Dimensions of Fluvial-Tidal Meanders: Are They Disproportionally Large? Jasper R.F.W

Total Page:16

File Type:pdf, Size:1020Kb

Dimensions of Fluvial-Tidal Meanders: Are They Disproportionally Large? Jasper R.F.W https://doi.org/10.1130/G45144.1 Manuscript received 9 May 2018 Revised manuscript received 26 July 2018 Manuscript accepted 16 August 2018 © 2018 The Authors. Gold Open Access: This paper is published under the terms of the CC-BY license. Published online 11 September 2018 Dimensions of fluvial-tidal meanders: Are they disproportionally large? Jasper R.F.W. Leuven*, Barend van Maanen, Bente R. Lexmond, Bram V. van der Hoek, Matthijs J. Spruijt, and Maarten G. Kleinhans Faculty of Geosciences, Utrecht University, Princetonlaan 8A, 3584 CB Utrecht, The Netherlands ABSTRACT meandering channel deposits in Palaeozoic Many of the world’s major river systems seemingly have one or a few disproportionally outcrops are orders of magnitude smaller than large meanders, with tight bends, in the fluvial-tidal transition (e.g., the Thames in the UK, in modern systems (Davies and Gibling, 2011, and the Salmon River in Canada). However, quantitative studies on meanders have so far 2013) and are possibly biased toward maximum primarily focused on rivers without tidal influence or on small tidal meanders without river meander dimensions and sinuosity, because inflow, providing relations between channel geometry and meander characteristics (length, meanders at the point of cut-off have the highest amplitude, and sinuosity). Physics-based predictions of meander size and shape for the fluvial- preservation potential (e.g., Durkin et al., 2017). tidal transition zone remain untested for a lack of data. Therefore, it remains unclear whether A possible exception is found in seismic data of the dimensions of meanders in the fluvial-tidal transition zone are indeed disproportionally the Cretaceous McMurray Formation (Canada), large, and whether meander characteristics can be used as an indicator for tidal influence. which has kilometer-scale meander bends (Hub- Here, data from 823 meanders in 68 fluvial-tidal transition zones worldwide are presented bard et al., 2011; Durkin et al., 2017). Both the that reveal broad-brush relations between channel geometry and meander dimensions. Our morphology and the facies in core data are simi- results show that fluvial-tidal meanders indeed become larger in the seaward direction, but lar to that of a fluvial environment (Mossop and the dimensions are proportional to local channel width, as in rivers. Sinuosity maxima are Flach, 1983; Hubbard et al., 2011), although an exception, rather than the rule, in the fluvial-tidal transition zone. Surprisingly, the width trace fossils indicate brackish water, which is of the upstream river correlates with estuarine channel width and tidal meander size even interpreted as the fluvial-tidal transition zone though river discharge constitutes only a fraction of the tidal prism. The new scaling relations (La Croix and Dashtgard, 2015; Gingras et al., can be used to constrain dimensions of rivers and estuaries and their meanders. 2016). Therefore, it would be useful to have a complementary indicator that can discriminate INTRODUCTION are much smaller (typically 2–200 m wide) than between fluvial, fluvial-tidal, and tidal meanders The shapes and dimensions of meanders fluvial and estuarine meanders. Moreover, they on the basis of geometry for the full range of are a major characteristic of meandering rivers predominantly form under ebb-dominant flow scales on which they occur on Earth. (Leopold and Wolman, 1960). Typical scaling and may thus be comparable with small river Lack of data and empirical generalizations relations exist between meander dimensions, meanders (Kleinhans et al., 2009). leave hypotheses untested, such as the hypoth- river discharge, and local channel width (e.g., The majority of the world’s largest cities are esis that fluvial-tidal