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CIAION

Simmons, H.L., and M.H. Alford. 2012. Simulating the long-range swell of internal waves

generated by ocean storms. Oceanography25(2):3041, http://dx.doi.org/10.5670/

oceanog.2012.39.

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Oceanography | Vol. 25, No. 230

Simulating theLong-Range Swell of Internal Waves

Generated by Ocean StormsB Y H A R P E R L . S I M M O N S A N D M A H E W H . A L F O R D

S P E C I A L I S S U E O N I N E R N A L W AV E S

ABSRAC. Near-inertial waves (NIWs) are a special class o internal gravity waves

with periods set by planetary rotation and latitude (e.g., at 30 latitude, one cycle

per 24 hours). Tey are notable because they contain most o the observed shear in

the ocean and around hal the kinetic energy. As such, they have been demonstrated

to mix the upper ocean and to have the potential to mix the deep ocean enough to

be important or climate simulations. NIWs are principally generated as a result o

a resonant coupling between upper-ocean currents and mid-latitude atmospheric

cyclones. Here, we report on simulated NIWs in an eddy-resolving general circulation

model that is orced by a realistic atmosphere, and we make comparisons to NIWs

observed rom moored and shipboard measurements o currents. Te picture that

emerges is that as much as 16% o NIW energy (which is season dependent) radiates

out o the mixed layer and equatorward in the orm o low-mode, long-lived internal

gravity waves; they transmit energy thousands o kilometers rom their regions o

generation. Te large amount o energy in near-inertial motions at a given site is a

combination o a local response to wind orcing and waves that have traveled ar rom

where they were generated.

INRODUCION

Motivation

Near-inertial waves (NIWs) are one

o the most energetic modes o ocean

variability, containing about hal the

oceans kinetic energy at most sites

(and even more beneath storm tracks).

Hence, they are o central importance

to a variety o ocean processes, includ-

ing mixed-layer deepening (Price et al.,

1986); submesoscale processes, larval

dispersion, and ormation o thin layers

(Franks, 1995); restratification o mixed

layers and thermohaline intrusions

(Hosegood et al., 2008); and mixing o

both the upper and deep ocean (Hebert

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Oceanography | June 2012 31

and Moum, 1994; Alord, 2003b). Yet, an

understanding o NIW energy sources

and redistribution by wave radiation is

lacking, causing NIWs to be poorly rep-

resented in regional and global models.

Over the last decade, there has been

significant community ocus on internaltides, which produce large thermocline

displacements, affect sound propagation,

and control some hotspots o elevated

turbulent mixing. Near-inertial internal

gravity waves are probably o similar or

greater importance, providing compara-

ble kinetic energy and the vast majority

o shear variance (Alord and Whitmont,

2007; oole, 2007), and likely leading to a

substantial amount o turbulent mixing.Significant deficiencies remain in our

understanding o the physical processes

that determine their generation, evolu-

tion, and destruction. NIWs appear to be

primarily orced by the wind (DAsaro,

1985; Alord and Whitmont, 2007). Te

amount o energy input to the ocean in

the orm o NIWs has been estimated to

be 0.50.7 W (Watanabe and Hibiya,

2002; Alord, 2003a), based on orcing a

slab model (Pollard and Millard, 1970)

with reanalysis winds. However, Jiang

et al. (2005) demonstrated sensitivity to

the choice o wind product used, obtain-

ing values ranging rom 0.361.4 W.

Tough uncertain, these calculations

represent a large raction o the 2 W

o energy demand required to maintain

deep-ocean stratification (Munk and

Wunsch, 1998; Wunsch and Ferrari,

2004; St. Laurent and Simmons, 2006).

Tese calculations give the source o

NIWs, specifically, the lateral distribution

o the power input. However, analogous

to internal tides, NIWs appear to be able

to travel ar rom their orcing regions

downward into the ocean interior rom

their generation at the surace and also

equatorward. Understanding their dis-

sipation clearly requires understanding

this lateral and vertical propagation. In

a study using a global model similar to

the one used here, Furiuchi et al. (2008)

obtained a global wind work total o

0.35 W, but without mesoscale flows.Tough they obtained good agreement

with some observational estimates o

inertial energy in the mixed layer, they

concluded that most NIW energy dis-

sipates in the upper 150 m o the ocean.

On the other hand, data rom the Ocean

Storms Experiment (DAsaro, 1995;

Levine and Zervakis, 1995) and historical

moored current meters (Alord, 2003a)

suggest that a substantial portion o NIW

energy is radiated ar rom generation

regions in ast-moving, low-mode waves.

Additionally, observations show energetic

NIWs at all depths (Silverthorne and

oole, 2006; Alord, 2010), with a greater

percentage penetrating to depth (Alord

et al., in press) than concluded by theFuruichi study. One possibility or these

discrepancies is that mesoscale flows can

affect generation (Weller, 1982), reract

the waves once generated (Kunze, 1986),

and ampliy deep propagation (Lee and

Niiler, 1998; Zhai et al., 2005).

