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Internal Wave Reflection on Shelf Slopes with Depth-Varying Stratification

Rob A. HallSchool of Environmental Sciences, University of East Anglia, Norwich, United Kingdom

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John M. HuthnanceNational Oceanography Centre, Liverpool, United Kingdom

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Richard G. WilliamsSchool of Environmental Sciences, University of Liverpool, Liverpool, United Kingdom

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Abstract

Reflection of internal waves from sloping topography is simple to predict for uniform stratification and linear slope gradients. However, depth-varying stratification presents the complication that regions of the slope may be subcritical and other regions supercritical. Here, a numerical model is used to simulate a mode-1, M2 internal tide approaching a shelf slope with both uniform and depth-varying stratifications. The fractions of incident internal wave energy reflected back offshore and transmitted onto the shelf are diagnosed by calculating the energy flux at the base of slope (with and without topography) and at the shelf break. For the stratifications/topographies considered in this study, the fraction of energy reflected for a given slope criticality is similar for both uniform and depth-varying stratifications. This suggests the fraction reflected is dependent only on maximum slope criticality and independent of the depth of the pycnocline. The majority of the reflected energy flux is in mode 1, with only minor contributions from higher modes due to topographic scattering. The fraction of energy transmitted is dependent on the depth-structure of the stratification and cannot be predicted from maximum slope criticality. If near-surface stratification is weak, transmitted internal waves may not reach the shelf break because of decreased horizontal wavelength and group velocity.

Corresponding author address: Rob A. Hall, School of Environmental Sciences, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, United Kingdom. E-mail: robert.hall@uea.ac.uk

Abstract

Reflection of internal waves from sloping topography is simple to predict for uniform stratification and linear slope gradients. However, depth-varying stratification presents the complication that regions of the slope may be subcritical and other regions supercritical. Here, a numerical model is used to simulate a mode-1, M2 internal tide approaching a shelf slope with both uniform and depth-varying stratifications. The fractions of incident internal wave energy reflected back offshore and transmitted onto the shelf are diagnosed by calculating the energy flux at the base of slope (with and without topography) and at the shelf break. For the stratifications/topographies considered in this study, the fraction of energy reflected for a given slope criticality is similar for both uniform and depth-varying stratifications. This suggests the fraction reflected is dependent only on maximum slope criticality and independent of the depth of the pycnocline. The majority of the reflected energy flux is in mode 1, with only minor contributions from higher modes due to topographic scattering. The fraction of energy transmitted is dependent on the depth-structure of the stratification and cannot be predicted from maximum slope criticality. If near-surface stratification is weak, transmitted internal waves may not reach the shelf break because of decreased horizontal wavelength and group velocity.

Corresponding author address: Rob A. Hall, School of Environmental Sciences, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, United Kingdom. E-mail: robert.hall@uea.ac.uk
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