meanders are very tight, Inglis, 1949; Leopold and Wolman, 1960; Hey located near estuaries and tidal rivers (Ashworth with sinuosities peaking above 2.5 at the bed- and Thorne, 1986) (Table DR1 in the GSA Data et al., 2015) in which meandering channels are load convergence zone (Dalrymple et al., 2012). Repository1). However, these empirical relations ecologically valuable but also threaten bank The limited number of analyzed cases so far have never been tested in the fluvial-tidal transi- stability, affect shipping lanes, and influence does not demonstrate whether sinuosity peaks tion zone and in estuaries (Fig. 1), where one of flood safety. Therefore, it is of interest whether significantly beyond the natural temporal and the signatures of the environment is that local the meander-forming mechanisms are similar to along-channel variability within meandering tidal prism (the volume of water leaving an estu- those of their fluvial counterparts. Physics-based systems, which occurs due to bend cutoffs, and ary at ebb tide) increases in the seaward direction theory can predict dominant meander lengths the scatter in combined observations from mul- (Leuven et al., 2018) with exponentially increas- based on forming mechanisms (e.g., Solari et tiple systems (Howard and Hemberger, 1991; ing channel width. Observations of tidal mean- al., 2002; Schramkowski et al., 2002; Seminara, Camporeale et al., 2007; Hubbard et al., 2011) ders show that their planform dimensions scale 2006; for review, see Leuven et al., 2016), but (Fig. 1B). Moreover, a sinuosity peak implies similarly as in rivers (Marani et al., 2002; Solari the resulting predictions have never been tested a disproportional scaling relation between et al., 2002; D’Alpaos et al., 2017; Finotello et al., due to a lack of data from natural systems. meander dimensions and channel dimensions 2018). However, these observations mainly cover Geological outcrops could provide an alter- predicted by theory, because it requires a peak meanders on tidal flats and salt marshes, which native source of data. However, preserved in meander amplitude or drop in meander length. 1 GSA Data Repository item 2018343, supplementary figures, tables, and a .kml file with the recorded polygons of fluvial-tidal meanders, is available online at http://www.geosociety.org/datarepository/2018/ or on request from [email protected]. *E-mail: [email protected] CITATION: Leuven, J.R.F.W., van Maanen, B., Lexmond, B.R., van der Hoek, B.V., Spruijt, M.J., and Kleinhans, M.G., 2018, Dimensions of fluvial-tidal mean- ders: Are they disproportionally large?: Geology, v. 46, p. 923–926, https://doi.org/10.1130/G45144.1. Geological Society of America | GEOLOGY | Volume 46 | Number 10 | www.gsapubs.org 923 Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/46/10/923/4338811/923.pdf by guest on 26 September 2021 Observations from aerial photography and pre- A fluvial-tidal transition zone (3) fluvial meanders dictions from physics-based theory (Solari et al., large 2002) suggest that these meanders are longer meander than those of their fluvial counterparts. (1) meanders in multi-threaded zone small meanders Therefore, we test whether fluvial-tidal mean- approximate ders are indeed disproportionally large when 1 km tidal limit (2) fluvial-tidal meanders 52°32’ N 4°01’ W compared with their local channel dimensions B and upstream and downstream meanders. We derive scaling relations that can be used to obtain former meanders broad-brush dimensions of meanders along the fluvial-tidal continuum, for application in geo- morphology and geological reconstruction of 3 km meander belts. To this end, a new data set was 12°28’ S 132°24’ E collected with characteristics of 823 meanders C in 68 fluvial-tidal transition zones from around the world. Data were compared with typical rela- tions previously found for rivers and for small tidal meanders. 