Our study, unlike the Furuichi

simulation, includes mesoscale eddies

(Figure 1). It is intended to shed some

light on these puzzles, and illustrate the

rela

tivevo

rticity

relat

ivevorticity

east

wes

tsurfacecu

rre

nt

vertical velocity

A B

C D

vert

icalve

locityat

750m40

30

20

10

0

10

20

30

40

50

40

30

20

10

0

10

Latitude

2007 Yearday

Metersperday

5 10 15 25 3020

Figure 1. (A) Relative vorticity of sea surface currents, scaled by the Coriolis frequency at 30N. Colormap

saturates at 0.1. (B) Snapshot of east-west sea surface currents. Colormap saturates at 25 cm s1.

(C) Vertical velocity at 750 m depth. Colormap saturates at 40 m per day. (D) ime-latitude plot of verti-

cal velocity at 750 m depth along the meridian indicated in (C). Te data visualized in panels BD have

not been filtered or band passed in any way.

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long-range-propagation aspects o the

wave field in a ully eddying ocean. We

find that rom 3% to 16% o the energy

radiates away in our model, depending

on the season and the storm strength.

Tough the exact percentage is likely

sensitive to details o the model andrequires urther study, we ocus on the

spatial structure o the radiated portion

here to learn more about these long-

propagating waves. Because we obtain

many o the same results as the Furuichi

study, the implication is that mesoscale

flows affect the long-propagating waves

only a little. However, they do likely

affect the radiated versus local portion o

the NIW wake o individual storms.

Wind Generation of

Near-Inertial Waves

Te first part o NIW generation, the

initial input o energy into the mixed

layer by resonant orcing, is the best

understood. Observed mixed-layer

velocities quickly grow as great as 1 m s1

(greater in hurricanes and typhoons).

A slab model by Pollard and Millard

(1970) generally reproduces the ini-

tial amplitude and phase o observed

mixed-layer oscillations. Te skill o the

slab model enables construction o theaorementioned global maps o wind

work, using only reanalysis wind prod-

ucts such as those rom the National

Centers or Environmental Prediction

(NCEP) and mixed-layer depth cli-

matology. Note that recent work using

high-resolution moored observations

(Plueddemann and Farrar, 2006) pointed

out that neglect o mixed-layer deepen-

ing by slab models likely causes theseestimates to be high, although the degree

o overestimation is uncertain and likely

varies rom place to place (om Farrar,

Woods Hole Oceanographic Institution,

pers. comm., 2012). Slab models predict

strong inputs in the western portion o

each basin at mid-latitudes, confirming

that mid-latitude storms provide the

bulk o the energy flux (with much o the

remainder rom hurricanes/typhoons).

Te general distribution o energy flux in

our model (Figure 2, gray scale) resem-

bles the observed near-inertial energy

in the mixed layer rom previous slab-model estimates and the observed dis-

tribution rom drifers (Chaigneau et al.,

2008), but the global total o 0.4 W, as

we will show, is on the low side o the

range o estimates.

Excitation of Interior Motions

Once near-inertial motions in the mixed

layer are generated, lateral variation leads

to convergences and divergences thatpump vertical motions at the base o

the mixed layer, driving motions in the

ocean interior (Figure 3). Anderson and

Gill (1979) and Gill (1985) developed

a modal ormalism or describing this

excitation o submixed-layer motions.

Much like the vibration o a guitar string,

waves in the stratified ocean take the

orm o standing vertical oscillations o

horizontal currents (with corresponding

vertical displacements o isopycnals),

which are termed the dynamic modes.

Te lowest mode, or, by analogy, har-

monic, o horizontal velocity cor-

responds to horizontal ocean currents

that are uniorm rom top to bottom.

Tis mode is commonly reerred to as

the barotropic mode or zeroth mode

60E 120E 180 120W 60W 0

60S

30S

0

30N

60N

1 kW/m

Wind Work (log10 mW/m2)1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0

J F M A M J J A S O N D0

0.1

0.2

0.3

0.4 Total

Northern

Southern

WindWork(x1012W

)

Figure 2. Model depth-integrated annual mean baroclinic energy flux (green arrows) and

mooring-derived total near-inertial fluxes of Alford (2003b) (red arrows) over annual mean wind

energy flux to near-inertial motions (gray scale). A 1 kW m1reference arrow is drawn over Africa.

Te model fluxes are smoothed over 3 3, and every 24thgridpoint is plotted. Te observed

fluxes have been averaged together over bins when multiple moorings occur in a bin. Te inset

over Asia shows the wind work integrated over the global ocean (indicated as otal) and inte-

grated over each hemisphere (northern and southern).

