Relativistic viscous hydrodynamic fits to RHIC data on the centrality dependence of multiplicity, transverse and elliptic flow for √ s = 200 GeV Au+Au collisions are presented. For standard (Glauber-type) initial conditions, while data on the integrated elliptic flow coefficient v2 is consistent with a ratio of viscosity over entropy density up to η/s ≃ 0.16, data on minimum bias v2 seems to favor a much smaller viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some caveats on this result are discussed.The success of ideal hydrodynamics for the description of heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) has led to the idea of a quark-gluon plasma behaving as a "perfect liquid", with a very small ratio of viscosity over entropy density [1,2,3,4]. An answer to the question "How perfect is the fluid observed at RHIC?" can, however, not be found using ideal hydrodynamics, but must involve a controlled quantitative understanding of non-idealities, e.g. viscous effects. If hydrodynamics can be applied to RHIC physics, then relativistic viscous hydrodynamics should be able to provide such an understanding. In particular, if one has control over the initial conditions, it should be possible to determine the size of various hydrodynamic transport coefficients, such as the shear viscosity, by a best fit of viscous hydrodynamics (VH) to experimental data. In this Letter, we aim to take a step in this direction.For RHIC physics, since particle number in the quarkgluon plasma is ill-defined, the relevant dimensionless parameter for VH is the ratio shear viscosity η over entropy density s. Based on the correspondence between Anti-deSitter (AdS) space and conformal field theory (CFT), it has been conjectured [5] that all relativistic quantum field theories at finite temperature and zero chemical potential have η/s ≥ 1 4π . To date, no physical system violating this bound has been found.Neglecting effects from bulk viscosity and heat conductivity, the energy momentum tensor for relativistic hydrodynamics in the presence of shear viscosity isIn Eq.(1), ǫ and p denote the energy density and pressure, respectively, and u µ is the fluid 4-velocity which obeys g µν u µ u ν = 1 when contracted with the metric g µν . The shear tensor Π µν is symmetric, traceless (Π µ µ = 0), and orthogonal to the fluid velocity, u µ Π µν = 0. Conservation of the energy momentum tensor and equation of state provide five equations for the evolution of the 10 independent components of ǫ, p, u µ , Π µν . The remaining five equations for the evolution of Π µν are not unambiguously agreed on at present [6,7,8,9,10]. The results in this work will be based on using the set of equationswhere d α is the covariant derivative, used to construct the time-like and space-like derivatives∆ µν ∇ α u α and the vorticity ω µν = ∇ ν u µ −∇ µ u ν . Both p and temperature T are related to ǫ via the QCD equation of state, for which we take the semi-realistic result from Ref. [11]. If the relaxation time τ Π is not too small, Eq...

Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions. PrefaceStrictly speaking, the subtitle of this work is somewhat misleading. Considerable progress on relativistic viscous fluid dynamics had been made earlier than 2007 both in the context of theoretical formulations as well as in numerical simulations. However, in particular for simulations of high energy nuclear collisions, typically an unrealistically high degree of symmetry had been assumed, making the resulting dynamics 0+1d or 1+1 dimensional. Only ten years ago, simulations in 2+1d became available, which is the minimum required to simulate the so-called elliptic flow observed in experiments. As one of the groups that first achieved 2+1d relativistic viscous fluid dynamics simulations ten years ago, we took the opportunity to celebrate this anniversary by compiling the present review of the current status of the field. Given the ongoing vibrant research activity on relativistic viscous fluid dynamics as well as continued experimental developments, we fully expect this review to be outdated in a few years. This is of course good news, and we hope it will require a new review subtitled "Twenty Years of Progress" when the time has come.Happy anniversary, relativistic viscous fluid dynamics!

Temporal and spatial variations of convection in South Asia are analyzed using eight years of Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data and NCEP reanalysis fields. To identify the most extreme convective features, three types of radar echo structures are defined: deep convective cores (contiguous 3D convective echo ≥40 dBZ extending ≥10 km in height) represent the most vertically penetrative convection, wide convective cores (contiguous convective ≥40 dBZ echo over a horizontal area ≥1000 km2) indicate wide regions of intense multicellular convection, and broad stratiform regions (stratiform echo contiguous over an area ≥50 000 km2) mark the mesoscale convective systems that have developed the most robust stratiform regions. The preferred locations of deep convective cores change markedly from India’s east coast in the premonsoon to the western Himalayan foothills in the monsoon. They form preferentially in the evening and over land as near-surface moist flow is capped by dry air aloft. Continental wide convective cores show a similar behavior with an additional nocturnal peak during the monsoon along the Himalayan foothills that is associated with convergence of downslope flow from the Himalayas with moist monsoonal winds at the foothills. The oceanic wide convective cores have a relatively weak diurnal cycle with a midday maximum. Convective systems exhibiting broad stratiform regions occur primarily in the rainiest season and regions—during the monsoon, over the ocean upstream of coastal mountains. Their diurnal patterns are similar to those of the wide convective cores.

Eight years of Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data show how convective systems of different types contribute to precipitation of the South Asian monsoon. The main factor determining the amount of precipitation coming from a specific system is its horizontal size. Convective intensity and/or number of embedded convective cells further enhance its precipitation production. The precipitation of the monsoon is concentrated in three mountainous regions: the Himalayas and coastal ranges of western India and Myanmar. Along the western Himalayas, precipitation falls mainly from small, but highly convective systems. Farther east along the foothills, systems are more stratiform. These small and medium systems form during the day, as the monsoon flow is forced upslope. Nighttime cooling leads to downslope flow and triggers medium-sized systems at lower elevations. At the mountainous western coasts of India and Myanmar, small and medium systems are present throughout the day, as an orographic response to the southwesterly flow, with a slight superimposed diurnal cycle. Medium systems are favored over the eastern parts of the Arabian Sea and large systems are favored over the Bay of Bengal when an enhanced midlevel cyclonic circulation occurs over the northern parts of these regions. The systems forming upstream of coastal mountains over the Bay of Bengal are larger than those over the Arabian Sea, probably because of the moister conditions over the bay. The large systems over the bay exhibit a pronounced diurnal cycle, with systems forming near midnight and maximizing in midday.