Energetics of lateral eddy diffusion/advection: Part III. Energetics of horizontal and isopycnal diffusion/ advection

Gravitational Potential Energy （GPE） change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps： stirring and sub scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.

Regime Shifts in the North Pacific Simulated by a COADS-driven Isopycnal Model

The Miami Isopycnal Coordinate Ocean Model (MICOM) is adopted to simulate the intevdecadal variability in the Pacific Ocean with most emphasis on regime shifts in the North Pacific. The computational domain covers 60°N to 40°S with an enclosed boundary condition for momentum flux, whereas there are thermohalirie fluxes across the southern end as a restoring term. In addition, sea surface salinity of the model relaxes to the climatological season cycle, which results in climatological fresh water fluxes. Surface forcing functions from January 1945 through December 1998 are derived from the Comprehensive Ocean and Atmospheric Data Set (COADS). Such a numerical experiment reproduces the observed evolution of the interdecadal variability in the heat content over the upper 400-m layer by a two-year lag. Subduction that occurs at the ventilated thermocline in the central North Pacific is also been simulated and the subducted signals propagate from 35°N to 25°N, taking about 8 to 10 years, in agreement with the expendable Bathy Thermograph observation over recent decades. Interdecadal signals take a southwest-ward and downward path rather than westward propagation, meaning they are less associated with the baroclinic planetary waves. During travel, the signals appear to conserve potential vorticity. Therefore, the ventilated thermocline and related subduction are probably the fundamental physics for interdecadal variability in the mid-latitude subtropics of the North Pacific.

Energetics of lateral eddy diffusion/advection: Part II. Numerical diffusion/diffusivity and gravitational potential energy change due to isopycnal diffusion

Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and ad vection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial hori zontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models; therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with hori zontal advection in the commonly used Eulerian coordinates may become one of the most challenging ob stacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion （mixing） has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps： stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.

Seasonal variability of the isopycnal surface circulation in the South China Sea derived from a variable-grid global ocean circulation model

In this study, we develop a variable-grid global ocean general circulation model （OGCM） with a fine grid （1/6）° covering the area from 20°S-50°N and from 99°-150°E, and use the model to investigate the isopycnal surface circulation in the South China Sea （SCS）. The simulated results show four layer structures in vertical： the surface and subsurface circulation of the SCS are characterized by the monsoon driven circulation, with basin-scaled cyclonic gyre in winter and anti-cyclonic gyre in summer. The intermediate layer circulation is opposite to the upper layer, showing anti-cyclonic gyre in winter but cyclonic gyre in summer. The circulation in the deep layer is much weaker in spring and summer, with the maximum velocity speed below 0.6 cm/s. In fall and winter, the SCS deep layer circulation shows strong east boundary current along the west coast of Philippine with the velocity speed at 1.5 m/s, which flows southward in fall and northward in winter. The results have also revealed a fourlayer vertical structure of water exchange through the Luzon Strait. The dynamics of the intermediate and deep circulation are attributed to the monsoon driving and the Luzon Strait transport forcing.

The eastward subtropical countercurrent on isopycnal surface in the western North Pacific

The monthly circulations on isopycnal surface in the western North Pacific are calculated based on the Navy’s Generalized Digital Environmental Model climatological tem- perature and salinity data on a 1/2° × 1/2° grid using a P-vector method. The eastward Sub- tropical Countercurrent (STCC) in the central subtropical gyre has been studied with emphasis on its spatial distribution, vertical structure, volume transport and its nearby eddy phenomenon. The results reproduce the observed feature of STCC, and reveal some new phenomena on isopycnal surface, such as: (1) At σθ = 24.6, there is strong seasonal variability in the distribution, origin and flow status of STCC. There is no STCC in January, February and March. (2) From May to October, a branch of the Kuroshio Countercurrent to the south of Japan merges into STCC, which increases the velocity of STCC and widens its width. (3) The velocity vector field shows that STCC and nearby eddies coexist. (4) The eastward volume transport of STCC across 137.5°E is the strongest in summer with the maximum of 6.9 Sv ( 1 Sv ≡ 106 m3 s?1) in August, and weaker in spring and autumn with 1.7 Sv in April and 1.6 Sv in November. Most of the transports of STCC occur between isopycnal surfaces 24.0σθ and 25.0σθ. (5) The distributions of the zonal flow along 137.5°E show that the flow core of STCC is between 24.3σθ and 24.7σθ .