Harper L. Simmons(hlsimmons@alaska.

edu) is Associate Professor of Marine

Science, School of Fisheries and Ocean

Sciences, University of Alaska Fairbanks,

Fairbanks, AK, USA. Matthew H. Alfordis

Principal Oceanographer, Applied Physics

Laboratory, and Associate Professor,

School of Oceanography, University of

Washington, Seattle, WA, USA.
http://www.ncep.noaa.gov/http://www.ncep.noaa.gov/mailto:[email protected]:[email protected]:[email protected]:[email protected]://www.ncep.noaa.gov/http://www.ncep.noaa.gov/

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and is not an internal gravity wave. Te

first baroclinic or depth-dependent

mode, indicated schematically in gray

in Figure 3, is an internal gravity wave

that takes the orm o an oscillation,

with flow going in one direction at the

surace and in the opposite direction atdepth, and with a node at the depth

o the thermocline. Higher modes have

higher numbers o nodes and hence a

more complicated vertical structure.

An important eature o internal grav-

ity waves is that the horizontal rate o

propagation, or the phase speed, asso-

ciated with each given baroclinic mode

decreases with increasing mode number.

For typical ocean depths and stratifica-tion, the first baroclinic mode travels at

about 3 m s1and the second at 1.5 m s1

zeroth mode. Te expected vertical

structure o the modes can be computed

rom stratification alone, and profiles can

be described by fitting the velocity pro-

file to a linear combination o the modes.

o compute the ocean interior

response, the slab velocity profile

(motion in the mixed layer and none

below) is projected onto the modes

computed or pre-storm stratification.

As the modes propagate away, energy

travels downward into the ocean inte-

rior, with the details controlled by the

phasing between the various modes (see

Figure 3). Far rom the storm site, suc-

cessive modes will arrive in the order o

their phase speed so that we can expect

to see the first mode arrive first, ollowed

by the second, and so orth.

Te initial puzzle o Gills work was

how energy evolved rom the large

lateral scales o the orcing to smaller

scales, which transer energy more

rapidly. Te initial atmospheric orcing

o the mixed layer tends to occur over

hundreds o kilometers, the typical scale

o mid-latitude storms. Internal waves

that are imprinted with these horizon-

tal scales propagate downward into the

ocean very slowly (one-year timescales),

as group velocity is inversely propor-

tional to wavelength. Several processes

act to decrease the scales o mixed-layermotion coherence, allowing generation

o waves with shorter horizontal wave-

lengths that can propagate downward

into the stratified interior. Te domi-

nant process is the variation o inertial

requency with latitude, the so-called

beta effect (DAsaro, 1989). Mixed-layer

motions at different latitudes oscil-

late at slightly different requencies,

so in the days ollowing a storm pas-sage, the meridional scale o coherence

steadily shrinks to less than 100 km.

In the groundbreaking Ocean Storms

Experiment, DAsaro (1995) validated

this dynamical explanation. In particular,

the role o the beta effect in leading to

the initial growth o horizontal gradients

was clearly demonstrated, leading to a

qualitative agreement with the theory

or low modes. However, Gills ormal-

ism could not reproduce an observed

beam, wherein energy migrated down-

ward in time away rom the mixed layer

ollowing storm events (see Figure 5or recent evidence o downward-

propagating energy).

While the beta effect is the most

important process in generating the

smaller scales that can propagate, the

variability in the ocean response or

similar wind events at station Papa in

the North Pacific (50N, 145W; Alord

et al., in press) clearly implicates a role

or other processes. Weller (1982) sug-gested that mesoscale eddies modiy

the near-inertial response in the mixed

layer. Recent theoretical and numerical

work has given still more credibility to

the notion. Te vorticity associated with

energetic eddies can create an effective

inertial requency (the combination o

(z)

Low modepropagation

Highmoderadiation

Upward ???

Topographicscattering

characteristicalong

Mixed layerNear-fresponse

Coriolis (f)

large

Coriolis (f)small

South

North

Figure 3. Processes associated with near-inertial generation, dissipation, and propagation. As storms

move along the storm track, a local response occurs with frequencies near the local Coriolis frequency.

Both high- and low-mode internal gravity waves are excited. High modes propagate along curving char-

acteristics downward and equatorward. Te higher modes have strong shear that results in mixing ().

Low-mode wave radiation, indicated in gray, takes the form of oscillations that propagate equatorward.

Upward characteristics and topographic scattering have been observed, but the processes involved are

not completely understood.

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relative and planetary vorticity; Kunze,

1985). Hence, in addition to imprint-

ing mesoscales and submesoscales on

NIWs (effectively reducing their wave-

lengths and increasing their propagation

speeds), anticyclonic eddies can create

regions known as inertial chimneyswherein a locally lowered effective iner-

tial requency allows rapid deep propa-

gation. First proposed by Lee and Niiler

(1998), inertial chimneys are also seen in

numerical models (Zhai et al., 2005).

Local Dissipation vs.

