Two-dimensional turbulence on a sphere

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

Subseasonal Meteorological Drought Development over the Central United States during Spring

Diagnosis of rapidly developing springtime droughts in the central U.S. has mostly been made via numerous individual case studies rather than in an aggregate sense. This study investigates common aspects of subseasonal “meteorological drought” evolution, here defined as persistent precipitation minus evapotranspiration (P-ET) deficits, revealed in early (April 1-May 15) and late (May 16-June 30) spring composites of 5-day running mean JRA-55 reanalysis data for three different central U.S. regions during 1958-2018. On average, these droughts are initiated by a quasi-stationary Rossby wave packet (RWP), propagating from the western North Pacific, which arises about a week prior to drought onset. The RWP is related to a persistent ridge west of the incipient drought region and strong subsidence over it. This subsidence is associated with low-level divergent flow that dries the atmosphere and suppresses precipitation for roughly 1-2 weeks, and generally has a greater impact on the moisture budget than does reduced poleward moisture transport. The resulting “dynamically driven” evaporative demand corresponds to a rapid drying of the root-zone soil moisture, which decreases ∼40 percentiles within ∼10 days. Anomalous near-surface warmth develops only after P-ET deficit onset, as does anomalously low soil moisture that then lingers a month or more, especially in late spring. The horizontal scale of the RWPs, and of the related drought anomalies, decreases from early to late spring, consistent with the climatological change in the Pacific Rossby waveguide. Finally, while this composite analysis is based upon strong, persistent P-ET deficits, it still appears to capture much of the springtime development of so-called “flash droughts” as well.

Potential-vorticity dynamics of troughs and ridges within Rossby wave packets during a 40-year reanalysis period

Rossby wave packets (RWPs) are fundamental to midlatitude dynamics and govern weather systems from their individual life cycles to their climatological distributions. Renewed interest in RWPs as precursors to high-impact weather events and in the context of atmospheric predictability motivates this study to revisit the dynamics of RWPs. A quantitative potential-vorticity (PV) framework is employed. Based on the well-established PV thinking of midlatitude dynamics, the processes governing RWP amplitude evolution comprise group propagation of Rossby waves, baroclinic interaction, the impact of upper-tropospheric divergent flow, and direct diabatic PV modification by nonconservative processes. An advantage of the PV framework is that the impact of moist processes is more directly diagnosed than in alternative, established frameworks for RWP dynamics. The mean dynamics of more than 6000 RWPs from 1979–2017 are presented using ERA5 data, complemented with nonconservative tendencies from the Year of Tropical Convection data (available 2008–2010). Confirming a pre-existing model of RWP dynamics, group propagation within RWPs is consistent with linear barotropic theory, and baroclinic and divergent amplifications occur most prominently during the mature stage and towards the trailing edge of RWPs. Refining the pre-existing model, the maximum of divergent amplification occurs in advance of maximum baroclinic growth, and baroclinic interaction tends to weaken RWP amplitude towards the leading edge. “Downstream baroclinic development” is confirmed to provide a valid description of RWP dynamics in both summer and winter, although baroclinic growth is substantially smaller (about 50 %) in summer. Longwave radiative cooling makes a first-order contribution to ridge and trough amplitude, with the potential that this contribution is partly associated with cloud-radiative effects. The direct impact of other nonconservative tendencies, including latent heat release, is an order of magnitude smaller than longwave radiative cooling. Arguably, latent heat release still has a substantial impact on RWPs by invigorating upper-tropospheric divergence. The divergent flow amplifies ridges and weakens troughs. This impact is of leading order and larger than that of baroclinic growth. To the extent that divergence is associated with latent heat release below, our results show that moist processes contribute to the well-known asymmetry in the spatial scale of troughs and ridges. For ridges, divergent amplification is strongly coupled to baroclinic growth and enhanced latent heat release. We thus propose that the life cycle of ridges is best described in terms of downstream moist-baroclinic development. Consistent with theories of moist-baroclinic instability, both the amplitude and the relative location of latent heat release within the developing wave pattern depend on the state of the baroclinic development. Taking this “phasing” aspect into account, we provide some evidence that variability in the strength of divergent ridge amplification can predominantly be attributed to variability in latent heat release below rather than to secondary circulations associated with the dry dynamics of a baroclinic wave.

