory. Difficulties of understanding fluids are profound. e.g. the global-in-time solution of the Navier-Stokes equations in 3 dimensions is a Clay Millennium Problem! Waves, jets, drops come to mind when thinking of fluids. They involve one or more fluids separated by an unknown surface. In the mathematical community, they go by free boundary problems. (Image from the Internet) Free boundaries are mathematically challenging in their own right. They occur in many other situations, such as melting of ice stretching a membrane over an obstacle.
    [Show full text]
  • Modified Shallow Water Equations for Significantly Varying Seabeds Denys Dutykh, Didier Clamond
    Modified Shallow Water Equations for significantly varying seabeds Denys Dutykh, Didier Clamond To cite this version: Denys Dutykh, Didier Clamond. Modified Shallow Water Equations for significantly varying seabeds: Modified Shallow Water Equations. Applied Mathematical Modelling, Elsevier, 2016, 40 (23-24), pp.9767-9787. 10.1016/j.apm.2016.06.033. hal-00675209v6 HAL Id: hal-00675209 https://hal.archives-ouvertes.fr/hal-00675209v6 Submitted on 26 Apr 2016 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 - NonCommercial| 4.0 International License Denys Dutykh CNRS, Université Savoie Mont Blanc, France Didier Clamond Université de Nice – Sophia Antipolis, France Modified Shallow Water Equations for significantly varying seabeds arXiv.org / hal Last modified: April 26, 2016 Modified Shallow Water Equations for significantly varying seabeds Denys Dutykh∗ and Didier Clamond Abstract. In the present study, we propose a modified version of the Nonlinear Shal- low Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints.
    [Show full text]
  • ATM 500: Atmospheric Dynamics End-Of-Semester Review, December 4 2018 Here, in Bullet Points, Are the Key Concepts from the Second Half of the Course
    ATM 500: Atmospheric Dynamics End-of-semester review, December 4 2018 Here, in bullet points, are the key concepts from the second half of the course. They are not meant to be self-contained notes! Refer back to your course notes for notation, derivations, and deeper discussion. Static stability The vertical variation of density in the environment determines whether a parcel, disturbed upward from an initial hydrostatic rest state, will accelerate away from its initial position, or oscillate about that position. For an incompressible or Boussinesq fluid, the buoyancy frequency is g dρ~ N 2 = − ρ~dz For a compressible ideal gas, the buoyancy frequency is g dθ~ N 2 = θ~dz (the expressions are different because density is not conserved in a small upward displacement of a compressible fluid, but potential temperature is conserved) Fluid is statically stable if N 2 > 0; otherwise it is statically unstable. Typical value for troposphere: N = 0:01 s−1, with corresponding oscillation period of 10 minutes. Dry adiabatic lapse rate g −1 Γd = = 9:8 K km cp The rate at which temperature decreases during adiabatic ascent (for which Dθ Dt = 0) \Dry" here means that there is no latent heating from condensation of water vapor. Static stability criteria for a dry atmosphere Environment is stable to dry con- vection if dθ~ dT~ > 0 or − < Γ dz dz d and otherwise unstable. 1 Buoyancy equation for Boussinesq fluid with background stratification Db0 + N 2w = 0 Dt where we have separated the full buoyancy into a mean vertical part ^b(z) and 0 2 d^b 2 everything else (b ), and N = dz .
    [Show full text]
  • Multilayer Shallow Water Equations with Complete Coriolis Force. Part I: Derivation on a Non-Traditional Beta-Plane
    Accepted for publication in the Journal of Fluid Mechanics °c 2010 Cambridge University Press 1 doi:10.1017/S0022112009993922 Multilayer shallow water equations with complete Coriolis force. Part I: Derivation on a non-traditional beta-plane By ANDREW L. STEWART and PAUL J. DELLAR OCIAM, Mathematical Institute, 24–29 St Giles’, Oxford, OX1 3LB, UK [email protected], [email protected] (Received 22 May 2009; revised 9 December 2009; accepted 9 December 2009) We derive equations to describe the flow of multiple superposed layers of inviscid, incompressible fluids with con- stant densities over prescribed topography in a rotating frame. Motivated by geophysical applications, these equations incorporate the complete Coriolis force. We do not make the widely used “traditional approximation” that omits the contribution to the Coriolis force from the locally horizontal part of the rotation vector. Our derivation is performed by averaging the governing Euler equations over each layer, and from two different forms of Hamilton’s variational principle that differ in their treatment of the coupling between layers. The coupling may be included implicitly through the map from Lagrangian particle labels to particle coordinates, or explicitly by adding terms representing the work done on each layer by the pressure exerted by the layers above. The latter approach requires additional terms in the Lagrangian, but extends more easily to many layers. We show that our equations obey the expected conservation laws for energy, momentum, and potential vorticity. The conserved momentum and potential vorticity are modified by non-traditional effects. The vertical component of the rotation vector that appears in the potential vorticity for each layer under the traditional approximation is replaced by the component perpendicular to the layer’s midsurface.
