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Physical Modelling of Tidal Resonance in a Submarine

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Physical Modelling of Tidal Resonance in a Submarine PHYSICAL MODELLING OF TIDAL RESONANCE IN A SUBMARINE CANYON by Kate Elizabeth Le Sou¨ef B.E., The University of Western Australia, 2006 B.Sc., The University of Western Australia, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate and Postdoctoral Studies (Oceanography) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2013 c Kate Elizabeth Le Sou¨ef,2013 Abstract The Gully, Nova Scotia (44◦N) is unique amongst studied submarine canyons ◦ poleward of 30 due to the dominance of the diurnal (K1) tidal frequency, which is subinertial at these latitudes. Length scales suggest the diurnal frequency may be resonant in the Gully. A physical model of the Gully was constructed in a tank and tidal currents were observed using a rotating table. Resonance curves were fit to measurements in the laboratory canyon for a range of stratifica- tions, background rotation rates and forcing amplitudes. Resonant frequency increased with increasing stratification and was not affected by changing back- ground rotation rates, as expected. Dense water was observed upwelling onto the continental shelf on either side of the laboratory canyon and travelled at least one canyon width along the shelf. Most of this upwelled water was pulled back into the canyon on the second half of the tidal cycle. Friction values measured in the laboratory were much higher than expected, possibly due to upwelled water surging onto the shelf on each tidal cycle, similar to a tidal bore. By scaling ob- servations from the laboratory to the ocean and assuming friction in the ocean is also affected by water travelling onto the shelf, a resonance curve for the Gully was created. Resonance curves explain why the diurnal frequency dominates over the semi-diurnal (M2) frequency throughout the year at the Gully, even if stratification at the shelf break varies. ii Preface This thesis contains details of experiments and analysis designed and undertaken primarily by the author, Kate Le Sou¨ef.Susan Allen was the supervisor on this project and was involved in concept formation, interpretation of results and manuscript edits. This work is previously unpublished, although a manuscript based on Chapter 2 will be submitted for publication in the future. iii Table of Contents Abstract .................................... ii Preface ..................................... iii Table of Contents .............................. iv List of Tables ................................. vii List of Figures ................................ viii Acknowledgements ............................. x 1 Introduction ............................... 1 1.1 Submarine canyons . 1 1.2 Internal waves in submarine canyons . 2 1.3 Studying submarine canyons . 4 1.4 Oscillating flow in submarine canyons . 6 1.5 The Gully, Nova Scotia . 7 1.6 Tidal resonance . 10 1.7 Analytical models of the Gully . 11 1.8 Research questions . 13 2 Physical modelling of resonance ................... 15 2.1 Introduction . 15 iv 2.2 Methods . 16 2.2.1 Scaling analysis . 16 2.2.2 Rotating table . 16 2.2.3 Canyon insert . 18 2.2.4 Stratifying the tank . 18 2.2.5 Light sheet . 20 2.2.6 Running an experiment . 21 2.2.7 Flow visualisation . 21 2.2.8 Image processing . 22 2.3 Results . 24 2.3.1 Velocity fields . 24 2.3.2 General circulation over tidal cycle . 27 2.3.3 Resonance curve fitting . 31 2.3.4 Amplification and phase lag . 34 2.3.5 Repeatability . 40 2.4 Discussion . 44 2.4.1 Experimental considerations . 44 2.4.2 Factors affecting resonant frequency . 45 2.4.3 Structure of resonance . 47 2.4.4 Friction in the laboratory . 49 2.4.5 Resonance in the Gully . 50 2.4.6 Conclusion . 57 3 Conclusion ................................ 58 3.1 Research questions . 58 3.2 Implications and future research . 61 3.3 Broader context . 62 v References ................................... 63 A Non-dimensional parameters ..................... 67 B Additional laboratory methods ................... 68 B.1 Canyon insert . 68 B.2 Neutrally buoyant particles . 69 C Standard error calculation ...................... 70 D Separate resonance curves ....................... 71 vi List of Tables 2.1 Parameters and non-dimensional parameters . 17 2.2 List of experiments . 17 2.3 Fit parameters for each stratification (N) . 36 2.4 Fit parameters for each background rotation (f) . 36 2.5 Fit parameters for each forcing amplitude (∆f) . 36 2.6 Fit parameters for three locations along canyon . 43 2.7 Fit parameters for repeated experiments . 43 2.8 Parameters for resonance curves using representative stratifica- tions from three different depths in the Gully . 54 2.9 Parameters for resonance curves at different stratifications in the Gully . 56 vii List of Figures 1.1 Location of the Gully, Nova Scotia . 8 2.1 Isobaths in the Gully and the laboratory canyon . 19 2.2 Density profile and buoyancy frequency in the tank . 20 2.3 Velocity field for Experiment 3 (! = 0:359s−1) . 25 2.4 Velocity field for Experiment 3 (! = 0:8s−1) . 