# GFD III , Winter 2019

**Professors Jen MacKinnon and Bill Young**

**T/Th 9:30-10:50, Nierenberg Hall 101**

### Course Overview

The goal of SIO212C --- 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 student led 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

1/8: NO CLASS

1/10: Overview of submesoscale processes and dynamics, governing equations, parameter space for the quarter, plan for the class

1/15: Review of basic internal wave equations, dynamics [Paper of the day: tbd…]

1/17: More internal wave basics, propagation, WKB, ray tracing.

1/22: Internal tides: generation, modes, global patterns, power.

1/24, ** 2:30-4pm: Near-inertial waves. Slab model wind generation. Interaction with ambient vorticity field. Global maps, power.

1/29: Wave / mean flow interaction

1/31: The kinematics of passive scalars and passive vectors. Stirring, mixing, gradient amplification and enhanced dispersion.

2/5: The internal wave continuum. Garrett-Munk. Triad interactions and energy transfer. Mechanics and patterns of wave breaking. Global patterns and budgets.

2/7: Continuum discussion continued.

**Some GM+wave-wave interaction +finescale parameterization slides**2/12: Continuum part 3, and a few lee waves.

2/14: Fronts of the world, and QG basics.

**Lecture notes (click)**and**Slides**2/19: Quasigeostrophic frontogenesis. Semigeostrophic frontogenesis: balanced frontogenesis --- the Hoskins \& Bretherton model and unbalanced frontogenesis --- Blumen's model.

2/21: Frontogenesis and instabilities continued

2/26: Frontogenesis and instabilities continued

2/28: Frontogenesis and instabilities continued

3/5: Frontogenesis and instabilities continued

3/7: Back to wave / mean flow interactions, the complicated version, part I

3/12: Back to wave / mean flow interactions, the complicated version, part II

3/14: Student presentations

**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.

*Homework #1** *(click on it), due Thursday Jan 17th in class.

*Homework #2**,* due 14 Feb in class

** Homework #2**.5, due 21 Feb in class. Associated matlab file of data here

** Homework #3**, due tbd

** Homework #n**, student presentations and short write up.

**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 talked about in class. **

**Internal tides: generation and propagation**

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

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

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

**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**

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:**

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 II: Energetics and results from PolyMode, Polzin 10Wave 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