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Miller, AJ, Neilson DJ, Luther DS, Hendershott MC, Cornuelle BD, Worcester PF, Dzieciuch MA, Dushaw BD, Howe BM, Levin JC, Arango HG, Haidvogel DB.  2007.  Barotropic Rossby wave radiation from a model Gulf Stream. Geophysical Research Letters. 34   10.1029/2007gl031937   AbstractWebsite

The barotropic Rossby wave field in the North Atlantic Ocean is studied in an eddy-resolving ocean model simulation. The meandering model Gulf Stream radiates barotropic Rossby waves southward through preferred corridors defined by topographic features. The smoother region between the Bermuda Rise and the mid-Atlantic Ridge is a particularly striking corridor of barotropic wave radiation in the 20-50 day period band. Barotropic Rossby waves are also preferentially excited at higher frequencies over the Bermuda Rise, suggesting resonant excitation of topographic Rossby normal modes. The prevalence of these radiated waves suggests that they may be an important energy sink for the equilibrium state of the Gulf Stream.

Lerczak, JA, Winant CD, Hendershott MC.  2003.  Observations of the semidiurnal internal tide on the southern California slope and shelf. Journal of Geophysical Research-Oceans. 108   10.1029/2001jc001128   AbstractWebsite

[1] We give a detailed description of the semidiurnal-band current and temperature variability observed during the Internal Waves on the Continental Margin (IWAVES) field experiments of 1996 and 1997 off of Mission Beach, California. This variability was dominated by the internal tide, and the structure of the internal tide on the slope and shelfbreak region was different from that on the narrow shelf. On the slope and shelfbreak, the internal tide was dominated by alongshore propagating coastal-trapped waves. In this region, semidiurnal-band currents were predominantly oriented in the alongshore direction. In the lower half of the water column at a water depth H of 350 m, current and temperature variability were consonant with a short wavelength (similar to8 km) bottom trapped wave propagating in the alongshore direction to the north. In the upper 120 m of the water column (above the depth of the shelfbreak), slope and shelfbreak currents were highly coherent with a zero phase lag; that is, there was no phase propagation in the cross-shore direction. On the narrow (similar to10 km) shelf, cross-shore currents u were much more energetic than on the slope and had the structure of a mode-one internal wave. The alongshore currents v decreased monotonically from the surface to the bottom of the water column with a phase that did not change with depth. The near-bottom u signal propagated toward the coast during all mooring deployments, faster in the summer than in the fall. The near-bottom u and mid-column temperature relative phase was neither consistent with a purely progressive nor a purely standing mode-one internal wave. We conclude that the internal tide on the shelf was partially reflected.

Winant, CD, Dever EP, Hendershott MC.  2003.  Characteristic patterns of shelf circulation at the boundary between central and southern California. Journal of Geophysical Research-Oceans. 108   10.1029/2001jc001302   AbstractWebsite

[1] The coastal circulation in the Santa Barbara Channel (SBC) and the southern central California shelf is described in terms of three characteristic flow patterns. The upwelling pattern consists of a prevailing equatorward flow at the surface and at 45 m depth, except in the area immediately adjacent to the mainland coast in the SBC where the prevailing cyclonic circulation is strong enough to reverse the equatorward tendency and the flow is toward the west. In the surface convergent pattern, north of Point Conception, the surface flow is equatorward while the flow at 45 m depth is poleward. East of Point Conception, along the mainland coast, the flow is westward at all depths and there results a convergence at the surface between Point Conception and Point Arguello, with offshore transport over a distance on the order of 100 km. Beneath the surface layer the direction of the flow is consistently poleward. The relaxation pattern is almost the reverse of the upwelling pattern, with the exception that in the SBC the cyclonic circulation is such that the flow north of the Channel Islands remains eastward, although weak. The upwelling pattern is more likely to occur in March and April, after the spring transition, when the winds first become upwelling favorable and while the surface pressure is uniform. The surface convergent pattern tends to occur in summer, when the wind is still strong and persistently upwelling favorable, and the alongshore variable upwelling has build up alongshore surface pressure gradients. The relaxation pattern occurs in late fall and early winter, after the end of the period of persistent upwelling favorable winds.