1 km 45°42’ N 63°18’ W DATA COLLECTION AND ANALYSIS We recorded channel planform polygons Figure 1. Aerial photographs of fluvial-tidal meanders (Google Earth™). River flow is from right to left. A: Dovey River, Wales, UK. B: South Alligator River, Northern Territory, Australia. for 68 rivers that transition into seas (Table C: Salmon River, Cobequid Bay, Canada. DR2). Because hydrodynamic data are gen- erally unavailable, the tidal limit was defined as the landward location where channel width approaches a constant value within a factor two of the most upstream river width. Meanders were digitized beyond that point, such that sub- A 66 B sequently, the tidal limit could be derived from 4 the along-channel width profile (Figs. DR1 and 10 DR2). To allow for comparison between sys- 57 ) tems, along-channel distance was normalized with the tidal limit. In cases where the single threaded river transitions into an estuary with 103 braided channels and bars, we digitized the main 20 continuous channel. This approach resulted in a y R2 ±2σ 2 13x1.2 0.6 3.3 y R ±2σ classification of (1) main meanders in the multi- 1.1 0.88 0.75 2.8 Meander length (m 23x 0.42 4.3 25x 1.2 threaded zone, (2) single-threaded fluvial-tidal 52x 0.54 4.1 Data Leopold (1964) 102 meanders, or (3) fluvial meanders (Fig. 1A). Fluvial meanders Data Marani (2002) The channel centerlines and along-channel Single-threaded fluvial-tidal meanders Marani et al. (2002) width profiles were automatically determined Main meanders in multi-threaded zone using GIS software (following the approaches C D of Davies and Woodroffe [2010] and Leuven et al. [2018]). All centerlines were smoothed with a Polynomial Approximation with Exponential 101 ) Kernel (PAEK) algorithm using a tolerance of 0.6× the local channel width, to prevent the cen- terlines from being too sensitive to local varia- tions in channel width. 3 10 Meander length (λ) and amplitude (a) were calculated from the centerlines as follows (Fig. y R2 ±2σ DR3). Inflection points were determined from Meander amplitude (m 0.73x 1.5 0.21 8.9 channel curvature (Howard and Hemberger, 2 2x1.4 0.02 9.6 10 1.4 2 ±2 1991; Marani et al., 2002; Schwenk et al., 2015).
Recommended publications
  • Field Studies and 3D Modelling of Morphodynamics in a Meandering River Reach Dominated by Tides and Suspended Load
    fluids Article Field Studies and 3D Modelling of Morphodynamics in a Meandering River Reach Dominated by Tides and Suspended Load Qiancheng Xie 1,* , James Yang 2,3 and T. Staffan Lundström 1 1 Division of Fluid and Experimental Mechanics, Luleå University of Technology, 97187 Luleå, Sweden; [email protected] 2 Vattenfall AB, Research and Development, Hydraulic Laboratory, 81426 Älvkarleby, Sweden; [email protected] 3 Resources, Energy and Infrastructure, Royal Institute of Technology, 10044 Stockholm, Sweden * Correspondence: [email protected]; Tel.: +4672-2870-381 Received: 9 December 2018; Accepted: 20 January 2019; Published: 22 January 2019 Abstract: Meandering is a common feature in natural alluvial streams. This study deals with alluvial behaviors of a meander reach subjected to both fresh-water flow and strong tides from the coast. Field measurements are carried out to obtain flow and sediment data. Approximately 95% of the sediment in the river is suspended load of silt and clay. The results indicate that, due to the tidal currents, the flow velocity and sediment concentration are always out of phase with each other. The cross-sectional asymmetry and bi-directional flow result in higher sediment concentration along inner banks than along outer banks of the main stream. For a given location, the near-bed concentration is 2−5 times the surface value. Based on Froude number, a sediment carrying capacity formula is derived for the flood and ebb tides. The tidal flow stirs the sediment and modifies its concentration and transport. A 3D hydrodynamic model of flow and suspended sediment transport is established to compute the flow patterns and morphology changes.
