scholarly journals Quasigeostrophic Turbulence with Explicit Surface Dynamics: Application to the Atmospheric Energy Spectrum

2009 ◽  
Vol 66 (2) ◽  
pp. 450-467 ◽  
Author(s):  
Ross Tulloch ◽  
K. Shafer Smith
Keyword(s):  
Surface Temperature ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Temperature Gradients ◽  
Vertical Shear ◽  
Model Driven ◽  
Function Solution ◽  
Mean Temperature ◽  
Small Scales ◽  
Quasigeostrophic Model

Abstract The horizontal wavenumber spectra of wind and temperature near the tropopause have a steep −3 slope at synoptic scales and a shallower −5/3 slope at mesoscales, with a transition between the two regimes at a wavelength of about 450 km. Here it is demonstrated that a quasigeostrophic model driven by baroclinic instability exhibits such a transition near its upper boundary (analogous to the tropopause) when surface temperature advection at that boundary is properly resolved and forced. To accurately represent surface advection at the upper and lower boundaries, the vertical structure of the model streamfunction is decomposed into four parts, representing the interior flow with the first two neutral modes, and each surface with its Green’s function solution, resulting in a system with four prognostic equations. Mean temperature gradients are applied at each surface, and a mean potential vorticity gradient consisting both of β and vertical shear is applied in the interior. The system exhibits three fundamental types of baroclinic instability: interactions between the upper and lower surfaces (Eady type), interactions between one surface and the interior (Charney type), and interactions between the barotropic and baroclinic interior modes (Phillips type). The turbulent steady states that result from each of these instabilities are distinct, and those of the former two types yield shallow kinetic energy spectra at small scales along those boundaries where mean temperature gradients are present. When both mean interior and surface gradients are present, the surface spectrum reflects a superposition of the interior-dominated −3 slope cascade at large scales, and the surface-dominated −5/3 slope cascade at small scales. The transition wavenumber depends linearly on the ratio of the interior potential vorticity gradient to the surface temperature gradient, and scales with the inverse of the deformation scale when β = 0.

scholarly journals Role of Surface-Layer Coherent Eddies in Potential Vorticity Transport in Quasigeostrophic Turbulence Driven by Eastward Shear

Fluids ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 2
Author(s):  
Wenda Zhang ◽  
Christopher L. P. Wolfe ◽  
Ryan Abernathey
Keyword(s):  
Surface Layer ◽  
Potential Vorticity ◽  
Model Driven ◽  
Wide Range ◽  
Stirring Effect ◽  
Geophysical Turbulence ◽  
Quasigeostrophic Model ◽  
Vorticity Transport ◽  
Pv Gradient

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10–20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient PV transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 15% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. These results clarify the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence.

scholarly journals Self-Organization of Atmospheric Macroturbulence into Critical States of Weak Nonlinear Eddy–Eddy Interactions

2006 ◽  
Vol 63 (6) ◽  
pp. 1569-1586 ◽  
Author(s):  
Tapio Schneider ◽  
Christopher C. Walker
Keyword(s):  
Surface Temperature ◽  
Thermal Stratification ◽  
Nonlinear Models ◽  
Thermal Structure ◽  
Baroclinic Instability ◽  
Temperature Gradients ◽  
Tropopause Height ◽  
Weakly Nonlinear ◽  
Critical States ◽  
Inverse Energy Cascade

Abstract It is generally held that atmospheric macroturbulence can be strongly nonlinear. Yet weakly nonlinear models successfully account for scales and structures of baroclinic eddies in Earth's atmosphere. Here a theory and simulations with an idealized GCM are presented that suggest weakly nonlinear models are so successful because atmospheric macroturbulence organizes itself into critical states of weak nonlinear eddy–eddy interactions. By modifying the thermal structure of the extratropical atmosphere such that its supercriticality remains limited, macroturbulence inhibits nonlinear eddy–eddy interactions and the concomitant inverse energy cascade from the length scales of baroclinic instability to larger scales. For small meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are set by radiation and convection, and the supercriticality is less than one; for sufficiently large meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are modified by baroclinic eddies such that the supercriticality does not significantly exceed one. In either case, the scale of the energy-containing eddies is similar to the scale of the linearly most unstable baroclinic waves, and eddy kinetic and available potential energies are equipartitioned. The theory and simulations point to fundamental constraints on the thermal structures and global circulations of the atmospheres of Earth and other planets, for example, by providing limits on the tropopause height and estimates for eddy scales, eddy energies, and jet separation scales.

