GFD III , Winter 2025

Professors Jen MacKinnon and Bill Young

T/Th 11-12:20, Nierenberg Hall 101

Course Overview

The goal of GFD 3 --- a third course on geophysical fluid dynamics --- is to provide physical oceanography students with the background required to work at the frontier of research on unbalanced processes with an emphasis on upper-ocean and mixed layer dynamics. Some of these were once balanced but have ceased to be so (e.g. frontal instabilities), some were never balanced (e.g. internal waves), and some are nonlinear interactions between the two. These topics are of increasing community interest and are central to many ongoing SIO research projects but are not accommodated in parts I and II of the geophysical fluid dynamics sequence SIO 212. Most of these topics are not covered in any pedagogical textbooks, and students (and PIs!) are left to pick up what they can from individual research papers. Here we hope to put together a systematic treatment, an broad intellectual framework in which to understand many of these hot topic issues. This material is intended primarily for second year and above students who have at least taken the first year Fluids and GFD courses. Other interested scientists at any level are quite welcome to sit in and join the discussion.

Each class will involve a combination of lectures and discussion of relevant papers that connect lecture material to areas of active research. The paper associated with each lecture is listed below. Additional reference material of possible interest is listed further down.

Schedule

• 1/7: [Jen] Overview of the class, parameter space, non-dimensional numbers, phenomena

• 1/9: [Jen] Internal wave dynamics

• 1/14: [Jen] More internal waves, propagation

• 1/16: [Jen] Internal waves in variable stratification: vertical modes and WKB

• 1/21: [Jen] More non-constant media: ray tracing

• 1/23: [Bill] What is the near-inertial band and why does it deserve three lectures?

• 1/28: [Bill] (NI continued)

• 1/30: [Bill] (NI continued)

• 2/4:  [Bill] (NI continued)

• 2/6: [Bill] (NI continued)

• 2/11: [Jen] Internal tides and lee waves

• 2/13 [Jen] Continued lee waves

• 2/18 [Jen] Ray tracing

• 2/20: [Bill] Stirring and mixing

• 2/25: [Bill] Shear Dispersion

• 2/27: [Bill] Frontogenesis and Frontolysis

• 3/4: [Bill] Frontogenesis and Frontolysis

• 3/6: [Bill] Instabilities of the Surface Boundary Layer

• 3/11: [Jen] Bringing back advective terms to internal waves, part I: wave-wave interactions and the G-M continuum

• 3/13: [Jen] Bringing back advective terms to internal waves, part II: internal wave / mesoscale nteractions

Office hours:  contact either professor individually to figure out a good time to stop by.

HOMEWORK

The classes will involve a combination of formal lectures on the underlying theoretical framework coupled with class discussion and presentation of research papers --- both classic and cutting edge. There will be a few formal homeworks, as we think there are some things you will (later) appreciate having had to derive yourself, and thus understand thoroughly. However befitting a senior graduate student class the majority of the work expected will be a combination of reading assigned cutting edge papers (and coming to class prepared to discuss them), and a modest size term project of flexible nature. There are no written exams.

GRADING

Grades will be based on a combination of written assignments and class participation.

Additional Reference material (click on each one to go to the paper). As a disclaimer, these are not meant be comprehensive or particularly representative, but are some of the papers we will talk about in class. Note that this is still being updated, other suggestions also welcome!

Internal tides: generation and propagation

• Internal tide generation in the deep ocean, Garrett and Kunze, 2007

• Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data, Egbert and Ray, 2000

• Global observations of Open Ocean Mode-1 M2 internal tides, Zhao et al 16

• The role of internal tides in mixing the deep ocean, St. Laurent and Garrett, 2002

• Tidal conversion by subcritical topography, Balmforth, Irely and Young, 2002

• Conversion of the barotropic tide, Llewellyn Smith and Young, 2002

• Internal Waves across the Pacific, Alford et al, 2007

• Climate process team on internal wave–driven ocean mixing, MacKinnon et al, 2017

• Abyssal recipes II: Energetics of tidal and wind mixing, Munk and Wunsch 98

Near-inertial internal waves: generation and propagation

• Near-inertial internal gravity waves in the ocean, Alford et al, 2015

• Propagation of near-inertial oscillations through a geostrophic flow, Young and Ben Jelloul, 97