Anisotropic Statistics of Lagrangian Structure Functions and Helmholtz Decomposition

We present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition into rotational and divergent components, from sparse data collected along Lagrangian observations. The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field and also in the collection of the Lagrangian data. Specifically, we assume only stationarity and spatial homogeneity of the data and that the cross covariance between the rotational and divergent flow components is either zero or a function of the separation distance only. No further assumptions are made and the anisotropy of the underlying flow components can be arbitrarily strong. We demonstrate our new method by testing it against synthetic data and applying it to the Lagrangian Submesoscale Experiment (LASER) dataset. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy.

How does the diurnal cycle of incoming solar radiation affect self-aggregation of convective clouds?

<p>This study investigates the impact of the diurnal cycle of incoming solar radiation on the spontaneous organization of convective clouds, hereafter self-aggregation. We run 3D cloud-resolving simulations in the RCE framework with interactive sea surface temperature (SST). SST is allowed to interact with the atmosphere using a slab ocean ( H = 1 - 200 meters) with a fixed mean but locally varying temperature. The self-aggregation of deep clouds starts with the appearance of dry patches that grow in size while getting drier, and confine the moist convention into a small fraction of the domain, consistent with previous studies of self-aggregation.</p><p>Interactive SST has been confirmed to decelerate or prevent self-aggregation. However, our finding shows that including the diurnal cycle reduces the impact of slab depth on the self-aggregation so that the aggregation proceeds much faster for shallower slabs (1,2 or 5 meters). For deeper slabs (50 and 200 meters) the self-aggregation progress is negligibly affected by the diurnal cycle. The accelerated self-aggregation with shallow slabs is found to be related to the mechanism by which the dry patches are triggered.</p><p>The triggering of dry patches is typically assumed to be a random process; however, we find that, especially with shallow ocean slabs, the dry patches form in places of cold pools. In other words, the lower tropospheric and boundary layer dryness induced by cold pools as well as surface temperature cooling by cloud shading can persist long enough to ensure a divergent flow, which was found to be important for self-aggregation. With shallow slabs, the negative SST anomaly under the cold pools thermally enhances the radiatively driven night time divergent flow and dries the boundary layer rapidly. The negative moisture anomaly persists even during daytime when the surface warms in dry regions and ensures a divergent flow, however weak, that then leads to the formation of dry patches in the following days. This process significantly accelerates the appearance of first dry patches. Moreover, this mechanism results in the occurrence of self-aggregation for shallow slabs (H=1 or 2 meters ) for which the self-aggregation does not proceed with constant solar radiation in our simulations. The enhanced divergent flow does not play a role for deep slabs as the SST anomalies are very small. Once the self-aggregation is triggered, its progress becomes negligibly affected by the diurnal cycle.</p>

Influence of local splitting behavior at intersections on infiltration in an unsaturated fracture network

<p>Understanding and predicting the macro-scale flow characteristics in the fractured vadose zone is of great importance for subsurface hydrological applications. Here we develop a network model to study infiltration in unsaturated fracture networks. We consider an idealized honeycomb-like fracture network composed of a series of Y-shaped and inverted Y-shaped intersections. At the scale of intersections, liquid storage/release and splitting/convergence behaviors are modeled according to local splitting relationships obtained from detailed laboratory work and numerical simulations. By varying the splitting relationships, the influence of local flow behaviors on large scale flow structures is systematically investigated. We find that when the water split tends to split equally at the intersection, a divergent flow structure forms in the network. Conversely, unequal splitting leads to preferential pathways. We also find that an avalanche infiltration mode, i.e., sudden release of a large amount of water from the network, emerges spontaneously, and is modulated by the local splitting behavior. The pathways of preferential flow is controlled by the liquid volume triggered by avalanches and the network structure. The improved understanding from this study may shed new light on the complex flow dynamics for unsaturated flow in fractured media.</p>