Mean Overflow Research Articles

Hydraulics and Mixing of the Deep Overflow in the Lifamatola Passage of the Indonesian Seas

AbstractHydrographic measurements recently acquired along the thalweg of the Lifamatola Passage combined with historical moored velocity measurements immediately downstream of the sill are used to study the hydraulics, transport, mixing, and entrainment in the dense overflow. The observations suggest that the mean overflow is nearly critical at the mooring site, suggesting that a weir formula may be appropriate for estimating the overflow transport. Our assessment suggests that the weir formulas corresponding to a rectangular, triangular, or parabolic cross section all result in transports very close to the observation, suggesting their potential usage in long-term monitoring of the overflow transport or parameterizing the transport in numerical models. Analyses also suggest that deep signals within the overflow layer are blocked by the shear flow from propagating upstream, whereas the shallow wave modes of the full-depth continuously stratified flow are able to propagate upstream from the Banda Sea into the Maluku Sea. Strong mixing is found immediately downstream of the sill crest, with Thorpe-scale-based estimates of the mean dissipation rate within the overflow up to 1.1 × 10−7 W kg−1 and the region-averaged diapycnal diffusivity within the downstream overflow in the range of 2.3 × 10−3 to 10.1 × 10−3 m2 s−1. Mixing in the Lifamatola Passage results in 0.6–1.2-Sv (1 Sv ≡ 106 m3 s−1) entrainment transport added to the overflow, enhancing the deep-water renewal in the Banda Sea. A bulk diffusivity coefficient estimated in the deep Banda Sea yields 1.6 × 10−3 ± 5 × 10−4 m2 s−1, with an associated downward turbulent heat flux of 9 W m−2.

Variability of the Denmark Strait overflow: Moored time series from 1996–2011

The Denmark Strait overflow provides about half of the total dense water overflow from the Nordic Seas into the North Atlantic Ocean. The velocity of the overflow has been monitored in the Strait with two moored Acoustic Doppler Current Profilers since 1996 with several interruptions due to mooring losses or instrument failure. So far, overflow transports were only calculated when data from both moorings were available. In this work, we introduce a linear model to fill gaps in the time series when data from only one instrument is available. The mean overflow transport is 3.4 Sv and exhibits a variance of 2.0 Sv2. No significant trend was detected in the time series. The highest variability in the transport is associated with the passage of mesoscale eddies with time scales of 2–10 days (associated with a variance of 1.5 Sv2). Seasonal variability is weak and explains less than 5% of the variance in all time series, which is in contrast to the strong seasonal cycle found in high resolution model simulations. Interannual variability is on the order of 10% of the mean. A relation to atmospheric forcing such as the local wind stress curl, as well as to larger scale phenomena, e.g. the North Atlantic Oscillation, is not detected. Since 2005 data from moored temperature, conductivity and pressure recorders have been available as well, monitoring the hydrographic variability at the bottom of Denmark Strait. In recent years the temperature time series of the Denmark Strait overflow revealed a cooling, while the salinity stayed nearly constant.

Bounds and Approximations for the Fixed-Cycle Traffic-Light Queue

This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic light alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals. The key performance characteristic in the FCTL queue is the so-called mean overflow, defined as the mean queue length at the end of a green period. An exact solution for the mean overflow is available, but it has been considered to be of little practical value because it requires some numerical procedures. Therefore, most of the literature on the FCTL queue is about deriving approximations for the mean overflow. In deriving these approximations, most authors first approximate the FCTL queue by a bulk-service queue, approximate the mean overflow in the bulk-service queue, and use this as an approximation for the mean overflow in the FCTL queue. So far no quantitative comparison of both models has been given. We compare both models and assess the quality of the approximation for various settings of the parameter values. In this comparison and throughout the paper we do not restrict ourselves to Poisson arrivals, but consider a more general arrival process instead. We discuss the numerical issues that need to be resolved to calculate the exact expression for the mean overflow in both queues and show that clear computational schemes are available. Next, we present several bounds and approximations of the mean overflow that do not require numerical procedures. In particular, we derive a new approximation based on the heavy traffic limit and a scaling argument. We compare the new bounds and approximation with the existing ones. We elaborate on the impact of several parameters, like the length of the green and red period and the variance of the arrival distribution. Each of these parameters turns out to be crucial.

Chernoff bounds for mean overflow rates

A number of independent traffic streams arrive at a queueing node which provides a finite buffer and a non-idling service at constant rate. Customers which arrive when the buffer is full are droppe...