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Youyu Lu

Abstract

A set of equations is derived to modify z-level Boussinesq ocean circulation models to account for non-Boussinesq effects. These equations take the same form as those of the Boussinesq models except for the addition of a few correction terms that require the calculation of integral density sources. These corrections are estimated to be significant based on a scale analysis.

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Youyu Lu and Detlef Stammer

Abstract

The vorticity budget of the vertically integrated circulation from two global ocean simulations is analyzed using a horizontal spacing of 2° × 2° in longitude/latitude. The two simulations differ in their initial hydrographic conditions and surface wind and buoyancy forcing. The constrained simulation obtains optimal initial condition and surface forcing through assimilating observational data using the model's adjoint, whereas the unconstrained simulation uses Levitus climatological conditions for initialization and is driven by NCEP–NCAR reanalysis forcing, plus restoring to the monthly surface temperature and salinity climatological conditions. The goal is to examine the dynamics that sets the time-mean circulation and to understand the differences between the constrained and unconstrained simulations. It is found that, similar to eddy-permitting simulations, the bottom pressure torque (BPT) in coarse-resolution models plays an important role in the western boundary currents and in the Southern Ocean, and largely balances the difference between wind stress curl and βV for the depth-integrated flow. BPT is a controlling factor of the interior abyssal flow. The geostrophic vorticity relation holds in the interior basins in intermediate and deep layers and breaks down in the upper ocean toward the surface. In the upper layer of the interior basins, the model simulations show statistically significant deviation from the Sverdrup balance. In the subtropical gyre regions, the deviation from Sverdrup balance is confined to zonal bands that are balanced by the curls of lateral friction and nonlinear advection. The differences between the constrained and unconstrained simulations are significant in vorticity terms. The adjustment to Levitus hydrographic climatological data as the model's initial condition causes the most significant changes in BPT, which is the main reason for changes in abyssal flow. The analysis also points to needs for further improvement of models and controlling the influence of data errors in ocean state estimation.

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Youyu Lu and Rolf G. Lueck

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This paper discusses the principles of measuring the mean velocity and its vertical shear in a turbulent flow using an acoustic Doppler current profiler (ADCP), and presents an analysis of data gathered in a tidal channel. The assumption of horizontal homogeneity of the first moments is fundamental to the derivation of the mean velocity vector because the velocity is never homogeneous over the span of the beams in a turbulent flow. Two tests of this assumption are developed—a comparison of the mean error velocity against its standard deviation and against the mean speed. The fraction of the samples that pass these tests increases with increasing spatial averaging and exceeds 95% for distances longer than 55 beam separations. The statistical uncertainty of the velocity and shear vector, averaged over 10 min and longer, stems from turbulent fluctuations rather than Doppler noise. Estimation of the vertical velocity requires a correction for the bias in the measured tilt.

The mean velocity and shear estimates from this natural tidal channel show more complex depth–time variations than found in idealized one-dimensional channel flow, which seldom occurs in nature. The ADCP measurements reveal the secondary circulation, bursts of up- and downwelling, shear reversals, and transverse velocity shear.

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Youyu Lu and Rolf G. Lueck

Abstract

A four-transducer, 600-kHz, broadband acoustic Dopple current profiler (ADCP) was rigidly mounted to the bottom of a fully turbulent tidal channel with peak flows of 1 m s−1. Rapid samples of velocity data are used to estimate various parameters of turbulence with the covariance technique. The questions of bias and error sources, statistical uncertainty, and spectra are addressed. Estimates of the Reynolds stress are biased by the misalignment of the instrument axis with respect to vertical. This bias can be eliminated by a fifth transducer directed along the instrument axis. The estimates of turbulent kinetic energy (TKE) density have a systematic bias of 5 × 10−4 m2 s−2 due to Doppler noise, and the relative statistical uncertainty of the 20-min averages is usually less than 20%–95% confidence. The bias in the Reynolds stress due to Doppler noise is less than ±4 × 10−5 m2. The band of zero significance is never less than 1.5 × 10−5 m2 s−2 due to Doppler noise, and this band increases with increasing TKE density. Velocity fluctuations with periods longer than 20 min contribute little to either the stress or the TKE density. The rate of production of TKE density and the vertical eddy viscosity are derived and in agreement with expectations for a tidal channel.