    [Show full text]
  • CLASSIFICATION of CALIFORNIA ESTUARIES BASED on NATURAL CLOSURE PATTERNS: TEMPLATES for RESTORATION and MANAGEMENT Revised
    CLASSIFICATION OF CALIFORNIA ESTUARIES BASED ON NATURAL CLOSURE PATTERNS: TEMPLATES FOR RESTORATION AND MANAGEMENT Revised David K. Jacobs Eric D. Stein Travis Longcore Technical Report 619.a - August 2011 Classification of California Estuaries Based on Natural Closure Patterns: Templates for Restoration and Management David K. Jacobs1, Eric D. Stein2, and Travis Longcore3 1UCLA Department of Ecology and Evolutionary Biology 2Southern California Coastal Water Research Project 3University of Southern California - Spatial Sciences Institute August 2010 Revised August 2011 Technical Report 619.a ABSTRACT Determining the appropriate design template is critical to coastal wetland restoration. In seasonally wet and semi-arid regions of the world coastal wetlands tend to close off from the sea seasonally or episodically, and decisions regarding estuarine mouth closure have far reaching implications for cost, management, and ultimate success of coastal wetland restoration. In the past restoration planners relied on an incomplete understanding of the factors that influence estuarine mouth closure. Consequently, templates from other climatic/physiographic regions are often inappropriately applied. The first step to addressing this issue is to develop a classification system based on an understanding of the processes that formed the estuaries and thus define their pre-development structure. Here we propose a new classification system for California estuaries based on the geomorphic history and the dominant physical processes that govern the formation of the estuary space or volume. It is distinct from previous estuary closure models, which focused primarily on the relationship between estuary size and tidal prism in constraining closure. This classification system uses geologic origin, exposure to littoral process, watershed size and runoff characteristics as the basis of a conceptual model that predicts likely frequency and duration of closure of the estuary mouth.
    [Show full text]
  • Classifying Rivers - Three Stages of River Development
    Classifying Rivers - Three Stages of River Development River Characteristics - Sediment Transport - River Velocity - Terminology The illustrations below represent the 3 general classifications into which rivers are placed according to specific characteristics. These categories are: Youthful, Mature and Old Age. A Rejuvenated River, one with a gradient that is raised by the earth's movement, can be an old age river that returns to a Youthful State, and which repeats the cycle of stages once again. A brief overview of each stage of river development begins after the images. A list of pertinent vocabulary appears at the bottom of this document. You may wish to consult it so that you will be aware of terminology used in the descriptive text that follows. Characteristics found in the 3 Stages of River Development: L. Immoor 2006 Geoteach.com 1 Youthful River: Perhaps the most dynamic of all rivers is a Youthful River. Rafters seeking an exciting ride will surely gravitate towards a young river for their recreational thrills. Characteristically youthful rivers are found at higher elevations, in mountainous areas, where the slope of the land is steeper. Water that flows over such a landscape will flow very fast. Youthful rivers can be a tributary of a larger and older river, hundreds of miles away and, in fact, they may be close to the headwaters (the beginning) of that larger river. Upon observation of a Youthful River, here is what one might see: 1. The river flowing down a steep gradient (slope). 2. The channel is deeper than it is wide and V-shaped due to downcutting rather than lateral (side-to-side) erosion.
    [Show full text]
  • Appendices for the White River Base Flow Study
    APPENDIX 1 Habitat types and descriptions adapted from Bisson et al. 1982 and Upper Colorado River Basin Database _____________________________________________________________________________ Habitat Category Habitat Description _____________________________________________________________________________ Riffles Shallow (<20 cm deep), moderate current velocity (20-50 cm/sec), moderate turbulence, substrate gravel, pebble, and cobble-sized particles (2-256 mm), gradient <4% Rapids Gradient >4%, swiftly flowing water (>50 cm/sec), considerable turbulence, substrate largely composed of boulders Pools A portion of stream that is deep and less velocity than run; often lies between riffles Eddies Presence of counter- current; usually deep and less velocity than main- channel Runs Possess attributes of both riffles and pools; characterized by moderately shallow water (10-30 cm deep) with laminar flow; substrate gravel and cobble. _____________________________________________________________________________ 50 APPENDIX 2 - Habitat Suitability Criteria Table 1. Habitat use curve for adult Colorado pikeminnow for daytime resting (bottom velocities); from Miller and Modde (1999). ________________________________________ Velocity HSI Depth HSI (m/s) (m) ________________________________________ 0.000 0.25 0.000 0.00 0.027 0.50 0.427 0.00 0.030 1.00 0.792 0.125 0.244 1.00 0.914 0.25 0.366 0.500 1.158 0.50 0.396 0.25 1.280 1.00 0.427 0.00 6.096 1.00 ________________________________________ Table 2. Habitat use curve for adult Colorado pikeminnow for