Summertime Subtropical Countercurrent on isopycnals in the western North Pacific

Circulations on isopycnals (σθ) in the western North Pacific were investigated by using P-vector method; the data were taken from the U.S. Navy’s climatological temperature and salinity dataset (public domain) with 1/2°×1/2° resolution. Results not only show the main circulation systems on isopycnals in the western North Pacific such as the North Equatorial Current (NEC), Kuroshio and Ku-roshio Countercurrent, but also reveal the Subtropical Countercurrent (STCC) clearly. In this note we pay attention to discussing the distribution of STCC in summer (in June). The STCC flows eastward along a winding road; on shallow isopycnals, the STCC originates from the area east of Bashi Strait at about 122.5°E; with the isopycnals increasing, the origin and flow core of STCC move to north and east, but the main part of STCC is still between 18?and 23.5°N, i.e. near the Tropic of Cancer. There exists STCC on all isopycnals between the sea surface and 25.8σθ.The current vectors of STCC on isopycnals are

Energetics of lateral eddy diffusion/advection: Part IV. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy （GPE） source and sink due to stirring and cabbeling associated with sigma dif fusion/ advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the exces sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.

Fundamental Framework and Experiments of the ThirdGeneration of IAP/LASG World OceanGeneral Circulation Model

A new generation of the IAP / LASG world ocean general circulation model is designed and presented based on the previous 20-layer model, with enhanced spatial resolutions and improved parameterizations. The model uses a triangular-truncated spectral horizontal grid system with its zonal wave number of 63 (T63) to match its atmospheric counterpart of a T63 spectral atmosphere general circulation model in a planned coupled ocean-atmosphere system. There are 30 layers in vertical direction, of which 20 layers are located above 1000 m for better depicting the permanent thermocline. As previous ocean models developed in IAP / LASG, a free surface (rather than “rigid-lid” approximation) is included in this model. Compared with the 20-layer model, some more detailed physical parameterizations are considered, including the along / cross isopycnal mixing scheme adapted from the Gent-MacWilliams scheme. The model is spun up from a motionless state. Initial conditions for temperature and salinity are taken from the three-dimensional distributions of Levitus’ annual mean observation. A preliminary analysis of the first 1000-year integration of a control experiment shows some encouraging improvements compared with the twenty-layer model, particularly in the simulations of permanent thermocline, thermohaline circulation, meridional heat transport, etc. resulted mainly from using the isopycnal mixing scheme. However, the use of isopycnal mixing scheme does not significantly improve the simulated equatorial thermocline. A series of numerical experiments show that the most important contribution to the improvement of equatorial thermocline and the associated equatorial under current comes from reducing horizontal viscosity in the equatorial regions. It is found that reducing the horizontal viscosity in the equatorial Atlantic Ocean may slightly weaken the overturning rate of North Atlantic Deep Water.

Analysis of interdecadal variation of tropical Pacific thermocline based on assimilated data

The interdecadal variation of Pacific thermocline represented by depth anomalies of 25σθ isopycnal surface calculated from SODA data set is analyzed. The climatological depth of 25σθ isopycnal surface is quite close to the depth of 20 ℃ isotherm in the tropical Pacific. The EOF1 mode of the 25σθ isopycnal surface accounts for 26. 4% of the total variance and its associated pattern is of east-west direction. The centers of positive and negative extremes are located near 10oS over the southern Pacific and the correlation coefficient with zero-lag between the corresponding EOF1 time coefficient and PDO index is -0.67. This shows that there is very close relation between the southern tropical Pacific and PDO. The wavelet analysis of detrended EOF1 time coefficient reveals that there are two dominant time scales of about 3～7 and 30 a respectively. An apparent abruptness of mean value occurred in the late 1970s. EOF2 mode accounts for 12.4% of the total variance and its pattern is an ENSO-related one. The correlation coefficient between the EOF2 time coefficient and NINO3 index is -0.68. The wavelet analysis of EOF2 time coefficient reveals that there are two leading time scales of about 2～7 and 10～15 a respectively. On an interdecadal scale, the zonal change is consistent along the equator and is seesaw along 10oS; there is consistent polarity in the tropics along 165oE, but reverse polarity between around equator and other tropical region along 120oW. In all the four profiles mentioned above, the regime shift occurred in the late 1970s. The evolving characteristics of anomalies can be explained mostly by the anomalies of ocean currents during a complete cycle on an interdecadal scale.

Processes Leading to Second-Year Cooling of the 2010–12 La Ni?a Event,Diagnosed Using GODAS