Vortex Dipole Formation by Baroclinic Instability of Boundary Currents

2007 ◽  
Vol 37 (6) ◽  
pp. 1661-1677 ◽  
Author(s):  
L. Chérubin ◽  
X. Carton ◽  
D. G. Dritschel
Keyword(s):  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Point Vortex ◽  
Wave Dispersion ◽  
Finite Amplitude ◽  
Layer Potential ◽  
Weakly Nonlinear ◽  
In Situ Data ◽  
Vortex Dipole ◽  
Quasigeostrophic Model

Abstract In situ data of the Mediterranean Water undercurrents and eddies south of Portugal indicate that the undercurrents have a tubelike structure in potential vorticity and that dipole formation can occur when the lower undercurrent extends seaward below an offshore upper countercurrent. A two-layer quasigeostrophic model is used to determine the dynamical conditions under which dipole formation is possible. With piecewise-constant potential vorticity, the flow exhibits two linear modes of instability comparable to those found in the Phillips model with topography. Weakly nonlinear analysis and fully nonlinear simulations of the flow evolution agree on the regimes of either finite-amplitude perturbation saturation, corresponding to filamentation, or amplification, corresponding to vortex or dipole formation. This latter regime is more specifically studied: vortex dipole formation and ejection from the coast is obtained for long waves, with opposite-signed but similar amplitude layer potential vorticities. A simple point vortex model reproduces this phenomenon under the same conditions. It is then shown that dipole formation occurs for minimal wave dispersion, and hence for weak horizontal velocity shears. As observed at sea, dipoles are formed when the lower potential vorticity core extends seaward below a countercurrent.

Non-geostrophic instabilities of an equilibrium baroclinic state

2013 ◽  
Vol 734 ◽  
pp. 535-566 ◽  
Author(s):  
Alexandre B. Pieri ◽  
F. S. Godeferd ◽  
C. Cambon ◽  
A. Salhi
Keyword(s):  
Numerical Simulations ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Dimensionless Numbers ◽  
Stability Bound ◽  
Simultaneous Existence ◽  
The Stability ◽  
Symmetric Instability

AbstractWe consider non-geostrophic homogeneous baroclinic turbulence without solid boundaries, and we focus on its energetics and dynamics. The homogeneous turbulent flow is therefore submitted to both uniform vertical shear $S$ and stable vertical stratification, parametrized by the Brunt–Väisälä frequency $N$, and placed in a rotating frame with Coriolis frequency $f$. Direct numerical simulations show that the threshold of baroclinic instability growth depends mostly on two dimensionless numbers, the gradient Richardson number $\mathit{Ri}= {N}^{2} / {S}^{2} $ and the Rossby number $\mathit{Ro}= S/ f$, whereas linear theory predicts a threshold that depends only on $\mathit{Ri}$. At high Rossby numbers the nonlinear limit is found to be $\mathit{Ri}= 0. 2$, while in the limit of low $\mathit{Ro}$ the linear stability bound $\mathit{Ri}= 1$ is recovered. We also express the stability results in terms of background potential vorticity, which is an important quantity in baroclinic flows. We show that the linear symmetric instability occurs from the presence of negative background potential vorticity. The possibility of simultaneous existence of symmetric and baroclinic instabilities is also investigated. The dominance of symmetric instability over baroclinic instability for $\mathit{Ri}\ll 1$ is confirmed by our direct numerical simulations, and we provide an improved understanding of the dynamics of the flow by exploring the details of energy transfers for moderate Richardson numbers.

scholarly journals Stratification Analysis and Behaviour of a Real Industrial Thermocline Thermal Energy Storage Tank for Cogeneration Purposes

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 120
Author(s):  
Francisco Fernández ◽  
José Díaz ◽  
María Folgueras ◽  
Inés Suárez
Keyword(s):  
Energy Storage ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Control Strategies ◽  
Storage System ◽  
Good Control ◽  
Energy Storage System ◽  
Temperature Gradients ◽  
Operation Conditions ◽  
Mean Temperature

Thermal energy storage systems help to couple thermal energy generation and process demand in cogeneration facilities. One single deposit with two design temperatures and one main temperature step in sensible thermal energy storage define the thermocline systems. Performance of one high size real thermocline thermal energy storage system is analysed. Starting from temperature and mass flow rate data registered by the plant control system, one advanced thermodynamic analysis is performed. The quality of heat storage is analysed in terms of evaluation of the stratification in the thermocline zone. The temperature data registered at 21 positions is extended by displacement analysis generating detailed profiles. Fraction of recoverable heat, thermocline width, stratification indices based on energy and exergy analysis, and mean temperature gradients in the thermocline region are calculated. These parameters are monitored under real operation conditions of the plant. The calculated parameters are studied to check their distribution and correlation. First and Second Law indices show parallel behaviour and two values are found that delimit situations of high and low values of mean temperature gradients. It was observed that buoyancy generates uniform forced movement with the right water temperature entering the diffusers, but good control strategies are essential to avoid mixing. The system demonstrated great stability in this use.