Long-Range Propagation

NIW evolution depends on vertical and

horizontal wavelengths imparted ontointerior motions by storms. Te initial

orcing excites all vertical modes in a

red spectrum, with most energy going

to the lowest modes. Horizontal scales

are set through a combination o storm

size and storm translation speed, plus the

mesoscale vorticity field. Fundamental

to understanding the energy cascade is

determining the relative importance o

(1) low-mode motions, which contain

appreciable energy but quickly propagate

away laterally, and (2) higher modes

that remain in the orcing region owing

to their slow vertical and meridional

group velocities, and contain much o

the vertical shear in the ocean. Te dis-

tribution o the dissipation rom a storm

thus depends on the relative raction o

energy in each mode. Depending on the

stratification, 30% or more o the energy

may be contained in vertical modes one

and two (DAsaro, 1995; Alord, 2010;

Alord et al., in press). Tese low-mode

disturbances propagate horizontally

out o the generation region and may

break as a result o topographic scatter-

ing, as do internal tides (Mller and Liu,

2000; Johnston and Merrifield, 2003), or

nonlinear transers within the internal

wave field. Te remainder o the energy

is in higher wavenumber waves that have

slow group velocities and greater shear,

and are thereore likely to break rela-

tively locally. Te ormer are the ocus

o our study, in large part because ournumerical model only resolves the first

ew vertical modes.

Blue Shift of the Ocean

Current Spectrum Near the

Inertial Frequency

Near-inertial waves are special or a ew

reasons (Garrett, 2001), most notably or

our purposes because o their nearness

to the lower end o the range o possiblerequencies or propagating internal

gravity waves, which can only exist

betweenf(the local Coriolis requency)

and N(the buoyancy requency). For

this reason, near-inertial waves can only

propagate slightly toward the pole on a

beta plane, because they quickly reach a

latitude where their requency is equal to

the local value of, which is higher than

their generation latitude, and then turn

they toward the equator. Alord (2003b)

first observationally demonstrated this

tendency to propagate toward the equa-

tor. Note that this view contrasts with the

original explanation o the near-inertial

peak by Fu (1980) in terms o higher-

requency waves propagatingpoleward.

As a group o NIWs propagates down

rom the surace and toward the equa-

tor, it maintains the requency associated

with its generation latitude, which will

exceed the local value of. Tis phe-

nomenon is commonly reerred to as a

blue shif, but it really arises rom the

reduction ofwith latitude rather than

an increase in the wave requency. Te

terms red and blue reer to relatively

lower and higher requencies, analogous

to the relative requencies o red and blue

visible light. Te consequence is that at

any given latitude and depth, the internal

gravity wave spectrum (as measured by,

or instance, horizontal velocity) will

have a locally generated peak nearfplus

a higher-requency (bluer) contribu-tion by waves that originated shallower

than and poleward o the given loca-

tion wherefwas higher. Te blue shif

can be quantified by a ratio o the local

Coriolis requencyfto the near-inertial

peak so that anfpeak /flocallarger than one

represents a blue shif and, conversely,

a ratio smaller than one reveals a red

shif. A blue shif o the near-inertial

peak has been reported throughout theworld ocean (e.g., Fu, 1981; DAsaro

and Perkins, 1984).

MODEL DESCRIPION

For this study, we used the Generalized

Ocean Layer Dynamics (GOLD) model,

an isopycnal-coordinate ocean model

developed at the National Oceanic

and Atmospheric Administration

Geophysical Fluid Dynamics Laboratory.

It is an evolution o the Hallberg

Isopycnal Coordinate Model (HIM;

Hallberg, 1997). Previously, HIM has

been used to study global surace tides

(Arbic et al., 2004) and baroclinic

tides (Simmons et al., 2004a, 2011;

Simmons, 2008).

opography data were taken rom

the thirtieth-degree resolution EOPO2

dataset (National Geophysical Data

Center), bicubically interpolated to the

target model grid resolution. Horizontal

resolution is nominally one-eighth

degree globally with resolution scaling

rom approximately 1414 km at the

equator to 77 km at 60N (quasi-

Mercator), transitioning to a quasi-

regular bipolar grid (Murray, 1996)

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poleward o 60N where the resolution

remains a nearly constant 7 7 km.

Isopycnal viscosity was set by

two additive schemes. Te first is a

biharmonic scheme whereby a fixed

parameter that has units o velocity set

to 0.05 m s1is multiplied by the thirdpower o the grid resolution. Te sec-

ond scheme is a Smagorinsky nonlinear

eddy viscosity computed by multiplying

a fixed parameter with units o velocity

set to 0.001 m s1times the grid spacing.

Te model time stepping uses a mode-

splitting scheme with a time step o

360 seconds and 7.5 seconds or the baro-

clinic and barotropic modes, respectively.

Te nondimensional quadratic bottomdrag coefficient is 0.003. Diapycnal mix-

ing was calculated using the shear-driven

entrainment scheme o Jackson et al.

(2008). Te mixed layer is modeled using

a refined bulk mixed layer (Hallberg,

2003) extension to the traditional Krauss-

urner scheme employed in most isopyc-

nal coordinate models.

