On the Thickness Ratio in the Quasigeostrophic Two-Layer Model of Baroclinic Instability

2013 ◽  
Vol 70 (5) ◽  
pp. 1505-1511 ◽  
Author(s):  
Noboru Nakamura ◽  
Lei Wang
Keyword(s):  
Growth Rate ◽  
Vertical Structure ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Thickness Ratio ◽  
Layer Model ◽  
Optimal Thickness ◽  
Zonal Wavenumber ◽  
The Mean ◽  
Two Layer Model

Abstract It is shown that the classical quasigeostrophic two-layer model of baroclinic instability possesses an optimal ratio of layer thicknesses that maximizes the growth rate, given the basic-state shear (thermal wind), beta, and the mean Rossby radius. This ratio is interpreted as the vertical structure of the most unstable mode. For positive shear and beta, the optimal thickness of the lower layer approaches the midheight of the model in the limit of strong criticality (shear/beta) but it is proportional to criticality in the opposite limit. For a set of parameters typical of the earth’s midlatitudes, the growth rate maximizes at a lower-layer thickness substantially less than the midheight and at a correspondingly larger zonal wavenumber. It is demonstrated that a turbulent baroclinic jet whose statistical steady state is marginally critical when run with equal layer thicknesses can remain highly supercritical when run with a nearly optimal thickness ratio.

scholarly journals How Does the Vertical Profile of Baroclinicity Affect the Wave Instability?

2011 ◽  
Vol 68 (4) ◽  
pp. 863-877 ◽  
Author(s):  
Toshiki Iwasaki ◽  
Chihiro Kodama
Keyword(s):  
Growth Rate ◽  
Kinetic Energy ◽  
Wave Energy ◽  
Vertical Profile ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Instability Waves ◽  
P Flux ◽  
The Mean ◽  
Mean Kinetic Energy

Abstract The growth rate of baroclinic instability waves is generalized in terms of wave–mean flow interactions, with an emphasis on the influence of the vertical profile of baroclinicity. The wave energy is converted from the zonal mean kinetic energy and the growth rate is proportional to the mean zonal flow difference between the Eliassen–Palm (E-P) flux convergence and divergence areas. Mass-weighted isentropic zonal means facilitate the expression of the lower boundary conditions for the mass streamfunctions and E-P flux. For Eady waves, intersections of isentropes with lower/upper boundaries induce the E-P flux divergence/convergence. The growth rate is proportional to the mean zonal flow difference between the two boundaries, indicating that baroclinicity at each level contributes evenly to the instability. The reduced zonal mean kinetic energy is compensated by a conversion from the zonal mean available potential energy. Aquaplanet experiments are carried out to investigate the actual characteristics of baroclinic instability waves. The wave activity is shown to be sensitive to the upper-tropospheric baroclinicity, though it may be most sensitive to baroclinicity near 800 hPa, which is the maximal level of the E-P flux. The local wave energy generation rate suggests that the increased upper-tropospheric zonal flow directly enhances the upper-tropospheric wave energy at the midlatitudes. Note that the actual baroclinic instability waves accompany a considerable amount of the equatorward E-P flux, which causes extinction of wave energy in the subtropical upper troposphere.

scholarly journals Examining cerebral hemodynamics in a two-layer model of the human head using broadband near-infrared spectroscopy

2021 ◽  
Author(s):  
Olivia Pucci
Keyword(s):  
Optical Properties ◽  
Near Infrared ◽  
Continuous Wave ◽  
Lower Layer ◽  
Homogeneous Medium ◽  
Human Head ◽  
Cerebral Hemodynamics ◽  
Layer Model ◽  
Adult Human ◽  
Two Layer Model

