scholarly journals On the Local Available Energetics in a Moist Compressible Atmosphere

2015 ◽  
Vol 72 (4) ◽  
pp. 1551-1561 ◽  
Author(s):  
Jun Peng ◽  
Lifeng Zhang ◽  
Yun Zhang
Keyword(s):  
Potential Temperature ◽  
Stable Stratification ◽  
Gravitational Energy ◽  
Reference State ◽  
Gradient Term ◽  
Available Energy ◽  
Energy Cycle ◽  
Compressible Atmosphere ◽  
Perturbation Pressure ◽  
Hydrostatic Balance

Abstract A new derivation of local available energetics for a fully compressible, nonhydrostatic, moist atmosphere is presented. The available energetics is defined relative to an arbitrary dry reference state in hydrostatic balance with stable stratification. By introducing the modified potential temperature, a positive-definite expression of the moist available potential energy (APE) is derived. The change of the moist APE must include the role of convection to function both as a source of latent heat and as an atmosphere dehumidifier. The sum of this moist APE and the available elastic energy (AEE) is the moist available energy. In the local energy cycle, the moist available energy is partly used to generate kinetic energy (KE) and partly used to lift the water vapor to the higher level where it precipitates, resulting in the increase of gravitational energy of moist species. The moist APE is converted into vertical KE through the buoyancy term; the vertical KE is converted into the AEE through the vertical perturbation pressure gradient term; and the AEE is converted into horizontal KE through the horizontal divergence/convergence term. In addition, there exist two adiabatic nonconservative processes, which act on the AEE and APE, respectively. A suitable choice of the reference state should make these two processes much less significant than the conversions between the available energy and KE. An alternative method is presented to construct such a reference state. Application to the idealized baroclinic atmosphere shows that this reference state is much more relevant to the local available energy analysis than the isothermal one.

scholarly journals Reexamining the Gradient and Countergradient Representation of the Local and Nonlocal Heat Fluxes in the Convective Boundary Layer

2018 ◽  
Vol 75 (7) ◽  
pp. 2317-2336 ◽  
Author(s):  
Bowen Zhou ◽  
Shiwei Sun ◽  
Kai Yao ◽  
Kefeng Zhu
Keyword(s):  
Boundary Layer ◽  
Temperature Gradient ◽  
Mixed Layer ◽  
Convective Boundary Layer ◽  
Correction Term ◽  
Potential Temperature ◽  
Heat Fluxes ◽  
Gradient Term ◽  
Convective Boundary ◽  
Upper Mixed Layer

Abstract Turbulent mixing in the daytime convective boundary layer (CBL) is carried out by organized nonlocal updrafts and smaller local eddies. In the upper mixed layer of the CBL, heat fluxes associated with nonlocal updrafts are directed up the local potential temperature gradient. To reproduce such countergradient behavior in parameterizations, a class of planetary boundary layer schemes adopts a countergradient correction term in addition to the classic downgradient eddy-diffusion term. Such schemes are popular because of their simple formulation and effective performance. This study reexamines those schemes to investigate the physical representations of the gradient and countergradient (GCG) terms, and to rebut the often-implied association of the GCG terms with heat fluxes due to local and nonlocal (LNL) eddies. To do so, large-eddy simulations (LESs) of six idealized CBL cases are performed. The GCG fluxes are computed a priori with horizontally averaged LES data, while the LNL fluxes are diagnosed through conditional sampling and Fourier decomposition of the LES flow field. It is found that in the upper mixed layer, the gradient term predicts downward fluxes in the presence of positive mean potential temperature gradient but is compensated by the upward countergradient correction flux, which is larger than the total heat flux. However, neither downward local fluxes nor larger-than-total nonlocal fluxes are diagnosed from LES. The difference reflects reduced turbulence efficiency for GCG fluxes and, in terms of physics, conceptual deficiencies in the GCG representation of CBL heat fluxes.

scholarly journals A Parameterization with a Constrained Potential Energy Conversion Rate of Vertical Mixing Due to Langmuir Turbulence