Lerczak, JA, Hendershott MC, Winant CD.  2001.  Observations and modeling of coastal internal waves driven by a diurnal sea breeze. Journal of Geophysical Research-Oceans. 106:19715-19729.   10.1029/2001jc000811   AbstractWebsite

During the Internal Waves on the Continental Margin (IWAVES) field experiments of 1996 and 1997 off of Mission Beach, California (32.75 degreesN), we observed energetic, diurnal-band motions across the entire study site in water depths ranging from 15 to 500 m and spanning a cross-shore distance of 15 kin. The spectral peak of the currents was at the diurnal frequency (sigma (Di) = 1 cpd) and was sufficiently well resolved to be clearly separated from the slightly higher local inertial frequency (f = 1.08 cpd). These motions were surface enhanced and clockwise circularly polarized and had an upward phase propagation speed of similar to 68 m d(-1), suggesting that the motions were driven predominantly by the diurnal sea breeze. However, the downward energy (upward phase) propagation seems irreconcilable with the subinertial diurnal period, and moreover, the intermittent diurnal current events were not obviously associated with diurnal sea breeze events. We rationalize these features using a flat-bottomed linear modal sum internal wave model that includes advection and refraction due to subtidal alongshore flow, V(x, t). Fluctuations in V at the observing site can change the "effective" local Coriolis parameter f + V-x by as much as 50%, thus making the diurnal motions at different times effectively either subinertial or superinertial. The model is integrated numerically for 200 days at a latitude of 32.75 degreesN under different wind and subtidal flow conditions: purely diurnal winds and no V, purely diurnal winds and a time-independent V, narrow-band diurnal winds and no V, and narrow-band diurnal winds and subtidal, time-dependent V. Model diurnal currents forced by narrow-band diurnal winds and subtidal V show complex offshore structure with realistic intermittency and spectral broadening. This study suggests that continental margins in the vicinity of the 30 degrees latitude (where sigma (Di) = f) are regions that could potentially produce energetic, sea breeze-driven baroclinic motions and that these motions could be regulated by the vorticity of the local subtidal currents.

Oey, LY, Wang DP, Hayward T, Winant C, Hendershott M.  2001.  "Upwelling" and "cyclonic" regimes of the near-surface circulation in the Santa Barbara Channel. Journal of Geophysical Research-Oceans. 106:9213-9222.   10.1029/1999jc000129   AbstractWebsite

The observed near-surface circulation in the Santa Barbara Channel indicates in particular two patterns: a dominant cyclonic circulation mode and a less frequent upwelling flow mode. To explain the dynamics that may govern these two flow regimes, momentum balance from a hindcast model of currents in the channel, forced by observed hourly winds and hydrographic data, was calculated. The along-channel balance was found to be between wind, which was eastward (i.e., equatorward), sea level tilt, which was westward (i.e., poleward), and Coriolis, which was westward if the wind was (1) intense west and east of the channel and was eastward if the wind was (2) weaker in the east. Wind condition 1 produced southward cross-channel flow in the midchannel, connected by eastward currents upstream (downstream) along the northern (southern) coast of the channel, while wind condition 2 produced northward cross-channel flow connected by cyclonic recirculation in the west and westward inflow in the east. It is suggested that the former corresponds to the dynamical balance that may occur in the upwelling flow mode, while the latter corresponds to the cyclonic circulation mode.

Winant, CD, Alden DJ, Dever EP, Edwards KA, Hendershott MC.  1999.  Near-surface trajectories off central and southern California. Journal of Geophysical Research-Oceans. 104:15713-15726.   10.1029/1999jc900083   AbstractWebsite

The near-surface circulation in the Santa Barbara Channel and off the coast of central and southern California is described based on 20 releases of drifters drogued 1 m beneath the surface from 12 sites within the channel at bimonthly intervals. This description includes small-scale features of the circulation which are not part of descriptions based on moored observations or of the statistics of the drifter releases. The eventual fate of drifters at long time intervals compared to the residence time in the channel (about 7 days) is also included. In the channel the trajectories document a persistent cyclonic circulation with a typical recirculation period between 3 and 5 days. In the spring, currents near the mainland are weaker than near the Channel Islands, and the overall flow is toward the southeast. Trajectories document the possibility for water parcels to leave the channel through the interisland passes. In the late fall and winter a poleward flow with velocities often exceeding 0.5 m s(-1) is confined within 20 km of the mainland. Between these two seasons the cyclonic tendency is enhanced, although most of the drifters eventually migrate westward. The trajectories of drifters released at the same time from sites only 20 km apart can be remarkably different. Once the drifters migrate out of the channel, their trajectories can be grouped into a few patterns. In spring and summer, drifters tend to remain in the Southern California Eight. Their trajectories often remain close over extended periods, as if they were caught in convergence zones. In fall the drifters often are caught in a poleward current.