• Simulating the long-range swell of internal waves generated by ocean storms, Simmons and Alford, 2012

• Upper-ocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory, D’Asaro et al 95

• Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer near-inertial motions, Alford 01

The role of surface waves

• Wave‐driven inertial oscillations, Hasselman 70

• On the theoretical form of ocean swell. On a rotating earth, Ursell 50

Wave-wave interactions, triad theory, G-M and the internal wave continuum

• Internal waves in the ocean, Garrett and Munk 1979

• Deep ocean internal waves: What do we really know?, Wunsch 75

• Nonlinear interactions among internal gravity waves, Muller et al 86

• Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean, Olbers 76

• A composite spectrum of vertical shear in the upper ocean, Gargett et al 81

• A heuristic description of internal wave dynamics, Polzin 04a

• Idealized solutions for the energy balance of the finescale internal wave field, Polzin 04b

• Advection, phase distortion, and the frequency spectrum of finescale fields in the sea, Pinkel 2008

• Toward regional characterizations of the oceanic internal wavefield, Polzin and Lvov 11

• Energy transfer from high-shear, low-frequency internal waves to high-frequency waves near Kaena Ridge, HawaiI, Sun and Pinkel 2012

• Subharmonic energy transfer from the semidiurnal internal tide to near-diurnal motions over Kaena Ridge, Hawaii, Sun and Pinkel 13

• Parametric subharmonic instability of the internal tide at 29 N, MacKinnon et al 13

• Subtropical catastrophe: Significant loss of low‐mode tidal energy at 28.9°, MacKinnon and Winters 05

Jody Klymak’s matlab representation of the G-M spectrum is here

Finescale parameterizations of mixing as applied to data:

• Scaling turbulent dissipation in the thermocline, Gregg 89

• Finescale parameterizations of turbulent dissipation, Polzin et al 95

• Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles, Kunze et al 06

• Spatial and temporal variability of global ocean mixing inferred from Argo profiles, Whalen et al 12

• Suppression of internal wave breaking in the Antarctic Circumpolar Current near topography, Waterman et al 14

• Finescale parameterizations of turbulent dissipation, Polzin et al 14 (I’m noting a theme in his titles)

• Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate, Waterhouse et al 14

• Estimating the mean diapycnal mixing using a finescale strain parameterization, Whalen et al 15

Parameterizations for models

• Abyssal recipes, Walter Munk, 66

• Parameterizing tidal dissipation over rough topography, Jayne et al 01

• Estimating tidally driven mixing in the deep ocean, St. Laurent et al 02

• An abyssal recipe, Polzin 09

• Sensitivity of the ocean state to the vertical distribution of internal-tide-driven mixing, Melet et al 13

Frontogenesis

• Atmospheric frontogenesis models: Mathematical formulation and solution, Hoskins and Bretherton ‘72

• Frontogenesis by horizontal wind deformation fields, Stone 66

• Quasi-geostrophic frontogenesis, Williams and Plotkin 68

• A new look at the ω‐equation, Hoskins et al 78

• Mixed layer restratification due to a horizontal density gradient, Tandon and Garrett ‘94

• Geostrophic adjustment: A mechanism for frontogenesis, Ou 84

• Frontogenesis in a fluid with horizontal density gradients, Simpson and Linden 89

Internal wave mesoscale interaction

• Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean, Nikurashin and Ferrari 11

• Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: Theory, Nikurasin and ferrari 10

• Mesoscale eddy–internal wave coupling. Part I: Symmetry, wave capture, and results from the Mid-Ocean Dynamics Experiment, Polzin 08

• Mesoscale eddy–internal wave coupling. Part II: Energetics and results from PolyMode, Polzin 10

• Wave capture and wave–vortex duality, buhler and mcintyre 05

• Near-inertial waves in strongly baroclinic currents, Whitt and Thomas 13

• Resonant generation and energetics of wind-forced near-inertial motions in a geostrophic flow, whitt and thomas 15

• On the modifications of near-inertial waves at fronts: implications for energy transfer across scales, Thomas 17

• Large-scale impacts of the mesoscale environment on mixing from wind-driven internal waves, Whalen et al 18