2019 ◽  
Vol 49 (11) ◽  
pp. 2935-2959 ◽  
Author(s):  
Brandon G. Reichl ◽  
Qing Li
Keyword(s):  
Turbulent Mixing ◽  
Vertical Mixing ◽  
Stable Stratification ◽  
Surface Boundary ◽  
Langmuir Turbulence ◽  
Surface Boundary Layer ◽  
Eddy Simulation ◽  
Available Energy ◽  
Climate Simulations ◽  
Surface Buoyancy

AbstractIn this study we develop a new parameterization for turbulent mixing in the ocean surface boundary layer (OSBL), including the effect of Langmuir turbulence. This new parameterization builds on a recent study (Reichl and Hallberg 2018, hereafter RH18), which predicts the available energy for turbulent mixing against stable stratification driven by shear and convective turbulence. To investigate the role of Langmuir turbulence in the framework of RH18, we utilize data from a suite of previously published large-eddy simulation (LES) experiments (Li and Fox-Kemper 2017, hereafter LF17) with and without Langmuir turbulence under different idealized forcing conditions. We find that the parameterization of RH18 is able to reproduce the mixing simulated by the LES in the non-Langmuir cases, but not the Langmuir cases. We therefore investigate the enhancement of the integrated vertical buoyancy flux within the entrainment layer in the presence of Langmuir turbulence using the LES data. An additional factor is introduced in the RH18 framework to capture the enhanced mixing due to Langmuir turbulence. This additional factor depends on the surface-layer averaged Langmuir number with a reduction in the presence of destabilizing surface buoyancy fluxes. It is demonstrated that including this factor within the RH18 OSBL turbulent mixing parameterization framework captures the simulated effect of Langmuir turbulence in the LES, which can be used for simulating the effect of Langmuir turbulence in climate simulations. This new parameterization is compared to the KPP-based Langmuir entrainment parameterization introduced by LF17, and differences are explored in detail.

Linking surface enthalpy fluxes to the forces driving the secondary circulation: towards a causal theory of tropical cyclone intensification

2020 ◽  
Author(s):  
Remi Tailleux ◽  
Bethan Harris ◽  
Christopher Holloway ◽  
Pier-Luigi Vidale
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Power Input ◽  
Causal Theory ◽  
Density Field ◽  
Secondary Circulation ◽  
Reference State ◽  
Available Potential Energy ◽  
Available Energy ◽  
Surface Enthalpy

<p>While it is well accepted that tropical cyclones (TCs) derive their energy from surface enthalpy fluxes over the ocean, there is still little understanding of the precise causes and effects by which the latter ends up as TC vortex kinetic energy. For example, Potential Intensity (PI) theory, which has been so far the main framework for predicting TC intensities, assumes a balance between the Carnot power input and the kinetic energy dissipated by surface friction, but says nothing of the detailed physical processes linking the two. A similar criticism pertains to the WISHE (Wind Induced Surface Heat Exchange) theory. To achieve a causal theory of TC intensification, the main difficulty is in linking the power input to kinetic energy production, rather than kinetic energy dissipation. Because kinetic energy is produced at the expense of available potential energy (APE), APE theory is arguably the most promising candidate framework for achieving a causal theory of TC intensification. However, in its current form, the usefulness of APE theory appears to be limited in a number of ways because of its reliance on a notional reference state of rest. First, APE production associated with standard reference states (i.e., horizontally averaged density field, density field of initial sounding, adiabatically sorted states, ...) is usually found to systematically overestimate the kinetic energy actually produced in ideal TC simulations, similarly as the Carnot theory of heat engines; moreover, the standard APE is only connected to vertical buoyancy forces, but says nothing of the radial forces required to drive the secondary circulation. To address these shortcomings, this work presents a new theory of available energy (AE) that is based on the use of an axisymmetric vortex reference state in gradient wind balance. This theory possesses the following advantages over previous frameworks:</p><p> </p><ul><li>The available energy (AE) thus constructed possesses both a mechanical and thermodynamic component. The thermodynamic component is analogous to the well-known Slantwise Convective Available Potential Energy (SCAPE), whereas the mechanical component is proportional to the anomalous azimuthal kinetic energy;</li> <li>The rate of AE production by surface enthalpy fluxes is found to be a very accurate predictor of the amount of potential energy actually converted into kinetic energy in idealised TC simulations based on the Rotunno and Emanuel (1986) axisymmetric model, although a few exceptions are found for cold SSTs;</li> <li>In addition to the expected thermodynamic efficiencies, the production term for AE also involves mechanical efficiencies predicting the fraction of the sinks/sources of angular momentum creating/destroying AE;</li> <li>The AE is related to a generalised buoyancy/inertial force that has both vertical and horizontal components; at low levels, such a generalised force has radially inward and vertically upward components, as required to drive the expected secondary circulation.</li> </ul><p>The new theory, therefore, appears to possess all the ingredients to form the basis for a causal theory of TC intensification.</p>

