Analytic Reconstruction of a Two-Dimensional Velocity Field from an Observed Diffusive Scalar

Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved if high-resolution tracer measurements, as well as velocity measurements along a curve transverse to the instantaneous scalar contours, are available. Such measurements enable solving a system of partial differential equations for the velocity components by the method of characteristics. If the value of the scalar diffusivity is known, then knowledge of just one velocity component along a transverse initial curve is sufficient. These conclusions extend to the shallow-water equations and to flows with spatially dependent diffusivity. We illustrate our results on velocity reconstruction from tracer fields for planar Navier- Stokes flows and for a barotropic ocean circulation model. We also discuss the use of the proposed velocity reconstruction in oceanographic applications to extend localised velocity measurements to larger spatial domains with the help of remotely sensed scalar fields.Comment: 20 pages, 10 figures, In press at J. Fluid Mechanic

Tidally Driven Processes Leading to Near-Field Turbulence in a Channel at the Crest of the Mendocino Escarpment*

In situ observations of tidally driven turbulence were obtained in a small channel that transects the crest of the Mendocino Ridge, a site of mixed (diurnal and semidiurnal) tides. Diurnal tides are subinertial at this latitude, and once per day a trapped tide leads to large flows through the channel giving rise to tidal excursion lengths comparable to the width of the ridge crest. During these times, energetic turbulence is observed in the channel, with overturns spanning almost half of the full water depth. A high-resolution, nonhydrostatic, 2.5-dimensional simulation is used to interpret the observations in terms of the advection of a breaking tidal lee wave that extends from the ridge crest to the surface and the subsequent development of a hydraulic jump on the flanks of the ridge. Modeled dissipation rates show that turbulence is strongest on the flanks of the ridge and that local dissipation accounts for 28% of the energy converted from the barotropic tide into baroclinic motion.United States. Office of Naval Research (Grant ONR N00014- 12-1-0943)National Science Foundation (U.S.). (Grant NSF OCE 1129763

The generation of Rossby waves and wake eddies by small islands

Author Posting. © Authors, 2018. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 76 (2018): 63-91, doi:10.1357/002224018824845929.The influence of small islands on zonal geostrophic currents is examined in a two-layer configuration. An analytic solution for steady quasigeostrophic flow is derived under the assumption of no upstream influence and is validated numerically in a time-dependent quasigeostrophic model. Under these conditions solutions are the sum of two eigenmodes, which are either arrested Rossby waves or evanescent depending on background flow conditions (layer speeds, stratification, and latitude). In contrast to homogeneous flows, arrested Rossby waves in two layers can occur even when the depth mean flow is westward and can be generated both to the east and west of the island. A third blocking mode may play a role in general, altering the meridional structure of the zonal flow upstream and downstream of the island. The influence of the quasigeostrophic modes on submesoscale island wake eddies is considered in a two-layer primitive equation model with no-slip boundary conditions at the island. Wake eddy formation is inhibited in the presence of an arrested Rossby wave, though the overall drag is similar.This work was supported by the Office of Naval Research Program 322, Physical Oceanography, Grant Number N000141512622

On the predictability of sea surface height around Palau

Author Posting. © American Meteorological Society, 2020. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 50(11), (2020): 3267–3294, https://doi.org/10.1175/JPO-D-19-0310.1.As part of the Flow Encountering Abrupt Topography (FLEAT) program, an array of pressure-sensor equipped inverted echo sounders (PIESs) was deployed north of Palau where the westward-flowing North Equatorial Current encounters the southern end of the Kyushu–Palau Ridge in the tropical North Pacific. Capitalizing on concurrent observations from satellite altimetry, FLEAT Spray gliders, and shipboard hydrography, the PIESs’ 10-month duration hourly bottom pressure p and round-trip acoustic travel time τ records are used to examine the magnitude and predictability of sea level and pycnocline depth changes and to track signal propagations through the array. Sea level and pycnocline depth are found to vary in response to a range of ocean processes, with their magnitude and predictability strongly process dependent. Signals characterized here comprise the barotropic tides, semidiurnal and diurnal internal tides, southeastward-propagating superinertial waves, westward-propagating mesoscale eddies, and a strong signature of sea level increase and pycnocline deepening associated with the region’s relaxation from El Niño to La Niña conditions. The presence of a broad band of superinertial waves just above the inertial frequency was unexpected and the FLEAT observations and output from a numerical model suggest that these waves detected near Palau are forced by remote winds east of the Philippines. The PIES-based estimates of pycnocline displacement are found to have large uncertainties relative to overall variability in pycnocline depth, as localized deep current variations arising from interactions of the large-scale currents with the abrupt topography around Palau have significant travel time variability.Support for this research was provided by Office of Naval Research Grants N00014-16-1-2668, N00014-18-1-2406, N00014-15-1-2488, and N00014-15-1-2622. R.C.M. was additionally supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Weston Howland Jr. Postdoctoral Scholarship

Observations of diurnal coastal-trapped waves with a thermocline-intensified velocity field

Author Posting. © American Meteorological Society, 2019. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 49(7), (2019): 1973-1994, doi: 10.1175/JPO-D-18-0194.1.Using 18 days of field observations, we investigate the diurnal (D1) frequency wave dynamics on the Tasmanian eastern continental shelf. At this latitude, the D1 frequency is subinertial and separable from the highly energetic near-inertial motion. We use a linear coastal-trapped wave (CTW) solution with the observed background current, stratification, and shelf bathymetry to determine the modal structure of the first three resonant CTWs. We associate the observed D1 velocity with a superimposed mode-zero and mode-one CTW, with mode one dominating mode zero. Both the observed and mode-one D1 velocity was intensified near the thermocline, with stronger velocities occurring when the thermocline stratification was stronger and/or the thermocline was deeper (up to the shelfbreak depth). The CTW modal structure and amplitude varied with the background stratification and alongshore current, with no spring–neap relationship evident for the observed 18 days. Within the surface and bottom Ekman layers on the shelf, the observed velocity phase changed in the cross-shelf and/or vertical directions, inconsistent with an alongshore propagating CTW. In the near-surface and near-bottom regions, the linear CTW solution also did not match the observed velocity, particularly within the bottom Ekman layer. Boundary layer processes were likely causing this observed inconsistency with linear CTW theory. As linear CTW solutions have an idealized representation of boundary dynamics, they should be cautiously applied on the shelf.An Australian Research Council Discovery Project (DP 140101322), and a UWA Research Collaboration Award funded this work. T. L. Schlosser acknowledges the support of an Australian Government Research Training Program (RTP) Scholarship. We thank the crew, volunteers and scientists who aided in the field data collection aboard the R/V Revelle, which was funded by the National Science Foundation (OCE-1129763). The continental slope moorings, T4 (M32) and T3 (M44), were also funded by the National Science Foundation (OCE-1129763) and were conceived, planned, and executed by Matthew Alford, Jennifer Mackinnon, Jonathan Nash, Harper Simmons, and Gunnar Voet. We also thank Harper Simmons for the combined R/V Revelle multibeam and Geoscience Australia bathymetry used in this study. We thank the two anonymous reviewers whose comments improved this work.2020-01-1

Climate Process Team on internal wave–driven ocean mixing

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 98 (2017): 2429-2454, doi:10.1175/BAMS-D-16-0030.1.Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.We are grateful to U.S. CLIVAR for their leadership in instigating and facilitating the Climate Process Team program. We are indebted to NSF and NOAA for sponsoring the CPT series.2018-06-0