Alex Mahalov

Invariant helical subspaces for the Navier-Stokes equations

AbstractThree-dimensional solutions with helical symmetry are shown to form an invariant subspace for the Navier-Stokes equations. Uniqueness of weak helical solutions in the sense of Leray is proved, and these weak solutions are shown to be regular (strong) solutions existing for arbitrary time t. The global universal attractor for the infinite-dimensional dynamical system generated by the corresponding semi-group of helical flows is shown to be compact and finite-dimensional. The Hausdorff and fractal dimensions of the global attractors are estimated in terms of the governing physical parameters and in terms of the helical parameters for several problems in the class, with the most detailed results obtained for rotating Hagen-Poiseuille (pipe) flow. In this case, the dimension, either Hausdorff or fractal, up to an absolute constant is bounded from above by

Seasonal hydroclimatic impacts of Sun Corridor expansion

\frac{{\operatorname{Re} }}{{\sqrt {\alpha ^2 + n^2 } }}

Quasi-equilibrium dynamics of shear-stratified turbulence in a model tropospheric jet

, where α is the axial wavenumber, n is the azimuthal wavenumber and Re is the Reynolds number based on the radius of the pipe. These upper bounds are independent of the rotation rate.

Variability of Turbulence and Its Outer Scales in a Model Tropopause Jet

This article investigates the effect of air conditioning (AC) systems on air temperature and examines their electricity consumption for a semiarid urban environment. We simulate a 10 day extreme heat period over the Phoenix metropolitan area (U.S.) with the Weather Research and Forecasting model coupled to a multilayer building energy scheme. The performance of the modeling system is evaluated against 10 Arizona Meteorological Network weather stations and one weather station maintained by the National Weather Service for air temperature, wind speed, and wind direction. We show that explicit representation of waste heat from air conditioning systems improved the 2 m air temperature correspondence to observations. Waste heat release from AC systems was maximum during the day, but the mean effect was negligible near the surface. However, during the night, heat emitted from AC systems increased the mean 2 m air temperature by more than 1°C for some urban locations. The AC systems modified the thermal stratification of the urban boundary layer, promoting vertical mixing during nighttime hours. The anthropogenic processes examined here (i.e., explicit representation of urban energy consumption processes due to AC systems) require incorporation in future meteorological and climate investigations to improve weather and climate predictability. Our results demonstrate that releasing waste heat into the ambient environment exacerbates the nocturnal urban heat island and increases cooling demands.

Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics

Conversion of natural to urban land forms imparts influence on local and regional hydroclimate via modification of the surface energy and water balance, and consideration of such effects due to rapidly expanding megapolitan areas is necessary in light of the growing global share of urban inhabitants. Based on a suite of ensemble-based, multi-year simulations using the Weather Research and Forecasting (WRF) model, we quantify seasonally varying hydroclimatic impacts of the most rapidly expanding megapolitan area in the US: Arizona’s Sun Corridor, centered upon the Greater Phoenix metropolitan area. Using a scenario-based urban expansion approach that accounts for the full range of Sun Corridor growth uncertainty through 2050, we show that built environment induced warming for the maximum development scenario is greatest during the summer season (regionally averaged warming over AZ exceeds 1 C). Warming remains significant during the spring and fall seasons (regionally averaged warming over AZ approaches 0.9 C during both seasons), and is least during the winter season (regionally averaged warming over AZ of 0.5 C). Impacts from a minimum expansion scenario are reduced, with regionally averaged warming ranging between 0.1 and 0.3 C for all seasons except winter, when no warming impacts are diagnosed. Integration of highly reflective cool roofs within the built environment, increasingly recognized as a cost-effective option intended to offset the warming influence of urban complexes, reduces urban-induced warming considerably. However, impacts on the hydrologic cycle are aggravated via enhanced evapotranspiration reduction, leading to a 4% total accumulated precipitation decrease relative to the non-adaptive maximum expansion scenario. Our results highlight potentially unintended consequences of this adaptation approach within rapidly expanding megapolitan areas, and emphasize the need for undeniably sustainable development paths that account for hydrologic impacts in addition to continued focus on mean temperature effects.

The instability of rotating fluid columns subjected to a weak external Coriolis force

Evaluation of built environment energy demand is necessary in light of global projections of urban expansion. Of particular concern are rapidly expanding urban areas in environments where consumption requirements for cooling are excessive. Here, we simulate urban air conditioning (AC) electric consumption for several extreme heat events during summertime over a semiarid metropolitan area with the Weather Research and Forecasting (WRF) model coupled to a multilayer building energy scheme. Observed total load values obtained from an electric utility company were split into two parts, one linked to meteorology (i.e., AC consumption) which was compared to WRF simulations, and another to human behavior. WRF-simulated non-dimensional AC consumption profiles compared favorably to diurnal observations in terms of both amplitude and timing. The hourly ratio of AC to total electricity consumption accounted for ?53% of diurnally averaged total electric demand, ranging from ?35% during early morning to ?65% during evening hours. Our work highlights the importance of modeling AC electricity consumption and its role for the sustainable planning of future urban energy needs. Finally, the methodology presented in this article establishes a new energy consumption-modeling framework that can be applied to any urban environment where the use of AC systems is prevalent.

Resonant triad interactions in symmetric systems

Direct numerical simulations are performed to study the dynamics of an inhomogeneous stratified shear flow that models an atmospheric jet centred at the tropopause across which the density stratification is non-uniform. Small to moderate background stratifications are selected, and simulations are conducted for a range of Reynolds and Froude numbers. A spectral domain decomposition method that is particularly suitable for simulations of non-uniformly stratified shear flows is developed to simulate the desired turbulent jet, and quasi-equilibrium flow fields are obtained by long-time integration of governing equations. The structures of the mean flow and turbulence fields are calculated, which are interpreted using relevant length scales (Ozmidov, buoyancy, shear, Ellison) and Richardson number profiles. The ratios of the Ellison to buoyancy scales are much smaller than unity at the jet core and approach unity at the edges, confirming that mechanical turbulence prevails in the jet core, while nonlinear waves and stratification effects are dominating at the jet edges. The jet core is found to support sustained mechanical (active) turbulence, outside which lay a region of patchy turbulence and nonlinear gravity wave activity characterized by spatially decaying velocity fluctuations and strong temperature fluctuations. Detailed energy budgets show how energy is partitioned within the flow, including the transport of energy from the jet to its immediate vicinity by nonlinear gravity waves.

Vertically nested nonhydrostatic model for multiscale resolution of flows in the upper troposphere and lower stratosphere

Abstract Variability of flow regimes and turbulence scalings in a model of an inhomogeneously stratified, tropopause jet is investigated through high-resolution, forced, three-dimensional numerical simulations (with 512 or 1024 vertical levels). Multivalued scaling branches, with respect to the local gradient Richardson number (Rig), are shown to occur in several turbulent quantities (such as variances, fluxes, mixing efficiency, outer scales, and their ratios, etc.). Two distinct scaling curves are found for the upper and lower flanks of the jet, each showing a clear branch switching at a critical height. Distinct scaling curves in the upper and lower flanks of the jet can be related to the doubling of buoyancy frequency (N) in the background profile (across the model tropopause). The vertical levels corresponding to the inflection points (maximal shearing) in the quasi-equilibrium turbulent mean jet velocity profile is identified as the best criterion for branch switching along each of the scaling curve...