scholarly journals Inherent dissipation of upwind-biased potential temperature advection and its feedback on model dynamics

2021 ◽  
Author(s):  
Almut Gaßmann
Keyword(s):  
Energy Conservation ◽  
Pressure Gradient ◽  
Potential Temperature ◽  
Gradient Term ◽  
Advection Scheme ◽  
Temperature Advection ◽  
Advection Schemes ◽  
Pressure Gradient Term ◽  
Diffusive Fluxes ◽  
Total Energy Conservation

<p>Higher order upwind biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and anti-diffusive fluxes are interpreted here as the effect of irreversible sub-gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes.</p><p>The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one-dimensional advection-dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.</p>

scholarly journals Buoyancy of Convective Vertical Motions in the Inner Core of Intense Hurricanes. Part I: General Statistics

2005 ◽  
Vol 133 (1) ◽  
pp. 188-208 ◽  
Author(s):  
Matthew D. Eastin ◽  
William M. Gray ◽  
Peter G. Black
Keyword(s):  
Pressure Gradient ◽  
Vertical Velocity ◽  
Potential Temperature ◽  
Vertical Acceleration ◽  
Water Loading ◽  
Mesoscale Structure ◽  
Convective Scale ◽  
The Mean ◽  
Gradient Forces ◽  
Perturbation Pressure

Abstract The buoyancy of hurricane convective vertical motions is studied using aircraft data from 175 radial legs collected in 14 intense hurricanes at four altitudes ranging from 1.5 to 5.5 km. The data of each leg are initially filtered to separate convective-scale features from background mesoscale structure. Convective vertical motion events, called cores, are identified using the criteria that the convective-scale vertical velocity must exceed 1.0 m s−1 for at least 0.5 km. A total of 620 updraft cores and 570 downdraft cores are included in the dataset. Total buoyancy is calculated from convective-scale virtual potential temperature, pressure, and liquid water content using the mesoscale structure as the reference state. Core properties are summarized for the eyewall and rainband regions at each altitude. Characteristics of core average convective vertical velocity, maximum convective vertical velocity, and diameter are consistent with previous studies of hurricane convection. Most cores are superimposed upon relatively weak mesoscale ascent. The mean eyewall (rainband) updraft core exhibits small, but statistically significant, positive total buoyancy below 4 km (between 2 and 5 km) and a modest increase in vertical velocity with altitude. The mean downdraft core not superimposed upon stronger mesoscale ascent also exhibits positive total buoyancy and a slight decrease in downward vertical velocity with decreasing altitude. Buoyant updraft cores cover less than 5% of the total area in each region but accomplish ∼40% of the total upward transport. A one-dimensional updraft model is used to elucidate the relative roles played by buoyancy, vertical perturbation pressure gradient forces, water loading, and entrainment in the vertical acceleration of ordinary updraft cores. Small positive total buoyancy values are found to be more than adequate to explain the vertical accelerations observed in updraft core strength, which implies that ordinary vertical perturbation pressure gradient forces are directed downward, opposing the positive buoyancy forces. Entrainment and water loading are also found to limit updraft magnitudes. The observations support some aspects of both the hot tower hypothesis and symmetric moist neutral ascent, but neither concept appears dominant. Buoyant convective updrafts, however, are integral components of the hurricane’s transverse circulation.

scholarly journals Tropical Cyclogenesis Associated with Rossby Wave Energy Dispersion of a Preexisting Typhoon. Part II: Numerical Simulations*