Auad, G, Hendershott MC, Winant CD.  1999.  Mass and heat balances in the Santa Barbara Channel: estimation, description and forcing. Progress in Oceanography. 43:111-155.   10.1016/s0079-6611(99)00006-3   AbstractWebsite

Current meter, temperature and wind observations from the 1984 MMS experiment are used to estimate the mass and heat budgets in the Santa Barbara Channel. The mass transports estimated at the western, eastern and southern boundaries of the channel are characterized by fluctuations whose energy is concentrated around three different periods: 5, 14 and 2.8 days respectively. These three transports fluctuate along with the dominant EOF modes obtained at those 3 entrances respectively. The mean transport passing through the channel from east to west is about 0.28 Sv. There rue two frequency bands where winds and mass transports are coherent: 2.5-3.0 and 4.7-5.2 day bands. Winds on the northern shelf lead the transports in both bands by about 1.0 day. At the western half of the channel there is a recirculating (counterclockwise) mean transport of about 0.30 Sv. The time dependent part of the recirculating transport is coherent with the wind in the 4.7-5.2 day band where it also shows an absolute maximum of variance. nle recirculating transport lags the local downwelling-favorable winds by about 1.5 day and stems to be the channel response to wind relaxations with respect to its most persistent upwelling-favorable state. The main mean balance in the channel-integrated heat equation is between the heat transport passing through the western mouth, which cools off the channel, and the heat transport caused by the mass transport (the transport heat Bur), which warms: up the channel. This latter transport results from the advection of the temperature difference between the channel boundaries (mainly east and west) by the mass transport. There are no two terms that dominate the heat equation for the time dependent heat transports, but it can be simplified by balancing the along channel heat divergence (heat transport passing through the mouth plus transport heat flux), the vertical heat flux and the local change of heat. A clear thermal-wind balance at the eastern and western ends of the channel is found, in agreement with the work of Brink and Muench (1986) [Journal of Geophysical Research, 91, 877-895] and with the recent ADCP-CTD comparisons done by Richards (personal communication). All the terms in the heat equation show a variance peak in the 2-4 day band. It is found that when upwelling favorable winds blow on the northern shelf of the channel there is first a decrease or even a reversal, with respect to its mean, in the amplitude of thr transport heat flux. Next, a cooling of the Santa Barbara Channel is observed, followed by a loss of heat through the western mouth first and through the eastern mouth later, This whole process takes about 24 h to complete. (C) 1999 Elsevier Science Ltd, All rights reserved.

Dever, EP, Hendershott MC, Winant CD.  1998.  Statistical aspects of surface drifter observations of circulation in the Santa Barbara Channel. Journal of Geophysical Research-Oceans. 103:24781-24797.   10.1029/98jc02403   AbstractWebsite

Argos-tracked drifters are used to study the near-surface circulation in the Santa Barbara Channel. The mean consists of a cyclonic cell in the western Santa Barbara Channel with weaker flow in the eastern Channel. Drifter mean velocities agree well with record means from near-surface current meters. At the eastern entrance to the channel, drifter velocities are biased toward outflow (eastward velocity) conditions. Drifter variability at synoptic and seasonal scales shows a tendency for upwelling and eastward flow in spring, a strong cyclonic circulation in summer, poleward relaxation in fall, and weak, variable circulation in winter. Drifter estimates of eddy stress divergence indicate advective terms play a secondary role in the mean surface momentum balance. Lagrangian time and space scales are about 1 day and under 10 km, respectively. The mismatch between Lagrangian and Eulerian timescales indicates advective terms are important to the fluctuating circulation.