    [Show full text]
  • Sediment Transport in River Mouth Estuary
    SEDIMENT TRANSPORT IN RIVER MOUTH ESTUARY Katsuhide YOKOYAMA, Dr.Eng. Assistant Professor Department of Civil Engineering dredge Tokyo Metropolitan University 1-1 Minami-Osawa, Hachioji, Tokyo, Japan 192-0397 [email protected] tel;81-426-77-2786 fax;81-426-77-2772 Introduction & Study Area 0 2km N The river mouth estuary and wetland are comprised of variety of view natural, morphologically and ecologically complex aquatic point environments. In this region, fresh water mixes with salt water, therefore the Tidal river stream runs more slowly, the suspended sediment supplied Sea from the upstream basin deposit and the shallow water area is flat created. River mouth estuary is very important area for ecosystem and 白川 fishery. On the other hand, it is necessary to dredge and enlarge the Port river channel in some cases in order to discharge the river flood into SHIRAKAWA sea safely. River The purpose of this study is to develop the rational management practices of river mouth estuarine resource. It is necessary to Flood and sediment Tidal pumping and explain the sediment transport and the topographical process. discharge sediment transport A field study was undertaken in the SHIRAKAWA river. The Sea topography change of tidal flat was surveyed and the sediment discharge by floods was measured and the annual sediment transport by tidal current was monitored. Using these results, the amount of sediment load was calculated and the influence of the sediment transport by flood and by tidal current on the topography Deposition of silt and change
    [Show full text]
  • Belt Width Delineation Procedures
    Belt Width Delineation Procedures Report to: Toronto and Region Conservation Authority 5 Shoreham Drive, Downsview, Ontario M3N 1S4 Attention: Mr. Ryan Ness Report No: 98-023 – Final Report Date: Sept 27, 2001 (Revised January 30, 2004) Submitted by: Belt Width Delineation Protocol Final Report Toronto and Region Conservation Authority Table of Contents 1.0 INTRODUCTION......................................................................................................... 1 1.1 Overview ............................................................................................................... 1 1.2 Organization .......................................................................................................... 2 2.0 BACKGROUND INFORMATION AND CONTEXT FOR BELT WIDTH MEASUREMENTS …………………………………………………………………...3 2.1 Inroduction............................................................................................................. 3 2.2 Planform ................................................................................................................ 4 2.3 Meander Geometry................................................................................................ 5 2.4 Meander Belt versus Meander Amplitude............................................................. 7 2.5 Adjustments of Meander Form and the Meander Belt Width ............................... 8 2.6 Meander Belt in a Reach Perspective.................................................................. 12 3.0 THE MEANDER BELT AS A TOOL FOR PLANNING PURPOSES...............................
    [Show full text]
  • Modification of Meander Migration by Bank Failures
    JournalofGeophysicalResearch: EarthSurface RESEARCH ARTICLE Modification of meander migration by bank failures 10.1002/2013JF002952 D. Motta1, E. J. Langendoen2,J.D.Abad3, and M. H. García1 Key Points: 1Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA, • Cantilever failure impacts migration 2National Sedimentation Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Oxford, Mississippi, through horizontal/vertical floodplain 3 material heterogeneity USA, Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA • Planar failure in low-cohesion floodplain materials can affect meander evolution Abstract Meander migration and planform evolution depend on the resistance to erosion of the • Stratigraphy of the floodplain floodplain materials. To date, research to quantify meandering river adjustment has largely focused on materials can significantly affect meander evolution resistance to erosion properties that vary horizontally. This paper evaluates the combined effect of horizontal and vertical floodplain material heterogeneity on meander migration by simulating fluvial Correspondence to: erosion and cantilever and planar bank mass failure processes responsible for bank retreat. The impact of D. Motta, stream bank failures on meander migration is conceptualized in our RVR Meander model through a bank [email protected] armoring factor associated with the dynamics of slump blocks produced by cantilever and planar failures. Simulation periods smaller than the time to cutoff are considered, such that all planform complexity is Citation: caused by bank erosion processes and floodplain heterogeneity and not by cutoff dynamics. Cantilever Motta, D., E. J. Langendoen, J. D. Abad, failure continuously affects meander migration, because it is primarily controlled by the fluvial erosion at and M.
