Structure of unsteady stably stratified turbulence with mean shear.

The statistics of unsteady turbulence with uniform stratification N (Brunt–Väisälä frequency) and shear α(=dU1/dx3) are analysed over the entire time range (00 and \it Ri>0.25 respectively, oscillatory momentum and positive and negative density fluxes develop. Above a critical value of \it Ri\scriptsize\it crit(∼0.3), their average values are persistently countergradient. This structural change in the turbulence is the primary mechanism whereby stable stratification reduces the fluxes and the production of variances. It is quite universal and differs from the energy and stability mechanisms of Richardson (1926) and Taylor (1931). The long-time asymptotics of the energy ratio ER(=\it PE/VKE) of the potential energy to the vertical kinetic energy generally decreases with \it Ri(≥0.25), reaching the smallest value of 3/2 when there is no shear (\it Ri→∞). For strong mean shear (\it Ri<0.25), RDT significantly overestimates ER since (as in unstratified shear flow) it underestimates the vertical kinetic energy VKE. The RDT results show that the asymptotic values of the energy ratio ER and the normalized vertical density flux are independent of the initial value of ER, in agreement with DNS. This independence of the initial condition occurs because the ratios of the contributions from the initial values PE0 and KE0 are the same for PE and VKE and can be explained by the linear processes. Stable stratification generates buoyancy oscillations in the direction of the energy propagation of the internal gravity wave and suppresses the generation of turbulence by mean shear. Because the shear distorts the wavenumber fluctuations, the low-wavenumber spectrum of the vertical kinetic energy has the general form E33(k)∝(αtk)−1, where (LXαt)−1≪k≪L−1X (LX: integral scale). The viscous decay is controlled by the shear, so that the components of larger streamwise wavenumber k1 decay faster. Then, combined with the spectrum distortion by the shear, the energy and the flux are increasingly dominated by the small-k1 components as time elapses. They oscillate at the buoyancy period π/N because even in a shear flow the components as k1→0 are weakly affected by the shear. The effects of stratification N and shear α at small scales are to reduce both VKE and PE. Even for the same \it Ri, larger N and α reduce the high-wavenumber components of VKE and PE. This supports the applicability of the linear assumption for large N and α. At large scales, the stratification and shear effects oppose each other, i.e. both VKE and PE decrease due to the stratification but they increase due to the shear. We conclude that certain of these unsteady results can be applied directly to estimate the properties of sheared turbulence in a statistically steady state, but others can only be applied qualitatively

Rapid distortion theory for differential diffusion

Rapid distortion theory (RDT) is used to examine differential diffusion of active and passive scalars in unsheared, initially isotropic turbulence. RDT is well suited to study differential diffusion because it applies to strongly stratified flows with weak turbulence—that is, the conditions under which differential diffusion occurs. The theory reproduces several key features of the evolution of scalar fluxes and scalar flux spectra observed in direct numerical simulations (DNS). Predictions of the diffusivity ratio match laboratory results well when a parameter of the theory is related to a parameter of the experiments. RDT also allows parameters such as molecular diffusivities to be varied over a wider range than DNS can currently reach. RDT may prove to be a useful tool for computing mixing in weakly turbulent parts of the stratified ocean interior and possibly for parameterizing subgrid scale mixing in general circulation models

Buoyancy generated turbulence in stably stratified flow with shear

The energy evolution in buoyancy-generated turbulence subjected to shear depends on the gradient Richardson number Ri and the stratification number St, which is a ratio of the time scale of the initial buoyancy fluctuations to the time scale of the mean stratification. During an initial period, the flow state evolves as in the unsheared case. After this period, shear generates fluctuating velocity components for St=0.25, but it depletes the fluctuating vertical velocity component and temperature variance faster than in the unsheared case for St=4. Weak shear causes the kinetic and total energy to decrease faster than in the unsheared case, whereas strong shear adds more energy in comparison with the unsheared case. Energy increased with time in only one case considered (St=0.1 and Ri=0.04). When St\u3e1, the nonlinearity of the flow does not become significant even when Ri is small. Thus, results from rapid distortion theory and direct numerical simulation compare well. In particular, the theory reproduces trends in the energy evolution for St\u3e1

Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes

We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model grants the existence of turbulence at any gradient Richardson number, Ri. Instead of its critical value separating - as usually assumed - the turbulent and the laminar regimes, it reveals a transition interval, 0.1< Ri <1, which separates two regimes of essentially different nature but both turbulent: strong turbulence at Ri<<1; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at Ri>1. Predictions from this model are consistent with available data from atmospheric and lab experiments, direct numerical simulation (DNS) and large-eddy simulation (LES).Comment: 40 pages, 6 figures, Boundary-layer Meteorology, resubmitted, revised versio

Determining the role of external beam radiotherapy in unresectable intrahepatic cholangiocarcinoma: a retrospective analysis of 84 patients

<p>Abstract</p> <p>Background</p> <p>Intrahepatic cholangiocarcinoma (ICC) is the second most common type of primary liver cancer. Only few studies have focused on palliative radiotherapy used for patients who weren't suitable for resection by surgery. This study was conducted to investigate the effect of external beam radiotherapy (EBRT) for patients with unresectable ICC.</p> <p>Methods</p> <p>We identified 84 patients with ICC from December 1998 through December 2008 for retrospective analysis. Thirty-five of 84 patients received EBRT therapy five times a week (median dose, 50 Gy; dose range, 30-60 Gy, in fractions of 1.8-2.0 Gy daily; EBRT group); the remaining 49 patients comprised the non-EBRT group. Tumor response, jaundice relief, and survival rates were compared by Kaplan-Meier analysis. Patient records were reviewed and compared using Cox proportional hazard analysis to determine factors that affect survival time in ICC.</p> <p>Results</p> <p>After EBRT, complete response (CR) and partial response (PR) of primary tumors were observed in 8.6% and 28.5% of patients, respectively, and CR and PR of lymph node metastases were observed in 20% and 40% of patients. In 19 patients with jaundice, complete and partial relief was observed in 36.8% and 31.6% of patients, respectively. Median survival times were 5.1 months for the non-EBRT group and 9.5 months for the EBRT group (<it>P </it>= 0.003). One-and two-year survival rates for EBRT versus non-EBRT group were 38.5% versus 16.4%, and 9.6% versus 4.9%, respectively. Multivariate analysis revealed that clinical symptoms, larger tumor size, no EBRT, multiple nodules and synchronous lymph node metastases were associated with poorer prognosis.</p> <p>Conclusions</p> <p>EBRT as palliative care appears to improve prognosis and relieve the symptom of jaundice in patients with unresectable ICC.</p

An Electrode Array for Limiting Blood Loss During Liver Resection: Optimization via Mathematical Modeling

Liver resection is the current standard treatment for patients with both primary and metastatic liver cancer. The principal causes of morbidity and mortality after liver resection are related to blood loss (typically between 0.5 and 1 L), especially in cases where transfusion is required. Blood transfusions have been correlated with decreased long-term survival, increased risk of perioperative mortality and complications. The goal of this study was to evaluate different designs of a radiofrequency (RF) electrode array for use during liver resection. The purpose of this electrode array is to coagulate a slice of tissue including large vessels before resecting along that plane, thereby significantly reducing blood loss. Finite Element Method models were created to evaluate monopolar and bipolar power application, needle and blade shaped electrodes, as well as different electrode distances. Electric current density, temperature distribution, and coagulation zone sizes were measured. The best performance was achieved with a design of blade shaped electrodes (5 × 0.1 mm cross section) spaced 1.5 cm apart. The electrodes have power applied in bipolar mode to two adjacent electrodes, then switched sequentially in short intervals between electrode pairs to rapidly heat the tissue slice. This device produces a ~1.5 cm wide coagulation zone, with temperatures over 97 ºC throughout the tissue slice within 3 min, and may facilitate coagulation of large vessels