scholarly journals Stability Analysis of the Labrador Current

2014 ◽  
Vol 44 (2) ◽  
pp. 445-463 ◽  
Author(s):  
Sören Thomsen ◽  
Carsten Eden ◽  
Lars Czeschel
Keyword(s):  
Stability Analysis ◽  
Growth Rates ◽  
Baroclinic Instability ◽  
Cross Flow ◽  
Vertical Shear ◽  
Maximal Growth ◽  
Phase Velocities ◽  
Labrador Current ◽  
Lateral Mixing ◽  
Weak Stratification

Abstract Mooring observations and model simulations point to an instability of the Labrador Current (LC) during winter, with enhanced eddy kinetic energy (EKE) at periods between 2 and 5 days and much less EKE during other seasons. Linear stability analysis using vertical shear and stratification from the model reveals three dominant modes of instability in the LC: 1) a balanced interior mode with along-flow wavelengths of about 30–45 km, phase velocities of 0.3 m s−1, maximal growth rates of 1 day−1, and surface-intensified but deep-reaching amplitudes; 2) a balanced shallow mode with along-flow wavelengths of about 0.3–1.5 km, phase velocities of 0.55 m s−1, about 3 times larger growth rates, but amplitudes confined to the mixed layer (ML); and 3) an unbalanced symmetric mode with the largest growth rates, vanishing phase speeds, and along-flow structure, and very small cross-flow wavelengths, also confined to the ML. Both balanced modes are akin to baroclinic instability but operate at moderate-to-small Richardson numbers Ri with much larger growth rates as for the quasigeostrophic limit of Ri ≫ 1. The interior mode is found to be responsible for the instability of the LC during winter. Weak stratification and enhanced vertical shear due to local buoyancy loss and the advection of convective water masses from the interior result in small Ri within the LC and up to 3 times larger growth rates of the interior mode in March compared to summer and fall conditions. Both the shallow and the symmetric modes are not resolved by the model, but it is suggested that they might also play an important role for the instability in the LC and for lateral mixing.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

Lagrangian pair dispersion in upper-ocean turbulent flows with mixed-layer instabilities

2021 ◽  
Author(s):  
Stefano Berti ◽  
Guillaume Lapeyre
Keyword(s):  
Turbulent Flows ◽  
Mixed Layer ◽  
Separation Distance ◽  
Vertical Shear ◽  
Spreading Process ◽  
Opposite Case ◽  
Dispersion Regime ◽  
Fluid Layers ◽  
Small Scales ◽  
Good Proxy

<p>Oceanic motions at scales larger than few tens of km are quasi-horizontal due to seawater stratification and Earth’s rotation and are characterized by quasi-two-dimensional turbulence. At scales around 300 km (in the mesoscale range), coherent vortices contain most of the kinetic energy in the ocean. At scales around 10 km (in the submesoscale range) the flow is populated by smaller eddies and filamentary structures associated with intense gradients (e.g. of temperature), which play an important role in both physical and biogeochemical budgets. Such small scales are found mainly in the weakly stratified mixed layer, lying on top of the more stratified thermocline. Submesoscale dynamics should strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the generation of energetic small scales that are not trapped at the surface, as those arising from mesoscale-driven processes, but extend down to the thermocline. The knowledge of the transport properties of oceanic flows at depth, which is essential to understand the coupling between surface and interior dynamics, however, is still limited.</p><p>By means of numerical simulations, we explore Lagrangian pair dispersion in turbulent flows from a quasi-geostrophic model consisting in two coupled fluid layers (representing the mixed layer and the thermocline) with different stratification. Such a model has been previously shown to give rise to both meso and submesoscale instabilities and subsequent turbulent dynamics that compare well with observations of wintertime submesoscale flows. We focus on the identification of different dispersion regimes and on the possibility to relate the characteristics of the spreading process at the surface and at depth, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the experimentally more accessible (e.g. by satellite altimetry) surface ones.</p><p>Using different statistical indicators, we find a clear transition of dispersion regime with depth, which is generic and can be related to the statistical features of the turbulent flows. The spreading process is local (namely, governed by eddies of the same size as the particle separation distance) at the surface. In the absence of a mixed layer it rapidly changes to nonlocal (meaning essentially driven by the largest eddies) at small depths, while in the opposite case this only occurs at larger depths, below the mixed layer. We then identify the origin of such behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. We further discuss the effect of vertical shear and address the properties of the relative motion of subsurface particles with respect to surface ones. In the absence of a mixed layer, the properties of the spreading process are found to rapidly decorrelate from those at the surface, but the relation between the surface and subsurface dispersion appears to be largely controlled by vertical shear. In the presence of mixed-layer instabilities, instead, the statistical properties of dispersion at the surface are found to be a good proxy for those in the whole mixed layer.</p>

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