Auad, G, Hendershott MC, Winant CD.  1998.  Wind-induced currents and bottom-trapped waves in the Santa Barbara Channel. Journal of Physical Oceanography. 28:85-102.   10.1175/1520-0485(1998)028<0085:wicabt>;2   AbstractWebsite

The Santa Barbara Channel (SEC) is a coastal basin about 100 km long bounded by the Southern California mainland on the north and by a chain of islands on the south. The SEC is at most 50 km wide and just over 600 m deep. The nature of current and wind variance peaks in the 2-4-day and 4-6-day bands in the channel are analyzed from January to July 1984. For both bands the dominant empirical mode of the currents is highly coherent with the dominant empirical mode of the winds over this region. Surface intensification of currents is revealed by measurements made between 25 and 300 m. In contrast the deeper currents are characterized by bottom trapping. Evidence for baroclinic bottom-trapped topographic Rossby waves is found on the northern shelf at the western mouth of the channel in both frequency bands. At 30 m the distribution of phases shows currents at the center of the western mouth leading the southern interisland passes by about 0.3 day and the eastern mouth by about 0.6 day. In both bands co-and quadrature vectors of currents and winds describe this wind-current system in detail. It is speculated from spatial and temporal eigenfunctions of currents and winds and from available satellite images that the dominant current mode described above is a channelwide response to upwelling north of Point Conception (northwestward of the SEC). The upwelling-related currents cause a net inflow of mass into the western end of the channel, which is compensated by an outflow passing through both the interisland passes and through the eastern mouth of the channel. As a result of the narrowness and shallowness of the passes and of the shallowness of the southern shelf in general, high flow speeds are attained there that, the authors speculate, seem to force deep high-frequency motions both at the center of the SEC and at the northern half of its western mouth.

Auad, G, Hendershott MC.  1997.  The low-frequency transport in the Santa Barbara Channel: Description and forcing. Continental Shelf Research. 17:779-802.   10.1016/s0278-4343(96)00062-3   AbstractWebsite

Current meter, wind and adjusted sea level (ASL) data from January to July 1984 are used to (a) isolate the currents inside the channel that are associated with low-frequency (6-18 day band) transport fluctuations which dominate the record of the eastern mouth transport and (b) find the forcing mechanism(s) and its(their) dynamical role(s) in the low-frequency transport. The dominant mode of the currents is highly coherent with the eastern mouth transport in the 6-18 day band. About 62% of the total variance of the eastern mouth transport can be hindcast by both wind stress and remote adjusted sea level (ASL). The comparison of the amplitudes, and phases of the regression coefficients of a multiple regression analysis, to the amplitudes and phases expected from momentum conservation suggests that both the alongshore remote pressure gradient and the local wind stress forcing are balanced at the eastern mouth of the channel by the local acceleration of the transport there, The ASL data analysis suggests evidence of low mode coastally trapped wave propagation from San Quintin in Mexico to Port San Luis in central California. A quasi-linear phase vs longshore distance implies a propagation speed of about 70 km day(-1) (period of 13.6 days), which compares well with the theoretical value of 75 km day(-1) (period of 13.3 days) for the Southern California Eight. (C) 1997 Elsevier Science Ltd.

Cerovecki, I, Orlic M, Hendershott MC.  1997.  Adriatic seiche decay and energy loss to the Mediterranean. Deep-Sea Research Part I-Oceanographic Research Papers. 44:2007-2029.   10.1016/s0967-0637(97)00056-3   AbstractWebsite