    [Show full text]
  • A Particle-In-Cell Method for the Solution of Two-Layer Shallow-Water Equations
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2000; 32: 515–543 A particle-in-cell method for the solution of two-layer shallow-water equations Benoit Cushman-Roisina,*, Oleg E. Esenkovb and Benedict J. Mathiasc a Thayer School of Engineering, Dartmouth College, Hano6er, NH 03755-8000, U.S.A. b Rosenstiel School of Marine and Atmospheric Science, Uni6ersity of Miami, Miami, FL 33149-1098, U.S.A. c i2 Technologies, 303 Twin Dolphin Dri6e, Redwood City, CA 94065, U.S.A. SUMMARY A particle-in-cell (PIC) numerical method developed for the study of shallow-water dynamics, when the moving fluid layer is laterally confined by the intersection of its top and bottom surfaces, is described. The effect of ambient rotation is included for application to geophysical fluids, particularly open-ocean buoyant vortices in which the underlying density interface outcrops to the surface around the rim of the vortex. Extensions to include the dynamical effect of a second moving layer (baroclinicity) and the presence of a lateral rigid boundary (sidewall) are also described. Although the method was developed for oceanographic investigations, applications to other fluid mechanics problems would be straightforward. Copyright © 2000 John Wiley & Sons, Ltd. KEY WORDS: open-ocean; particle-in-cell; shallow-water equation 1. INTRODUCTION There are a number of situations, mostly geophysical in nature, where fluid flows occur in layers that are much thinner than they are wide. In such cases, hydrostatic equilibrium is invoked in the vertical, and the equations of motion reduce to the so-called St. Venant or shallow-water equations [1].
    [Show full text]
  • The Shallow Water Equations and Their Application to Realistic Cases
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Repositorio Universidad de Zaragoza Noname manuscript No. (will be inserted by the editor) The shallow water equations and their application to realistic cases P. Garc´ıa-Navarro · J. Murillo · J. Fern´andez-Pato · I. Echeverribar · M. Morales-Hern´andez the date of receipt and acceptance should be inserted later Abstract The numerical modelling of 2D shallow flows in complex geome- tries involving transient flow and movable boundaries has been a challenge for researchers in recent years. There is a wide range of physical situations of environmental interest, such as flow in open channels and rivers, tsunami and flood modelling, that can be mathematically represented by first-order non-linear systems of partial differential equations, whose derivation involves an assumption of the shallow water type. Shallow water models may include more sophisticated terms when applied to cases of not pure water floods, such as mud/debris floods, produced by landslides. Mud/debris floods are unsteady flow phenomena in which the flow changes rapidly, and the properties of the moving fluid mixture include stop and go mechanisms. The present work re- ports on a numerical model able to solve the 2D shallow water equations even including bed load transport over erodible bed in realistic situations involving transient flow and movable flow boundaries. The novelty is that it offers accu- rate and stable results in realistic problems since an appropriate discretization of the governing equations is performed. Furthermore, the present work is P. Garc´ıa-Navarro Fluid Mechanics, Universidad Zaragoza/LIFTEC-CSIC E-mail: [email protected] J.
    [Show full text]
  • Observations and Modeling of the Surface Seiches of Lake Tahoe, USA
    Aquatic Sciences (2019) 81:46 https://doi.org/10.1007/s00027-019-0644-1 Aquatic Sciences RESEARCH ARTICLE Observations and modeling of the surface seiches of Lake Tahoe, USA Derek C. Roberts1,2 · Heather M. Sprague1,2,3 · Alexander L. Forrest1,2 · Andrew T. Sornborger4 · S. Geofrey Schladow1,2 Received: 24 October 2018 / Accepted: 13 April 2019 © Springer Nature Switzerland AG 2019 Abstract A rich array of spatially complex surface seiche modes exists in lakes. While the amplitude of these oscillations is often small, knowledge of their spatio-temporal characteristics is valuable for understanding when they might be of localized hydrodynamic importance. The expression and impact of these basin-scale barotropic oscillations in Lake Tahoe are evalu- ated using a fnite-element numerical model and a distributed network of ten high-frequency nearshore monitoring stations. Model-predicted nodal distributions and periodicities are confrmed using the presence/absence of spectral power in measured pressure signals, and using coherence/phasing analysis of pressure signals from stations on common and opposing antinodes. Surface seiches in Lake Tahoe have complex nodal distributions despite the relative simplicity of the basin morphometry. Seiche amplitudes are magnifed on shallow shelves, where they occasionally exceed 5 cm; elsewhere, amplitudes rarely exceed 1 cm. There is generally little coherence between surface seiching and littoral water quality. However, pressure–tem- perature coherence at shelf sites suggests potential seiche-driven pumping. Main-basin seiche signals are present in attached marinas, wetlands, and bays, implying reversing fows between the lake and these water bodies. On the shallow sill connecting Emerald Bay to Lake Tahoe, the fundamental main-basin seiche combines with a zeroth-mode harbor seiche to dominate the cross-sill fow signal, and to drive associated temperature fuctuations.
    [Show full text]