2006 ◽  
Vol 63 (5) ◽  
pp. 1390-1409 ◽  
Author(s):  
Tim Li ◽  
Xuyang Ge ◽  
Bin Wang ◽  
Yongti Zhu
Keyword(s):  
Large Scale ◽  
Wave Train ◽  
Deep Convection ◽  
Potential Temperature ◽  
Stable Stratification ◽  
Temperature Fields ◽  
Tropical Cyclogenesis ◽  
Mean Flow ◽  
Energy Dispersion ◽  
Vorticity Generation

Abstract The cyclogenesis events associated with the tropical cyclone (TC) energy dispersion are simulated in a 3D model. A new TC with realistic dynamic and thermodynamic structures forms in the wake of a preexisting TC when a large-scale monsoon gyre or a monsoon shear line flow is present. Maximum vorticity generation appears in the planetary boundary layer (PBL) and the vorticity growth exhibits an oscillatory development. This oscillatory growth is also seen in the observed rainfall and cloud-top temperature fields. The diagnosis of the model output shows that the oscillatory development is attributed to the discharge and recharge of the PBL moisture and its interaction with convection and circulation. The moisture–convection feedback regulates the TC development through controlling the atmospheric stratification, raindrop-induced evaporative cooling and downdraft, PBL divergence, and vorticity generation. On one hand, ascending motion associated with deep convection transports moisture upward and leads to the discharge of PBL moisture and a convectively stable stratification. On the other hand, the convection-induced raindrops evaporate, leading to midlevel cooling and downdraft. The downdraft further leads to dryness and a reduction of equivalent potential temperature. This reduction along with the recharge of PBL moisture due to surface evaporation leads to reestablishment of a convectively unstable stratification and thus new convection. Sensitivity experiments with both a single mesh (with a 15-km resolution) and a nested mesh (with a 5-km resolution in the inner mesh) indicate that TC energy dispersion alone in a resting environment does not lead to cyclogenesis, suggesting the important role of the wave train–mean flow interaction. A proper initial condition for background wind and moisture fields is crucial for maintaining a continuous vorticity growth through the multioscillatory phases.

scholarly journals Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves

2014 ◽  
Vol 142 (12) ◽  
pp. 4439-4457 ◽  
Author(s):  
Hilary Weller ◽  
Ava Shahrokhi
Keyword(s):  
Pressure Gradient ◽  
Gravity Waves ◽  
Acoustic Waves ◽  
Gradient Term ◽  
Test Case ◽  
Pressure Gradients ◽  
Terrain Following ◽  
Bubble Rising ◽  
A New Technique ◽  
Hydrostatic Balance

Abstract Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modeling flow over orography is introduced that guarantees curl-free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain-following grids. Curl-free gradients are achieved by using the covariant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with NΔt up to at least 10 (where N is the Brunt–Väisälä frequency). A warm bubble rising over orography is simulated and the curl-free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

scholarly journals The Pretornadic Phase of the Goshen County, Wyoming, Supercell of 5 June 2009 Intercepted by VORTEX2. Part I: Evolution of Kinematic and Surface Thermodynamic Fields

2012 ◽  
Vol 140 (9) ◽  
pp. 2887-2915 ◽  
Author(s):  
Paul Markowski ◽  
Yvette Richardson ◽  
James Marquis ◽  
Joshua Wurman ◽  
Karen Kosiba ◽  
...  
Keyword(s):  
Potential Temperature ◽  
Radar Data ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Vertical Vorticity ◽  
Low Level ◽  
The Past ◽  
Virtual Potential Temperature ◽  
Perturbation Pressure ◽  
Negative Buoyancy