    [Show full text]
  • Meander Bend Migration Near River Mile 178 of the Sacramento River
    Meander Bend Migration Near River Mile 178 of the Sacramento River MEANDER BEND MIGRATION NEAR RIVER MILE 178 OF THE SACRAMENTO RIVER Eric W. Larsen University of California, Davis With the assistance of Evan Girvetz, Alexander Fremier, and Alex Young REPORT FOR RIVER PARTNERS December 9, 2004 - 1 - Meander Bend Migration Near River Mile 178 of the Sacramento River Executive summary Historic maps from 1904 to 1997 show that the Sacramento River near the PCGID-PID pumping plant (RM 178) has experienced typical downstream patterns of meander bend migration during that time period. As the river meander bends continue to move downstream, the near-bank flow of water, and eventually the river itself, is tending to move away from the pump location. A numerical model of meander bend migration and bend cut-off, based on the physics of fluid flow and sediment transport, was used to simulate five future migration scenarios. The first scenario, simulating 50 years of future migration with the current conditions of bank restraint, showed that the river bend near the pump site will tend to move downstream and pull away from the pump location. In another 50-year future migration scenario that modeled extending the riprap immediately upstream of the pump site (on the opposite bank), the river maintained contact with the pump site. In all other future migration scenarios modeled, the river migrated downstream from the pump site. Simulations that included removing upstream bank constraints suggest that removing bank constraints allows the upstream bend to experience cutoff in a short period of time. Simulations show the pattern of channel migration after cutoff occurs.
    [Show full text]
  • Hydrology and Morphology of Two River Mouth Regions
    Hydrology OCEANOLOGIA, 47 (3), 2005. pp. 365–385. and morphology of two C 2005, by Institute of river mouth regions Oceanology PAS. (temperate Vistula Delta KEYWORDS and subtropical Red River River mouth Delta) Delta Sedimentation Discharge Waves Coastal currents Zbigniew Pruszak1 Pham van Ninh2 Marek Szmytkiewicz1 Nguyen Manh Hung2 Rafał Ostrowski1,∗ 1 Institute of Hydroengineering, Polish Academy of Sciences, Kościerska 7, PL–80–953 Gdańsk, Poland; e-mail: rafi@ibwpan.gda.pl ∗corresponding author 2 Institute of Mechanics, Center for Marine Environment, Survey, Research and Consultation, 264 Don Can, Hanoi, Vietnam Received 7 February 2005, revised 3 August 2005, accepted 29 August 2005. Abstract The paper presents a comparative analysis of two different river mouths from two different geographical zones (subtropical and temperate climatic regions). One is the multi-branch and multi-spit mouth of the Red River on the Gulf of Tonkin (Vietnam), the other is the smaller delta of the river Vistula on a bay of the Baltic Sea (Poland). The analysis focuses on the similarities and differences in the hydrodynamics between these estuaries and the adjacent coastal zones, the features of sediment transport, and the long-term morphodynamics of the river outlets. Salinity and water level are also discussed, the latter also in the context of the anticipated global effect of accelerated sea level rise. The analysis shows The complete text of the paper is available at http://www.iopan.gda.pl/oceanologia/ 366 Z. Pruszak, P. V. Ninh, M. Szmytkiewicz, N. M. Hung, R. Ostrowski that the climatic and environmental conditions associated with geographical zones give rise to fundamental differences in the generation and dynamic evolution of the river mouths.