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Yang Zhou, Keith R. Thompson, and Youyu Lu

Abstract

A regression-based modeling approach is described for mapping the dependence of atmospheric state variables such as surface air temperature (SAT) on the Madden–Julian oscillation (MJO). For the special case of a linear model the dependence can be described by two maps corresponding to the amplitude and lag of the mean atmospheric response with respect to the MJO. In this sense the method leads to a more parsimonious description than traditional compositing, which usually results in eight maps, one for each MJO phase. Another advantage of the amplitude and phase maps is that they clearly identify propagating signals, and also regions where the response is strongly amplified or attenuated. A straightforward extension of the linear model is proposed to allow the amplitude and phase of the response to vary with the amplitude of the MJO or indices that define the background state of the atmosphere–ocean system. Application of the approach to global SAT for boreal winter clearly shows the propagation of MJO-related signals in both the tropics and extratropics and an enhanced response over eastern North America and Alaska (further enhanced during La Niña years). The SAT response over Alaska and eastern North America is caused mainly by horizontal advection related to variations in shore-normal surface winds that, in turn, can be traced (via signals in the 500-hPa geopotential height) back to MJO-related disturbances in the tropics.

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Youyu Lu, Daniel G. Wright, and David Brickman

Abstract

A three-dimensional, z-level, primitive-equation ocean circulation model (DieCAST) is modified to include a free-surface and partial cells. The updating of free-surface elevation is implicit in time so that the extra computational cost is minimal compared with the original DieCAST code, which uses the rigid-lid approximation. The addition of partial cells allows the bottom cell of the model to have variable thickness, hence improving the ability to accurately represent topographic variations. The modified model is tested by solving a two-dimensional, linearized problem of internal tide generation over topography. method is modified to more cleanly separate the internal tide from the full solution. The model results compare favorably with the semianalytic solution of . In particular, the model reproduces the predicted variation of internal tide energy flux as a function of the ratio of bottom slope to characteristic slope.

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Youyu Lu, Rolf G. Lueck, and Daiyan Huang

Abstract

A broadband ADCP and a moored microstructure instrument (TAMI) were deployed in a tidal channel of 30-m depth and with peak speeds of 1 m s−1. The measurements enable us to derive profiles of stress, turbulent kinetic energy (TKE), the rate of production and dissipation of TKE, eddy viscosity, diffusivity, as well as mixing length, and to test the parameterization of dissipation rate in the model of Mellor and Yamada. At middepth in the channel where the influence of stratification was present, the Ellison length agrees with the Ozmidov length. The measured mixing length is smaller than the simple z-dependence formulation proposed for unstratified turbulence. The diffusivity of density and heat, and the viscosity for momentum, are correlated and comparable in magnitudes. The 20-min averaged production rate deduced from the ADCP agrees with the dissipation rate estimated from microstructure measurements. The dissipation rate calculated with the Mellor–Yamada model agrees with the measured values with TAMI, but the empirical constant B 1 derived from the data is larger than that conventionally used in the model. In the near-bottom layer, there is a tight correlation between the production rate and the closure-based dissipation rate. The Reynolds stress at 3.6 m above the bottom is consistently 2.5 times smaller than the shear velocity squared (u2), which is inferred from fitting the velocity profiles to a logarithmic form. A logarithmic velocity profile almost always exists and reaches heights of 5.6 to 20 m, but the Reynolds stress is seldom constant in any part of the logarithmic layer.