26 2.5 General circulation in the laboratory model, with tidal flow op- posite to rotation . 28 2.6 General circulation in the laboratory model, with tidal flow in the same direction as rotation . 29 2.7 Photographs of dye transported onto shelf . 30 2.8 Amplification and phase difference for each stratification . 36 2.9 Amplification and phase difference for each stratification against !=N .................................. 37 2.10 Amplification and phase difference for each background rotation 38 2.11 Amplification and phase difference for each forcing amplitude . 39 2.12 Amplification and phase difference for three locations along canyon 41 2.13 Amplification and phase difference for repeated experiment . 43 2.14 Amplification and phase difference in the Gully calculated using stratification chosen at three depths . 54 viii 2.15 Amplification in the Gully for a range of stratifications averaged in the canyon . 56 A.1 Non-dimensional parameters for each experiment . 67 B.1 Laboratory tank . 68 D.1 Amplification and phase difference for first stratification . 71 D.2 Amplification and phase difference for second stratification . 72 D.3 Amplification and phase difference for third stratification . 72 D.4 Amplification and phase difference for first stratification against !=N .................................. 73 D.5 Amplification and phase difference for second stratification against !=N .................................. 73 D.6 Amplification and phase difference for third stratification against !=N .................................. 74 D.7 Amplification and phase difference for first background rotation . 74 D.8 Amplification and phase difference for second background rotation 75 D.9 Amplification and phase difference for first forcing amplitude . 75 D.10 Amplification and phase difference for second forcing amplitude . 76 D.11 Amplification and phase difference for canyon head . 76 D.12 Amplification and phase difference for mid canyon . 77 D.13 Amplification and phase difference for canyon mouth . 77 ix Acknowledgements I have been extremely lucky to work in Susan Allen's lab. Susan is a patient, enthusiastic and understanding supervisor who always makes time for her grad- uate students. Susan, thank you for all the advice, support and assistance in the lab, during our meetings and every time I have come by your office. In particular, thank you for your unshakeable belief that we would make the table spin again! I would like to thank my supervisory committee members, Douw Steyn and Greg Lawrence, for their time, suggestions and enthusiasm throughout my project. And thank you to Douw for helping me formulate my research plan in EOSC571 and for the chats about skiing. Thank you to David Jones for constant, patient assistance with the elec- trical wiring and programming of the table, and also for preventing me from electrocuting myself, and to Doug Latornell for working evenings and weekends to repair the table. Thanks to David Jessop for being a great lab buddy in the dark second basement. I consider myself very fortunate to have shared the Waterhole with so many excellent companions, incredible MATLAB advisors and wonderful friends. Thank you to my wonderful parents and siblings for their ongoing support, to Az for convincing me to return to university and to Vince for constant en- couragement and love. x Chapter 1 Introduction 1.1 Submarine canyons Submarine canyons are topographic coastal features that cut into the continental shelf. Roughly 20% of the western North American shelf edge between Alaska and the Equator is interrupted by canyons [Hickey, 1995]. Submarine canyons are common in many regions of the world. They can vary greatly in size but have typical cross canyon length scales of approximately 10 kilometres, with topographic slopes along the longitudinal axis of up to 45 ◦ [Mirshak and Allen, 2005]. In general, exchange between the deep ocean and the continental shelf is lim- ited. Homogeneous, geostrophic flow cannot change its depth and is restricted to follow isobaths along the continental shelf, such that deep ocean exchange occurs only when ageostrophic dynamics occur [Allen and Durrieu de Madron, 2009]. Interruptions in the continental shelf, such as submarine canyons, disrupt along-shelf flow and can cause mixing, internal waves and upwelling [Hickey, 1995]. The presence of a canyon transports deep water further onto the shelf 1 than would occur for a straight continental shelf and provides enhanced mixing, particularly due to tides [Allen and Durrieu de Madron, 2009]. Submarine canyons play an important role in regional ecosystems and can be locations of enhanced species diversity and biological productivity [Hickey, 1995]. In many canyons, the accepted reason for this diversity is upwelling, which provides a nutrient source that increases phytoplankton and zooplankton density [Hickey, 1995]. For example, canyon upwelling at Barkley Canyon, British Columbia, can be observed close to the surface at 10 metres depth and zooplankton species are passively advected by the currents in and around the canyon [Allen et al., 2001]. Submarine canyons can therefore affect coastal biological processes.
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