The development of a continuous-wave method is presented, to quantify accurately the optical properties of a two-layer model of the human head using a broadband spectral approach. In particular, focus is put on the reconstruction of the absolute absorption and scattering properties of a two-layered phantom model of the human head with steady-state multi-distance measurements by performing differential fit analysis of the near-infrared (NIR) reflectance spectrum between 700 nm and 1000 nm. The two-layer model approximation was fitted to experimental broadband absorbance measurements obtained from two-layered phantoms with known optical properties. Results demonstrated that the suggested method was able to determine the optical properties of the lower layer with minimal error at specific source-detector distances. Preliminary results on the non-invasive measurement of the optical properties of the adult human brain in a two-layer approximation are presented. Finally, a mobile wireless NIR device is used to measure changes in the temporal characteristics of cerebral hemodynamic responses to functional brain activity, in particulaur the effect of smoking. Results suggest that assuming homogeneous medium for the adult human head severely underestimates the changes in cerebral hemodynamics. Hence, it is important to take surrounding layers into consideration when performing cerebral measurements using NIR spectroscopy.

scholarly journals Permanent bedforms in a theoretical model of wave-sea-bed interactions

2000 ◽  
Vol 7 (1/2) ◽  
pp. 31-35 ◽  
Author(s):  
J. M. Becker ◽  
D. Bercovici
Keyword(s):  
Theoretical Model ◽  
Nonlinear Response ◽  
External Surface ◽  
Lower Layer ◽  
Sea Waves ◽  
Layer Model ◽  
Periodic Forcing ◽  
Sea Bed ◽  
Two Layer Model ◽  
Large Wavelength

Abstract. The interaction between sea waves and a deformable sea-bed is studied with a simple two-layer model in which the upper-layer fluid is inviscid and the lower-layer fluid is bi-viscous to account for non-Newtonian behaviour of sand and sediments. The nonlinear response of the system to periodic forcing by an external surface pressure is determined. It is shown that a simple bi-viscous rheology allows small wavelength morphology in the lower layer to be generated from large wavelength surface waves in the upper inviscid layer, although the morphology is not permanent. For a bi-viscous rheology with a pressure-dependent yield stress (which accounts for the fact that sand yields less readily under loading than unloading), however, small wavelength and permanent features are formed in the seabed.

ELECTROMAGNETIC COUPLING BETWEEN GROUNDED WIRES AT THE SURFACE OF A TWO‐LAYER EARTH

Geophysics ◽  
1973 ◽  
Vol 38 (5) ◽  
pp. 854-863 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Numerical Solution ◽  
Lower Layer ◽  
Electromagnetic Coupling ◽  
Induced Polarization ◽  
Electrode Configuration ◽  
Smooth Transition ◽  
Layer Model ◽  
The Earth ◽  
Two Layer Model

A technique has been developed for computing the effects of electromagnetic coupling in induced polarization surveys, when the earth can be approximated by a two‐layer model. Results are given for the dipole‐dipole array, but the numerical solution described can be applied to any electrode configuration. No unusual effects were observed for the models computed. As the thickness of the upper layer is increased, there is a smooth transition between the coupling response of a homogeneous earth having the resistivity of the upper layer and that of a homogeneous earth having a resistivity equal to that of the lower layer.

Updraft/Downdraft Constraints for Moist Baroclinic Modes and Their Implications for the Short-Wave Cutoff and Maximum Growth Rate

2005 ◽  
Vol 62 (12) ◽  
pp. 4450-4458 ◽  
Author(s):  
Pablo Zurita-Gotor
Keyword(s):  
Growth Rate ◽  
Vertical Structure ◽  
Baroclinic Instability ◽  
Maximum Growth ◽  
Static Stability ◽  
Short Wave ◽  
Maximum Growth Rate ◽  
Unstable Solutions ◽  
Baroclinic Modes

Abstract This paper examines the dynamics of moist baroclinic modes, based on the idealized model of moist baroclinic instability devised by Emanuel et al. These authors found that the finite static stability along the downdraft prevents the explosive short-wave cyclogenesis of the zero stratification limit in the moist problem, and allows only moderate (order 2) changes in the growth rate and short-wave cutoff, even when the moist static stability vanishes. To understand the limiting role of the dry static stability, a constraint is derived in this paper that relates the updraft and downdraft structures. This constraint is based on continuity and implies that a bulk wavenumber (defined in the paper) scales as the relevant deformation radius in each region. Because neutral solutions are separable, the vertical structure can be encapsulated in terms of a single, equivalent wavenumber based on the downdraft width. This allows an interpretation of the results in terms of the equivalent dry mode. As the ratio between moist and dry static stability decreases, the downdraft width takes an increasingly larger fraction of the total wavelength. In the limit of moist neutrality all the wavelength is occupied by the downdraft, so that the short-wave cutoff is halved. The vertical phase tilt makes unstable solutions nonseparable, and prevents defining an equivalent wavenumber in that case. However, the constraint between the bulk wavenumbers still applies. As the moist stability is reduced, the updraft solution becomes more suboptimal; in the limit of moist neutrality, the updraft wavenumber equals the short-wave cutoff. This provides a bound to the maximum growth rate in the moist problem, which is in agreement with the results of Emanuel et al.