Te model was orced with wind

stress and buoyancy fluxes obtained

rom a modified version o the annual

repeating Common Ocean-ice Reerence

Experiments (CORE) atmospheric

orcing data (Griffies et al., 2009).

urbulent fluxes are calculated with

a Monin-Obhukov boundary layer

scheme (Griffies et al., 2009) using the

atmospheric state and the evolving

model ocean. Te CORE atmospheric

data have six-hourly variability or most

atmospheric fields, obtained rom the

NCEP analysis. It repeats annually, with

numerous corrections to address known

biases and to balance the fluxes when

integrated over the global ocean and over

a year. Notably, our orcing differs rom

the CORE scheme described by Griffies

et al. (2009) in one important regard:

atmospheric orcing is computed rom

the CORE fields (e.g., relative humidity,

radiative fluxes, and surace air tem-

perature) except that 10 m winds rom

the 2007 NOGAPS (Navy Operational

Global Atmospheric Prediction System)

data (Rosmond et al., 2002) at one-hal

degree spatial resolution and threehourly temporal resolution are used

instead o the CORE winds.

Te ocean was spun up or five years.

Beginning January 1 o the sixth year,

an intensive data archiving period was

initiated, with the ull global three-

dimensional model velocity and isopyc-

nal depth fields stored every two hours

or a year. We regard the high-requency

component o the solution as a hindcast

o actual wave events rom 2007 excited

by the NOGAPS winds, acknowledging

that NIWs are influenced by mesoscale

eddies, which are not expected to be rep-

resentative o 2007 in detail.

DAA DESCRIPI ON

Model output is compared to two types

o observational dataa shipboard

transect o shear in the North Pacific,

and a global dataset o about 80 moor-

ings. Tese datasets emphasize the

high- and low-mode portions o the

near-inertial signals, respectively. Te

shipboard transect was collected with

the Hydrographic Doppler Sonar System

installed on R/V Roger Revelle(recent

work o Andy Pickering, author Alord,

and colleagues). Because the transects

took one to three inertial periods to

conduct, a technique known as inertial

back rotation was used to reerence

observations to an arbitrary common

time by assuming that currents rotate at

the inertial period. Te moorings, which

were originally collected by a vast vari-ety o investigators over 30 years, were

selected by Alord (2003b) because they

offered sufficient resolution in the verti-

cal to estimate energy and energy flux.

Near-inertial motions were isolated via

band-pass filtering.

RESULS

As is typical or a model o this resolu-

tion, energetic mesoscale circulation

develops along with large-scale general

circulation. A three-day-average view

o sea surace vorticity rom the model

reveals many well-known eatures o

ocean circulation: western boundary cur-

rents, a strong equatorial countercurrent

system perturbed by tropical instability

waves, and mesoscale vorticity through-

out the world ocean (Figure 1A). I we

look at instantaneous snapshots o ocean

currents (Figure 1B), there are a great

many transient velocity fluctuations that

correspond to surace wind stress, most

clearly under the storm tracks, as well

as high-requency oscillations that are

NIWs (see below). Te NIWs that are

the subject o this paper are the zonally

banded eatures evident in Figure 1AC.

AS IS YPICAL FOR A MODEL OF HIS RESOLUIONENERGEIC MESOSCALE CIRCULAION DEVELOPS ALONGWIH LARGESCALE GENERAL CIRCULAION.

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he Basin-Scale Wake of

Near-Inertial Waves

Much as the splash rom a rock thrown

into a pond will organize itsel into a

wave train emanating rom a region o

disturbance, the initial orcing o NIWs

under the storm track is transormedinto a wave train radiating equator-

ward. Looking deeper in the ocean

(Figure 1C, vertical velocity at 750 m

depth) eliminates much o the conu-

sion o the upper ocean, which is subject

to direct orcing by the atmosphere. An

alternate view is revealed by plotting

the vertical velocity versus latitude and

time (Figure 1D) along the slice shown

in Figure 1C. Later, we present a spectralanalysis o the signals, confirming their

near-inertial properties.

Banded ronts o NIWs with near-

zonal transbasin coherence are somewhat

evident in the instantaneous surace

currents shown in Figure 1B, but they

are revealed much more clearly in

Figure 1C,D. Te latitude-time slice in

Figure 1D shows that these waves travel

thousands o kilometers, apparently with-

out disruption by the lower-requency

flows. For example, around yearday 17,

a wave train originating at 40N crossesthrough the equator into the Southern

Hemisphere. It should be noted that

these structures are also evident in the

deep vertical velocity response in the

simulations o Furiuchi et al. (2008,

their Figure 2), and in Komori et al.

(2008, their Figure 1). A shadow in

the lee o the Hawaiian Islands is evi-

dent (Figure 4). Komori et al. (2008)

also noted the shadowing behind theHawaiian Islands. It should be stressed

that Figure 1C,D has not been filtered

or band passed in any way. Te domi-

nance o the near-inertial velocity signal

emphasizes the act that inertial motions

have most o the oceans energy.