    [Show full text]
  • TRCA Meander Belt Width
    Belt Width Delineation Procedures Report to: Toronto and Region Conservation Authority 5 Shoreham Drive, Downsview, Ontario M3N 1S4 Attention: Mr. Ryan Ness Report No: 98-023 – Final Report Date: Sept 27, 2001 (Revised January 30, 2004) Submitted by: Belt Width Delineation Protocol Final Report Toronto and Region Conservation Authority Table of Contents 1.0 INTRODUCTION......................................................................................................... 1 1.1 Overview ............................................................................................................... 1 1.2 Organization .......................................................................................................... 2 2.0 BACKGROUND INFORMATION AND CONTEXT FOR BELT WIDTH MEASUREMENTS …………………………………………………………………...3 2.1 Inroduction............................................................................................................. 3 2.2 Planform ................................................................................................................ 4 2.3 Meander Geometry................................................................................................ 5 2.4 Meander Belt versus Meander Amplitude............................................................. 7 2.5 Adjustments of Meander Form and the Meander Belt Width ............................... 8 2.6 Meander Belt in a Reach Perspective.................................................................. 12 3.0 THE MEANDER BELT AS A TOOL FOR PLANNING PURPOSES...............................
    [Show full text]
  • Link to SRSB Dune Restoration and Management Plan
    The Greater Salinas River State Beach Dune Restoration and Management Plan Central Coast Wetlands Group at Moss Landing Marine Labs and Coastal Conservation and Research in partnership with California Department of Parks and Recreation Revised June 2020 This page intentionally left blank CONTENTS Existing Conditions and Background ....................................................................................... 1 Introduction ................................................................................................................. 1 Site Description ............................................................................................................ 1 Plants and Animals at the Dunes ........................................................................................ 5 Dunes and Iceplant ....................................................................................................... 10 Previous Restoration Efforts in Monterey Bay ...................................................................... 12 Dunes as Coastal Protection from Storms ........................................................................... 14 Restoration Plan ............................................................................................................. 16 Summary................................................................................................................... 16 Restoration Goals and Objectives ..................................................................................... 18 Goal 1. Eradicate
    [Show full text]
  • Approaches to the Enumerative Theory of Meanders
    Approaches to the Enumerative Theory of Meanders Michael La Croix September 29, 2003 Contents 1 Introduction 1 1.1 De¯nitions . 2 1.2 Enumerative Strategies . 7 2 Elementary Approaches 9 2.1 Relating Open and Closed Meanders . 9 2.2 Using Arch Con¯gurations . 10 2.2.1 Embedding Semi-Meanders in Closed Meanders . 12 2.2.2 Embedding Closed Meanders in Semi-Meanders . 14 2.2.3 Bounding Meandric Numbers . 15 2.3 Filtering Meanders From Meandric Systems . 21 2.4 Automorphisms of Meanders . 24 2.4.1 Rigid Transformations . 25 2.4.2 Cyclic Shifts . 27 2.5 Enumeration by Tree Traversal . 30 2.5.1 A Tree of Semi-Meanders . 31 2.5.2 A Tree of Meanders . 32 3 The Symmetric Group 34 3.1 Representing Meanders As Permutations . 34 3.1.1 Automorphisms of Meandric Permutations . 36 3.2 Arch Con¯gurations as Permutations . 37 3.2.1 Elements of n That Are Arch Con¯gurations . 38 C(2 ) 3.2.2 Completing the Characterization . 39 3.3 Expression in Terms of Characters . 42 4 The Matrix Model 45 4.1 Meanders as Ribbon Graphs . 45 4.2 Gaussian Measures . 49 i 4.3 Recovering Meanders . 53 4.4 Another Matrix Model . 54 5 The Temperley-Lieb Algebra 56 5.1 Strand Diagrams . 56 5.2 The Temperley-Lieb Algebra . 57 6 Combinatorial Words 69 6.1 The Encoding . 69 6.2 Irreducible Meandric Systems . 73 6.3 Production Rules For Meanders . 74 A Tables of Numbers 76 Bibliography 79 ii List of Figures 1.1 An open meander represented as a river and a road.
    [Show full text]