A salient feature of sea level records from the Adriatic Sea is the frequent occurrence of energetic seiches of period about 21 h. Once excited by a sudden wind event, such seiches often persist for days. They lose energy either to friction within the Adriatic, or by radiation through Otranto Strait into the Mediterranean. The free decay time of the dominant (lowest mode) seiche was determined from envelopes of bandpassed sea level residuals from three locations (Bakar, Split and Dubrovnik) along the Croatian coast during twelve seiche episodes between 1963 and 1986 by taking into consideration only time intervals when the envelopes decreased exponentially in time, when the modelled effects of along-basin winds were smaller than the error of estimation of decay time from the envelopes and when across-basin winds were small. The free decay time thus obtained was 3.2+/-0.5 d. This value is consonant with the observed width of the spectral peak. The decay caused by both bottom friction and radiation was included in a one dimensional variable cross section shallow water model of the Adriatic. Bottom friction is parameterized by the coefficient k appearing in the linearized bottom stress term k rho(0)u (where u is the along-basin velocity and eo the fluid density). The coefficient k is constrained by values obtained from linearization of the quadratic bottom stress law using estimates of near bottom currents associated with the seiche, with wind driven currents, with tides and with wind waves. Radiation is parameterized by the coefficient a appearing in the open strait boundary condition zeta = auh/c (where zeta is sea level, h is depth and c is phase speed). This parameterization of radiation provides results comparable to allowing the Adriatic to radiate into an unbounded half plane ocean. Repeated runs of the model delineate the dependence of model free seiche decay time on k and a, and these plus the estimates of k allow estimation of a. The principle conclusions of this work are as follows. (1) Exponential decay of seiche amplitude with time does not necessarily guarantee that the observed decay is free of wind influence. (2) Winds blowing across the Adriatic may be of comparable importance to winds blowing along the Adriatic in influencing apparent decay of seiches; across-basin winds are probably coupled to the longitudinal seiche on account of the strong along-basin variability of across-basin winds forced by Croatian coastal orography. (3) The free decay time of the 21.2 h Adriatic seiche is 3.2+/-0.5 d. (4) A one dimensional shallow water model of the seiche damped by bottom stress represented by Godin's (1988) approximation to the quadratic bottom friction law rho(0)C(D)u\u\ using the commonly accepted drag coefficient C-D = 0.0015 and quantitative estimates of bottom currents associated with wind driven currents, tides and wind waves, as well as with the seiche itself with no radiation gives a damping time of 9.46 d; radiation sufficient to give the observed damping time must then account for 66% of the energy loss per period. But independent estimates of bottom friction for Adriatic wind driven currents and inertial oscillations, as well as comparisons between quadratic law bottom stress and directly measured bottom stress, all suggest that the quadratic law with C-D = 0.0015 substantially underestimates the bottom stress. Based on these studies, a more appropriate value of the drag coefficient is at least C-D = 0.003. In this case, bottom friction with no radiation leads to a damping time of 4.73 d; radiation sufficient to give the observed damping time then accounts for 32% of the energy loss per period. (C) 1998 Elsevier Science Ltd. All rights reserved.

Munchow, A, Coughran CS, Hendershott MC, Winant CD.  1995.  Performance and Calibration of an Acoustic Doppler Current Profiler Towed Below the Surface. Journal of Atmospheric and Oceanic Technology. 12:435-444.   10.1175/1520-0426(1995)012<0435:pacoaa>;2   AbstractWebsite

A towed acoustic Doppler current profiler (ADCP) system was tested. The instrument was deployed from ships of opportunity and towed at depths between 5 and 25 m. The towed system carries upward- and downward-looking ADCPs. The instrument platform is stable in most operating conditions at ship speeds up to 4.5 m s(-1) Large discrepancies are found, however, between the ship's velocity obtained from bottom-tracking ADCP pulses and that from navigational data. These are explained with a magnetic compass bias that varies with the ship's heading direction. Both the ship and the tow platform induce magnetic fields that bias the ADCP compass. An in situ compass calibration scheme is thus necessary and requires accurate navigational data. In our main study area, it is found that the Global Position System provides absolute and relative positions to within 88 and 4 m, respectively. These accuracies are sufficient for calibration purposes. With our calibration scheme the towed ADCP system performs as well as vessel-mounted systems. The ease of deployment from ships of opportunity and the capacity of the tow system to carry additional instruments makes it a valuable research tool. Furthermore, the capability of our system to profile the water column above and below the platform with different frequencies and thus different vertical resolutions enhances its flexibility and usefulness, especially to study surface and bottom boundary-layer processes.

Boyd, TJ, Luther DS, Knox RA, Hendershott MC.  1993.  High-Frequency Internal Waves in the Strongly Sheared Currents of the Upper Equatorial Pacific - Observations and a Simple Spectral Model. Journal of Geophysical Research-Oceans. 98:18089-18107.   10.1029/93jc01798   AbstractWebsite

Statistics of high-frequency (0.24.5 cph) fluctuations are derived from moored upper ocean measurements of currents and temperatures at four latitudes spanning the equator along 140-degrees-W. Some of the more unusual statistics include (1) nonunity ratios of kinetic energy to potential energy; (2) nonunity ratios of zonal to meridional kinetic energy; (3) nonzero current-temperature coherence amplitudes, with depth-dependent phases; and (4) high vertical coherence amplitudes, with approximately 180-degrees phases, between current measurements spanning the thermocline. A simple model of shear-modified internal waves is employed to gain insight into the causes of the latitudinal variability of the statistics. Much of this variability can be attributed to the vertical advection of significantly different mean vertical shears by a spectrum of internal waves. The statistics also suggest that the spectrum of high-frequency internal waves in the upper equatorial Pacific differs in important ways from canonical spectral models. The statistics are consistent with a model based on vertical modes which neglect advection by the mean flow, provided the energy in the first mode is much less than (about 0.3 times) that in the spectrum described by Garrett and Munk (1972, 1975, 1979) and Munk (1981) and two to four times as much energy propagates eastward as westward. Some of the statistics are inconsistent with the simple internal wave model examined, possibly indicating contamination by mooring motion.