Modal Wake

A high-pass filter suppresses much o the

general circulation because its character-

istic timescale is days to months, and it

urther emphasizes near-inertial fluctua-

tions. Te pattern o NIWs is not partic-

ularly sensitive to the choice o filter, butwe choose one that passes requencies

higher than 1/72 hours using a sixth-

order Butterworth filter, and retains iner-

tial signals or all latitudes poleward o

10 o latitude. We fit the models high-

passed velocity fields to the dynamical

normal modes, calculated by the method

o Lighthill (1969). We only examine

the first three normal modes because

higher vertical modes have smallermeridional wavelengths and, hence,

would not be adequately resolved by the

models horizontal grid. Spatial maps o

the surace velocity signature associated

with the three modes are plotted in the

lef panels o Figure 4, and time-latitude

plots along the indicated meridian are

shown on the right. Radiation can be

seen or each mode propagating toward

the equator, with the slope in latitude-

time o the eatures corresponding to the

expected speed or each mode and with

north-south wavelengths that decrease

with increasing mode number. Te

ronts become increasingly zonal with

increasing mode.

Vertical Structure

A qualitative measure o the models

ability to resolve the signals is seen

by comparing the simulated verti-

cal shear o horizontal velocity along

a line north o Hawaii (upper panel,

Figure 5) with observations (lower

panel) rom the transect collected by

A. Pickering, author Alord, and col-

leagues on R/V Roger Revellemen-

tioned earlier. Propagation is along

1

15N

30N

45N

15N

30N

45N

15N

30N

45N

2

3

120E 150E 180 150W 120W

1

0.2

0

0.2

2

0.05

0

0.05

3

Days5 10 15 20

ms

1

ms

1

ms

1

0.01

0

0.01

Figure 4. Left panels: Snapshots of the basin-scale wave wake for baroclinic modes 13, as

indicated by the east-west surface currents associated with each mode. Te number in the

upper right of each panel indicates mode number. Right panels: latitude-time plot along the

meridian indicated in the left panels.

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characteristics (lines o characteristic

slope), consistent with a requency

somewhat abovef. Tough collected in

a different year, the general tendency to

propagate downward and equatorward

is seen in both model and observations.

However, the observed shear is muchgreater, highlighting the models limited

ability to resolve the higher modes. A

characteristic is drawn or a requency

(i.e., a 3% blue shif; Garrett, 2001).

Latitudinal Propagation and

Conservation of Frequency:

Blue Shifting

We examine the requency response

o the model in several ways. We com-pute horizontal velocity spectra every

hal-degree in latitude and every 2 in

longitude, and average at each latitude

to produce maps o spectral power as a

unction o requency and latitude or

the North Pacific. Te resulting spectra

o the modal, surace, and deep currents

(Figure 6) reveal strong inertial peaks.

As internal waves propagate equator-

ward, they preserve their requencies,

which smear the spectra equatorward,

as shown in the first three panels o

Figure 6. Te ourth panel shows the

effect o this painting o requency

equatorward: the inertial peaks, which

are combinations o local inertial

response and contamination rom sig-

nals that originated at higher latitudes

wherefis larger, has been blue-shifed tohigher requency. In the example given

here, the shif is between 5 and 10% at

35N or modes 14. Te spectrum o

the surace currents (green line) is nar-

rower and less shifed, suggesting that

the ull sea surace current response is

less contaminated by the long-range

swell o NIWs arriving rom higherlatitudes. Conversely, the deep currents

10*Model = 1.03f

0

200

400

600

800

Observations

Latitude

28.0 28.5 29.0 29.5 30.0 30.5 31.0

200

400

600

800

1000

S/s1

0.005

0.005

Depth(m)

Depth(m)

Figure 5. (top) Model shear in a section north of Hawaii. (bottom) R/V Roger Revellesonar

shear along the same section, inertially back rotated.

CW mode 1

log10

cph

Latitude

2.0 1.5 1.0

log10

cph

2.0 1.5 1.0

log10

cph log10

cph

2.0 1.5 1.0

10

20

30

40

50

60CW mode 2 CW mode 3

1.4 1.3 1.2

3

2

1

0.9f f 1.1f

log10

nondimensionalspectralpower

mode 1mode 2mode 3mode 4surfacedeep

Figure 6. First three panels: spectral energy of modally analyzed clockwise currents (logarithmic color scale, arbitrary units) as a function of latitude and

frequency for modes 13. White dots in the first three panels indicate the Coriolis (inertial) frequency at each latitude. Te rightmost panel shows the

near-inertial spectral power at 35N (scaled to have a peak magnitude of 1 for each spectrum). All spectra are averages of spectra along meridians sepa-

rated by 2 in the North Pacific.

7/24/2019 25 2 Simmons

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experience a stronger blue shif.

Te blue shifs o the ull model cur-

rents were computed over a range o

depths and latitudes in the North Pacific

and also compared to mooring esti-

mates o the blue shif (Figure 7). We

see that the model and moorings havecomparable blue shifs with latitude

and depth rom 2560 latitude, with a

small tendency or a weak red shif in the

upper ocean. Te model shows a very

strong blue shif equatorward o 25,

but, unortunately, there are so ew reli-

able estimates rom observations that no

comparison can be made.