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Richard J. Greatbatch, Youyu Lu, and Yi Cai

Abstract

There is a growing need for ocean circulation models that conserve mass rather than volume (as in traditional Boussinesq models). One reason is bottom pressure data expected to flow from satellite-mounted gravity-measuring instruments, and another is to provide a complete interpretation of data from satellite altimeters such as TOPEX/Poseidon. In this paper, it is shown that existing, hydrostatic Boussinesq ocean model codes can easily be modified, with only a modest increase in the CPU requirement, to integrate the hydrostatic, non-Boussinesq equations. The method can be used to integrate both coarse-resolution and eddy-resolving non-Boussinesq models. The basic equations can also be used to formulate a fully nonhydrostatic, non-Boussinesq model. The method is illustrated for the case of the Parallel Ocean Program (POP), the parallel version of the Bryan–Cox–Semtner code developed at Los Alamos National Laboratory. A comparison of eddy-permitting model solutions under double-gyre wind forcing shows that the error in making the Boussinesq approximation is, reassuringly, only a few percent. The authors also consider a coarse-resolution global ocean model under seasonal forcing. The non-Boussinesq model shows a seasonal variation in global mean sea surface height (SSH) with a range of about 3 cm, attributable mostly to changes in the mass of the ocean due to the freshwater flux forcing, but with a roughly 25% contribution from the steric expansion effect. The seasonal cycles of model-computed SSH are also compared with TOPEX/Poseidon data from the South Pacific and South Atlantic Oceans. It is shown that the seasonal cycle in global mean SSH contributes to the model-computed seasonal cycle, and improves the model performance compared to the data. It is found that the difference between the seasonal cycles in the Boussinesq and non-Boussinesq models is almost entirely accounted for by the seasonal cycle in global mean SSH. On the other hand, on longer timescales the difference field between the non-Boussinesq and Boussinesq models shows spatial variability of several centimeters that is not accounted for by a globally uniform correction to the Boussinesq model.

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Xu Zhang, Youyu Lu, and Keith R. Thompson

Abstract

Satellite observations of sea level and surface wind from the tropical Pacific Ocean, and their relationship to the Madden–Julian oscillation (MJO), are analyzed using a combination of statistical techniques and a simple, physically based model. Wavenumber–frequency analysis reveals that sea level variations at the equator contain prominent eastward-propagating signals as the intraseasonal Kelvin waves. The component of sea level variation that is coherent with the MJO (η MJO) is concentrated in a narrow strip along the equator between 150°E and 110°W. To explain the physical forcing of η MJO, the component of zonal wind stress that is coherent with the MJO is also calculated. It is shown that is strongest in the western Pacific, but the MJO accounts for a higher percentage of the wind variance in the central equatorial Pacific. A simple linear model of the Kelvin waves, based on a first-order wave equation forced by and with a linear damping term included, successfully reproduces η MJO. It is also shown that zonal wind variations to the east of the date line act to increase the apparent propagation speeds of the Kelvin waves.

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Richard J. Greatbatch, Youyu Lu, Brad DeYoung, and Jimmy C. Larsen

Abstract

A high-resolution, barotropic model of the North Atlantic is used to study the variation of transport through the Straits of Florida on timescales from a few days to seasonal. The model is driven by wind and atmospheric pressure forcing derived from ECMWF twice daily analyses for the years 1985, 1986, 1987, and 1988. The model-computed transports are compared with the cable-derived estimates of daily mean transport. Atmospheric pressure forcing is found to have an insignificant effect on the model results and can be ignored. A visual comparison between the model-computed transport and the cable data shows many similarities. Coherence squared between the two time series has peaks between 0.4 and 0.5 and is significant at the 95% confidence level in the period range from 6 to 100 days, with a drop in coherence near 10 days. The model overestimates the autospectral energy in the period range of 4 to 20 days but underestimates the energy at longer periods. The authors find that remote forcing to the north of the straits does not significantly affect coherence squared and phase between the model-computed transport and the cable data but is necessary to explain the autospectral energy in the model-computed transports at periods greater than 10 days. The most significant failing of the model is its inability to capture 8–10 mo timescale events in the cable data. Interestingly, the World Ocean Circulation Experiment Community Modeling Effort, driven by synoptic wind forcing, does exhibit roughly 8-month timescale events, as seen in the cable data but missed by the barotropic model.

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