Miller, AJ, Luther DS, Hendershott MC.  1993.  The Fortnightly and Monthly Tides - Resonant Rossby Waves or Nearly Equilibrium Gravity-Waves. Journal of Physical Oceanography. 23:879-897.   10.1175/1520-0485(1993)023<0879:tfamtr>;2   AbstractWebsite

The fortnightly and monthly tides are discussed in the light of recent sea level observations and numerical modeling results. Within the tide gauge network of the low-latitude Pacific, the fortnightly tide is shown to possess a large-scale phase lag of roughly 10-40 degrees. Although the nonequilibrium part of the fortnightly tide is traditionally thought to be dominated by Rossby wave dynamics, it is shown, via global shallow-water modeling studies, that this large-scale phase lag is explicable in terms of remotely forced gravity waves whose origin is mainly in the Arctic Ocean. Although future observations outside the low-latitude region of the Pacific may eventually reveal Rossby wave excitation, the fortnightly tidal signal in the tide gauge network at hand appears to reveal at most only weak excitation of Rossby waves compared to the phase lag due to remotely forced gravity waves. The observed monthly tide appears to be only slightly closer to equilibrium than the fortnightly tide. The reason for this remains unclear since the monthly tide is less affected by the remotely forced gravity waves than the fortnightly tide.

Hendershott, MC.  1989.  The Ventilated Thermocline in Quasigeostrophic Approximation. Journal of Marine Research. 47:33-53.   10.1357/002224089785076398   Website
Miller, AJ, Holland WR, Hendershott MC.  1987.  Open-Ocean Response and Normal Mode Excitation in an Eddy-Resolving General-Circulation Model. Geophysical and Astrophysical Fluid Dynamics. 37:253-278.   10.1080/03091928708210099   Website
Barale, V, Rizzoli PM, Hendershott MC.  1984.  Remotely Sensing the Surface Dynamics of the Adriatic Sea. Deep-Sea Research Part a-Oceanographic Research Papers. 31:1433-1459.   10.1016/0198-0149(84)90081-5   Website
Chapman, DC, Hendershott MC.  1982.  Shelf Wave-Dispersion in a Geophysical Ocean. Dynamics of Atmospheres and Oceans. 7:17-31.   10.1016/0377-0265(82)90003-3   Website
Chapman, DC, Hendershott MC.  1981.  Scattering of Internal Waves Obliquely Incident Upon a Step Change in Bottom Relief. Deep-Sea Research Part a-Oceanographic Research Papers. 28:1323-1338.   10.1016/0198-0149(81)90037-6   Website
Parke, ME, Hendershott MC.  1980.  M2, S2, K1 Models of the Global Ocean Tide on an Elastic Earth. Marine Geodesy. 3:379-408.Website
Malanotterizzoli, P, Hendershott MC.  1980.  Solitary Rossby Waves over Variable Relief and Their Stability .1. The Analytical Theory. Dynamics of Atmospheres and Oceans. 4:247-260.   10.1016/0377-0265(80)90030-5   Website
Wielicki, B, Hendershott M.  1979.  Further Development of a Spectrally Truncated Model Atmosphere for Climate Studies. Dynamics of Atmospheres and Oceans. 3:453-464.   10.1016/0377-0265(79)90024-1   Website
Holloway, G, Hendershott MC.  1977.  Stochastic Closure for Nonlinear Rossby Waves. Journal of Fluid Mechanics. 82:747-765.   10.1017/s0022112077000962   Website
Salmon, R, Holloway G, Hendershott MC.  1976.  Equilibrium Statistical-Mechanics of Simple Quasi-Geostrophic Models. Journal of Fluid Mechanics. 75:691-703.   10.1017/s0022112076000463   Website