EnergeticsDepth-Integrated Baroclinic

Energy Flux

Energy flux was computed rom the

high-pass-filtered density and baroclinic

velocity fields (Althaus et al., 2003;

Simmons et al., 2004a). In the annual

mean, NIWs propagate equatorward

rom Northern Hemisphere storm

tracks, directed to the southeast, as

shown in Figure 2. We have overlain

the total mooring fluxes rom Alord

(2003a). It should be noted that the

comparison is imperect because the

model computed fluxes are averages

rom a simulation using 2007 winds,

whereas Alords estimates are a synthesis

o different mooring deployments over

many different years. Particularly in theNorth Pacific, the magnitude and direc-

tion o the model and mooring-derived

estimates o the low-mode flux are in

agreement. In the Southern Hemisphere,

the model energy flux is equatorward

across 30S in the Indian, South Pacific,

and South Atlantic Oceans. Within

the storm track (nominally the band

o enhanced wind work between 30S

and 60S), the energy propagates to thewest, in the opposite direction to the

weather systems. Te westward fluxes

in the Southern Ocean have not been

previously noted.

Wind Work on Near-Inertial Motions

Wind work on near-inertial motions is

calculated as the vector product o the

wind stress and the band-passed surace

current ( .uI

). Te spatial distribution

o the annual mean wind work closely

ollows the storm tracks that run along

the northwest margins o the North

Pacific and North Atlantic Ocean basins

and along the roaring 40s (i.e., 40S)

in the southern oceans (gray scale in

Figure 2). Te global averaged wind

work is 0.36 W (inset in Figure 2),ranging rom 0.25 W in boreal summer

(June and July) to 0.40 W in November,

a variation o 60%. Surprisingly, this

cycle occurs with roughly the same phase

in both hemispheres. Te Southern

Hemisphere is relatively uniorm (varia-

tion o 50%, annual mean o 0.22 W)

and is a actor o two stronger than in

the Northern Hemisphere in all seasons.

Te Northern Hemisphere varies rom0.06 to 0.18 W over the year (varia-

tion o 300%). Te low-mode signal

takes roughly 20 days to propagate rom

40N to the equator, a distance o over

4,000 km (2.6 m s1, Figure 1D).

Ratio of Energy Input to Radiation

Te average monthly wind work rom

30N to the pole ranges rom 35 GW

(July) to 150 GW (December). Te

net southward flux across 30N ranges

0.95 1.00 1.05 1.10

0

1000

2000

3000

4000

5000

6000

Depth(m

)

Blue shift

1.030 1.033

a

b

c

10 15 20 25 30 35 40 45 50 55 60

0

1000

2000

3000

4000

5000

6000

Abs (latitude)

Dept

m

Dept

m

0

1000

2000

3000

4000

5000

6000

fpeak

/ flocal

0.85 0.90 0.95 1.00 1.05 1.10

obs. (2560)

model (2560)

Figure 7. (a) Simulated

blue shift as a func-

tion of depth and

latitude. (b) Blue shift

from mooring analysis

by Alford (2003a).

(c) Profile of modeled

and observed blue shiftwith depth (panels a

and b), averaged from

25 to 60 latitude.

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rom 1 kW m1(July) to 16 kW m1

(December). Te area integrated energy

input south o 30S is 150 GW in

December (austral summer) and

230 GW in July (austral winter). Te

equatorward energy flux across 30S

ranges rom 4 GW (December, australsummer) to 20 GW (July, austral win-

ter). Tus, the ratio o the flux leaving

the equatorward end o the box to the

input ranges rom 2% to 16% in the

Northern Hemisphere and 2% to 13% in

the Southern Hemisphere. Te average

annual mean ratio or both hemispheres

is 7% (see Furiuchi et al., 2008), but an

annual average is somewhat misleading

because the ratio seems to scale withthe wind input and does not represent

a response to a specific storm. One pos-

sible explanation or the range o values

is that wintertime storms work on a

deeper mixed layer and thus avor the

generation o aster and less-dissipative

low modes. It should be stressed that the

amount o NIW energy lost rom the

model in the generation region will be

sensitive to the representation o vertical

viscous stresses at the base o the mixed

layer, to mixed-layer deepening, and to

model parameterization o horizontal

viscous stresses, so that the absolute ratio

o input to output is perhaps uncertain

and o less importance to this study than

the global patterns o flux.

SUMMARY AND DISCUSSION

We have presented some aspects

o near-inertial wave physics in an

eddy-resolving general circulation

model (GCM) and made comparisons

with moored estimates o peak shif

(2,200 estimates at various depths and

latitudes), moored estimates o energy

flux (80 moorings, mode-1 and -2), and

shipboard section(s). Te model predicts

that 0.36 W o energy is transerred to

near-inertial motions, which is on the

low end o other estimates. Tis energy

input occurs principally under storm

tracks and has significant hemispheric

and annual variability (Figure 2). Te

ratio o the spatially integrated windwork over an area to the wave radia-

tion leaving the region is a measure

o the amount o wind work that goes

into stable, radiating low-mode internal

waves, in other words, a measure o the

raction o the energy that dissipates

large distances rom the storm track. Te

general pattern is or the waves to radiate

equatorward (southeast in the Northern

Hemisphere). Tere is a markedanisotropy between wavenumber k(east-

west) and l(north-south), with l >> k.