Abstract The authors analyze the pretornadic phase (2100–2148 UTC; tornadogenesis began at 2152 UTC) of the Goshen County, Wyoming, supercell of 5 June 2009 intercepted by the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). The analysis relies on radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) in Cheyenne, Wyoming (KCYS), and a pair of Doppler-on-Wheels (DOW) radars, mobile mesonet observations, and mobile sounding observations. The storm resembles supercells that have been observed in the past. For example, it develops a couplet of counter-rotating vortices that straddle the hook echo within the rear-flank outflow and are joined by arching vortex lines, with the cyclonic vortex becoming increasingly dominant in the time leading up to tornadogenesis. The outflow in the hook echo region, where sampled, has relatively small virtual potential temperature θυ deficits during this stage of evolution. A few kilometers upstream (north) of the location of maximum vertical vorticity, θυ is no more than 3 K colder than the warmest θυ readings in the inflow of the storm. Forward trajectories originating in the outflow within and around the low-level mesocyclone rise rapidly, implying that the upward-directed perturbation pressure gradient force exceeds the negative buoyancy. Low-level rotation intensifies in the 2142–2148 UTC period. The intensification is preceded by the formation of a descending reflectivity core (DRC), similar to others that have been documented in some supercells recently. The DRC is associated with a rapid increase in the vertical vorticity and circulation of the low-level mesocyclone.

scholarly journals A Semihydrostatic Theory of Gravity-Dominated Compressible Flow

2014 ◽  
Vol 71 (12) ◽  
pp. 4621-4638 ◽  
Author(s):  
Thomas Dubos ◽  
Fabrice Voitus
Keyword(s):  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Potential Temperature ◽  
Normal Modes ◽  
Additional Term ◽  
Internal Gravity Waves ◽  
Least Action Principle ◽  
Vertical Coordinate ◽  
Hydrostatic Balance

Abstract From Hamilton’s least-action principle, compressible equations of motion with density diagnosed from potential temperature through hydrostatic balance are derived. Slaving density to potential temperature suppresses the degrees of freedom supporting the propagation of acoustic waves and results in a soundproof system. The linear normal modes and dispersion relationship for an isothermal state of rest on f and β planes are accurate from hydrostatic to nonhydrostatic scales, except for deep internal gravity waves. Specifically, the Lamb wave and long Rossby waves are not distorted, unlike with anelastic or pseudoincompressible systems. Compared to similar equations derived by A. Arakawa and C. S. Konor, the semihydrostatic system derived here possesses an additional term in the horizontal momentum budget. This term is an apparent force resulting from the vertical coordinate not being the actual height of an air parcel but its hydrostatic height (the hypothetical height it would have after the atmospheric column it belongs to has reached hydrostatic balance through adiabatic vertical displacements of air parcels). The Lagrange multiplier λ introduced in Hamilton’s principle to slave density to potential temperature is identified as the nonhydrostatic vertical displacement (i.e., the difference between the actual and hydrostatic heights of an air parcel). The expression of nonhydrostatic pressure and apparent force from λ allow the derivation of a well-defined linear symmetric positive definite problem for λ. As with hydrostatic equations, vertical velocity is diagnosed through Richardson’s equation. The semihydrostatic system has therefore precisely the same degrees of freedom as the hydrostatic primitive equations, while retaining much of the accuracy of the fully compressible Euler equations.

scholarly journals Coastal Zone Surface Stress with Stable Stratification

2016 ◽  
Vol 46 (1) ◽  
pp. 95-105 ◽  
Author(s):  
L. Mahrt ◽  
Edgar L Andreas ◽  
James B. Edson ◽  
Dean Vickers ◽  
Jielun Sun ◽  
...  
Keyword(s):  
Potential Temperature ◽  
Stable Stratification ◽  
Eddy Correlation ◽  
Stable Boundary Layers ◽  
Stable Conditions ◽  
Mean Wind Speed ◽  
The Mean ◽  
Submeso Motions ◽  
Weak Winds ◽  
Nonstationary Conditions

AbstractSummertime eddy correlation measurements from an offshore tower are analyzed to investigate the dependence of the friction velocity for stable conditions on the mean wind speed V, air–sea difference of virtual potential temperature δθυ, and nonstationary submeso motions. The quantity δθυ sometimes exceeds 3°C, usually because of the advection of warm air from land over cooler water at this site. Thin stable boundary layers result. Unexpectedly, does not depend systematically on the stratification δθυ even for weak winds. For weak winds, increases systematically with increasing submeso variations of the wind. The relationship for a given V is greater in nonstationary conditions. Additionally, this study examines as a function of wind direction. The relationship appears to be affected by swell direction for weak winds and advection from land for short fetches.

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