scholarly journals On the Sensitivity of Zonal-Index Persistence to Friction

2014 ◽  
Vol 71 (10) ◽  
pp. 3788-3800 ◽  
Author(s):  
Pablo Zurita-Gotor
Keyword(s):  
Internal Variability ◽  
Atmospheric Modeling ◽  
Spectral Structure ◽  
Layer Model ◽  
Internal Dynamics ◽  
Damping Effect ◽  
Long Time ◽  
Complex Models ◽  
The Mean ◽  
Two Layer Model

Abstract Friction is an important parameter in atmospheric modeling that may affect internal variability in a number of ways. It directly damps the annular-mode variability, but it also helps to maintain it through baroclinic feedbacks. Also, by determining the mean strength and position of the midlatitude jet, friction affects the internal dynamics that drive this variability. This work investigates the relevance of all of these factors for the sensitivity of the persistence of annular variability to changes in the zonal-mean friction using an idealized quasigeostrophic two-layer model. This model produces realistic variability, yet it is so simple that one can cleanly separate the different effects. It is found that the sensitivity of persistence to friction is dominated by the direct damping effect, while changes in the eddy momentum forcing and in the mean jet are not as important. As in more complex models, the persistence of the jet anomalies in this model decreases at all lags with increasing friction, but the long-time decorrelation decay rate of these anomalies is remarkably insensitive to friction. Although this implies that the eddy feedback must increase with friction to maintain the anomalies against the enhanced damping, it is shown that this is not due to baroclinic effects. A model that assumes that the eddy forcing does not change with friction can reproduce reasonably well the numerical results. The crucial factor that determines the model’s sensitivity to friction is the spectral structure of the eddy momentum forcing.

scholarly journals Baroclinic Flow around Planetary Islands in a Double Gyre: A Mechanism for Cross-Gyre Flow

2010 ◽  
Vol 40 (5) ◽  
pp. 1075-1086
Author(s):  
Joseph Pedlosky
Keyword(s):  
Vertical Structure ◽  
Vertical Mixing ◽  
Ocean Bottom ◽  
Layer Model ◽  
Buoyancy Forcing ◽  
Pressure Anomaly ◽  
Two Layer Model ◽  
Baroclinic Flow ◽  
Double Gyre

Abstract A quasigeostrophic, two-layer model is used to study the baroclinic circulation around a thin, meridionally elongated island. The flow is driven by either buoyancy forcing or wind stress, each of whose structure would produce an antisymmetric double-gyre flow. The ocean bottom is flat. When the island partially straddles the intergyre boundary, fluid from one gyre is forced to flow into the other. The amount of the intergyre flow depends on the island constant, that is, the value of the geostrophic streamfunction on the island in each layer. That constant is calculated in a manner similar to earlier studies and is determined by the average, along the meridional length of the island, of the interior Sverdrup solution just to the east of the island. Explicit solutions are given for both buoyancy and wind-driven flows. The presence of an island of nonzero width requires the determination of the baroclinic streamfunction on the basin’s eastern boundary. The value of the boundary term is proportional to the island’s area. This adds a generally small additional baroclinic intergyre flow. In all cases, the intergyre flow produced by the island is not related to topographic steering of the flow but rather the pressure anomaly on the island as manifested by the barotropic and baroclinic island constants. The vertical structure of the flow around the island is a function of the parameterization of the vertical mixing in the problem and, in particular, the degree to which long baroclinic Rossby waves can traverse the basin before becoming thermally damped.

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