Isopycnal analyses were performed on the Global Ocean Data Assimilation System （GODAS） to determine the oceanic processes leading to so-called second-year cooling of the La Nina event.In 2010-12,a horseshoe-like pattern was seen,connecting negative temperature anomalies off and on the Equator,with a dominant influence from the South Pacific.During the 2010 La Nina event,warm waters piled up at subsurface depths in the western tropical Pacific.Beginning in early 2011,these warm subsurface anomalies propagated along the Equator toward the eastern basin,acting to reverse the sign of sea surface temperature （SST） anomalies （SSTAs） there and initiate a warm SSTA.However,throughout early 2011,pronounced negative anomalies persisted off the Equator in the subsurface depths of the South Pacific.As isopycnal surfaces outcropped in the central equatorial Pacific,negative anomalies from the subsurface spread upward along with mean circulation pathways,naturally initializing a cold SSTA.In the summer,a cold SSTA reappeared in the central basin,which subsequently strengthened due to the off-equatorial effects mostly in the South Pacific.These SSTAs acted to initiate local coupled air-sea interactions,generating atmospheric-oceanic anomalies that developed and evolved with the second-year cooling in the fall of 2011.However,the cooling tendency in mid-2012 did not develop into another La Nina event,since the cold anomalies in the South Pacific were not strong enough.An analysis of the 2007-09 La Nina event revealed similar processes to the 2010-12 La Nina event.

Structure and Evolution of Decadal Spiciness Variability in the North Pacific during 2004-20,Revealed from Argo Observations

Ocean spiciness is referred to as density-compensated temperature and salinity variations with warm(cool)and salty(fresh)waters having high(low)spiciness,respectively.The structure and evolution of density-compensated(warm/salty or cool/fresh)spiciness anomalies are investigated in the North Pacific thermocline using Argo observations during the period 2004-20.Two well-organized decadal spiciness events are identified through isopycnal surface analyses.One warm/salty spiciness anomaly of about 0.15°C and 0.05 g kg^(−1)temperature and salinity perturbations on the 25 kg m^(−1)isopycnal surface appeared in the eastern subtropical North Pacific at(18°-30°N,120°-150°W)in 2007,which then migrated southwestward along the mean circulation and arrived in the western tropics at(~15°N,145°E-175°W)in 2012-13,with the reduced salinity perturbation of about 0.043 g kg^(−1).Another cool/fresh spiciness anomaly of about−0.2°C and−0.07 g kg^(−1)temperature and salinity perturbations originated from the eastern subtropics at(120°-150°W,~30°N)in 2014 and followed a similar advective pathway during the period from 2014-15 to 2019-20.The subduction pathway can be adequately determined by the mean Montgomery stream function on the isopycnal surface;the propagation direction and speed are in good agreement with the expectation for the role played by advection due to the mean geostrophic current.Moreover,the subducted decadal spiciness anomalies can have negative feedback on sea surface temperature(SST)variability in the western tropical Pacific through the diapycnal processes.The identifications of these density-compensated spiciness anomalies and their propagation pathways provide a clear illustration of the oceanic extratropics-tropics interactions in the North Pacific Ocean.

Formation and transport of intermediate water masses in a model of the Pacific Ocean

A basin-wide ocean general circulation model of the Pacific Ocean was used to investigate how the interior restoration in the Okhotsk Sea and the isopycnal diffusion affect the circulation and intermediate water masses. Four numerical experiments were conducted, including a run with the same isopycnal and thickness diffusivity of 1.0×10^3 m2/s, a run employing the interior restoration of temperature and salinity in the Okhotsk Sea with a time scale of 3 months, a run that is the same as the first run except for the enhanced isopycnal mixing, and a final run with the combination of the restoration in the Okhotsk Sea and large isopycnal diffusivity. Simulated results show that the intermediate water masses reproduced in the first run are relatively weak. An increase in isopycnal diffusivity can improve the simulation of both Antarctic and North Pacific intermediate waters, mainly increasing the transport in the interior ocean, but inhibiting the outflow from the Okhotsk Sea. The interior restoration generates the reverse current from the observation in the Okhotsk Sea, whereas the simulation of the temperature and salinity is improved in the high latitude region of the Northern Hemisphere because of the reasonable source of the North Pacific Intermediate Water. A comparison of vertical profiles of temperature and salinity along 50°N between the simulation and observations demonstrates that the vertical mixing in the source region of intermediate water masses is very important.

UNSTEADY INTERACTION OF SHOCK WAVE DIFFRACTING AROUND A CIRCULAR CYLINDER IN AIR

The reflection and diffraction of a planar shock wave around a circular cylinder are a typical problem of the complex nonlinear shock wave phenomena in literature.It has long been studied experimentally,analytically as well as numerically.Takayama in 1987 obtained clear experimental pictures ofisopycnics in shock tube under the condi- tion that the impinging shock wave propagates as far as 3 diameters away from the cylinder.To know more complete- ly the whole unsteady process,it is desirable to get experimental results in a region which is more than 10 diameters away from the cylinder.This is what has been done in this paper by using the pulsed laser holographic interferometry for several shock Mach numbers of the impinging shock. Results for several moments are shown,giving more know- ledge about the whole unsteady flow field.This is useful for a reliable and complete understanding of the changing force acting on the cylinder,and provides interesting data to check the performance of many recently developed high resolution numerical methods for unsteady shock wave calculation.