We find a mode-1 wavelength o about

500600 km and a mode-3 wavelength o

about 200300 km. Te east-west wave-

length approaches basin scale. Westward

propagation in the Southern Ocean has

not been noted previously.

Equatorward fluxes range rom 3% to

16% o the energy input. Tis range o

values varies with season and may reflect

changes in seasonal mixed-layer depth

between July and December. Note that

the modeled fluxes are usually about

1020% weaker than Alord (2003a) and

the modeled wind work or the North

Pacific is 1020% higher than Alord

(2003a). Tese two competing differ-

ences conspire to reduce the overall esti-

mate o the percent o radiating energy

(i.e., their ratio). Note, however, that pre-

vious experience with idealized GOLD

suggests the simulated ratio can vary by

as much as a actor o two, with sensitiv-

ity to model resolution and treatment

o parameterized viscosity. Future work

should examine the role o the mesoscale

flows and other actors in determining

this raction on an event-by-event basis.

Horizontal energy fluxes (Figure 2)

agree well with mooring estimates.

Looking at depth-latitude sections,

energy propagates downward along

characteristics (Figure 5). When com-

pared to observed sections, slopes arequalitatively similar, but modeled wave-

numbers are substantially lower, and ver-

tical shear is 10 times weaker. Modeled

and observed blue shif (Figure 6 and 7)

increases rom somewhat less than unity

at high latitudes and near the surace

to 1.3 at depth and near the equator

(30% blue shif). Tis view o the ocean

corroborates the Garrett (2001) view,

but we find that blue shifing requentlyexceeds that predicted by Garrett (2001).

Te net effect is that the inertial peak

becomes increasingly broad and blue

shifed equatorward o the storm tracks.

We note the absence o reliable observa-

tional estimates at latitudes equatorward

o 25 precludes any definitive conclu-

sion about blue shif at low latitudes.

Te act that NIW groups can radiate

rom subpolar latitudes across the equa-

tor (Figure 1D) suggests that in the mid-

basins (away rom western boundary

currents), NIW groups are able to pass

relatively unscathed through a mesoscale

eddy field (Figure 1A). Tis phenom-

enon is likely only true or the lower

modes. Higher modes have smaller

spatial scales and slower phase speeds

and are expected to be more sensitive

to reraction by mesoscale eddies. We

caution that large-scale ocean models

are limited in their ability to resolve the

high modes, and, thereore, uture effort

should be directed toward refining our

understanding o the radiative versus

dissipative partitioning o the energy in

near-inertial oceanic motions.

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Consequences for Mixing

and Climate

GCMs show sensitivity to the mag-

nitude and vertical and horizontal

distribution o mixing (e.g., Simmons

et al., 2004b; Jayne, 2009). Te global

total near-inertial input o 0.36 W iscomparable to the 1 W o power con-

verted rom barotropic to baroclinic

tides (Egbert and Ray, 2000), and a

substantial raction o the 2 W needed

to maintain deep ocean stratification

(Munk and Wunsch, 1998; Wunsch and

Ferrari, 2004). Consequently, inclusion

o near-inertial wave supported mix-

ing in GCMs is expected to have an

effect on climate simulations (this hasalready been demonstrated in prelimi-

nary simulations by Markus Jochum,

National Center or Atmospheric

Research,pers. comm., 2012). We cau-

tion, however, that in spite o the basic

fidelity o slab models or predicting

currents, misrepresentation o mix-

ing at the mixed-layer base can lead to

uncertainties and biases in the work

predicted (Plueddemann and Farrar,

2006). Te difference between observed

and slab-model work underscores

that while we understand the basics o

mixed-layer generation, conounding

actors such as mixing in transition lay-

ers, mesoscale currents, and remotely

incident waves may play important roles

and, thereore, need to be understood

better. Parameterizations o the radia-

tive raction o internal gravity waves

are just beginning to be explored and

constitute the authors contribution to

the Internal Waves and Mixing Climate

Process eam (CP; unded by the

National Science Foundation, Jennier

MacKinnon, Scripps Institution o

Oceanography, PI).

ACKNOWLEDGMENS

Harper Simmons was supported by

ONR grant N00014-09-1-0399 and NSF

(CP) grant OCE-0968838. Matthew

Alord was supported by ONR grant

N00014-09-1-0401 and NSF (CP)

grant OCE0968131. Discussions withEric DAsaro, Jonathan Nash, and

Jennier MacKinnon, some o which led

to a version o Figure 3, are grateully

acknowledged. Tis work could not have

been accomplished without the assis-

tance o Robert Hallberg and Alistair

Adcrof o NOAAs Geophysical Fluid

Dynamics Laboratory.

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