scholarly journals A Note on the Numerical Representation of Surface Dynamics in Quasigeostrophic Turbulence: Application to the Nonlinear Eady Model

2009 ◽  
Vol 66 (4) ◽  
pp. 1063-1068 ◽  
Author(s):  
Ross Tulloch ◽  
K. Shafer Smith
Keyword(s):  
Numerical Models ◽  
Buoyancy Frequency ◽  
Complete Suppression ◽  
Numerical Representation ◽  
Vertical Resolution ◽  
Surface Dynamics ◽  
Coriolis Parameter ◽  
Theoretical Predictions ◽  
Vertical Grid ◽  
Similar Restriction

Abstract The quasigeostrophic equations consist of the advection of linearized potential vorticity coupled with advection of temperature at the bounding upper and lower surfaces. Numerical models of quasigeostrophic flow often employ greater (scaled) resolution in the horizontal than in the vertical (the two-layer model is an extreme example). In the interior, this has the effect of suppressing interactions between layers at horizontal scales that are small compared to Nδz/f (where δz is the vertical resolution, N the buoyancy frequency, and f the Coriolis parameter). The nature of the turbulent cascade in the interior is, however, not fundamentally altered because the downscale cascade of potential enstrophy in quasigeostrophic turbulence and the downscale cascade of enstrophy in two-dimensional turbulence (occurring layerwise) both yield energy spectra with slopes of −3. It is shown here that a similar restriction on the vertical resolution applies to the representation of horizontal motions at the surfaces, but the penalty for underresolving in the vertical is complete suppression of the surface temperature cascade at small scales and a corresponding artificial steepening of the surface energy spectrum. This effect is demonstrated in the nonlinear Eady model, using a finite-difference representation in comparison with a model that explicitly advects temperature at the upper and lower surfaces. Theoretical predictions for the spectrum of turbulence in the nonlinear Eady model are reviewed and compared to the simulated flows, showing that the latter model yields an accurate representation of the cascade dynamics. To accurately represent dynamics at horizontal wavenumber K in the vertically finite-differenced model, it is found that the vertical grid spacing must satisfy δz ≲ 0.3f/(NK); at wavenumbers K > 0.3f/(Nδz), the spectrum of temperature variance rolls off rapidly.

scholarly journals Buoyancy Arrest and Shelf–Ocean Exchange

2012 ◽  
Vol 42 (4) ◽  
pp. 644-658 ◽  
Author(s):  
K. H. Brink
Keyword(s):  
Boundary Layer ◽  
Numerical Models ◽  
Spatial Scales ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Strong Constraint ◽  
Bottom Boundary ◽  
Stratified Ocean

Abstract When steady flow in a stratified ocean passes between the continental slope and open ocean, its ability to cross isobaths is potentially limited by buoyancy arrest. If the bottom Ekman transport vanishes and there are no interior stresses, then steady linear flow on an f plane must be geostrophic and follow isobaths exactly. The influence of arrest on cross-shelf transport is investigated here to establish 1) whether there are substantial penetration asymmetries between cases with upwelling and downwelling in the bottom boundary layer; 2) over what spatial scales, hence in what parameter regime, buoyancy arrest is important; and 3) the effects of depth-dependent interior flow. The problem is approached using scalings and idealized numerical models. The results show that there is little or no asymmetry introduced by bottom boundary layer behavior. Further, if the stratification is weak or moderate, as measured by a slope Burger number s = αN/f (where α is the bottom slope, N is buoyancy frequency, and f is the Coriolis parameter), buoyancy arrest does not exert a strong constraint on cross-isobath exchange.

scholarly journals Length Scale of the Finite-Amplitude Meanders of Shelfbreak Fronts

2015 ◽  
Vol 45 (10) ◽  
pp. 2598-2620 ◽  
Author(s):  
Weifeng G. Zhang ◽  
Glen G. Gawarkiewicz
Keyword(s):  
Numerical Models ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Buoyancy Frequency ◽  
Length Scale ◽  
Initial Growth ◽  
Coriolis Parameter ◽  
Frontal Instability ◽  
Symmetric Instability ◽  
Empirical Constants

AbstractThrough combining analytical arguments and numerical models, this study investigates the finite-amplitude meanders of shelfbreak fronts characterized by sloping isopycnals outcropping at both the surface and the shelfbreak bottom. The objective is to provide a formula for the meander length scale that can explain observed frontal length scale variability and also be verified with observations. Considering the frontal instability to be a mixture of barotropic and baroclinic instability, the derived along-shelf meander length scale formula is [b1/(1 + a1S1/2)]NH/f, where N is the buoyancy frequency; H is the depth of the front; f is the Coriolis parameter; S is the Burger number measuring the ratio of energy conversion associated with barotropic and baroclinic instability; and a1 and b1 are empirical constants. Initial growth rate of the frontal instability is formulated as [b2(1 + a1S1/2)/(1 + a2αS1/2)]NH/L, where α is the bottom slope at the foot of the front, and a2 and b2 are empirical constants. The formulas are verified using numerical sensitivity simulations, and fitting of the simulated and formulated results gives a1 = 2.69, b1 = 14.65, a2 = 5.1 × 103, and b2 = 6.2 × 10−2. The numerical simulations also show development of fast-growing frontal symmetric instability when the minimum initial potential vorticity is negative. Although frontal symmetric instability leads to faster development of barotropic and baroclinic instability at later times, it does not significantly influence the meander length scale. The derived meander length scale provides a framework for future studies of the influences of external forces on shelfbreak frontal circulation and cross-frontal exchange.

scholarly journals Surface signature of Mediterranean water eddies in the Northeastern Atlantic: effect of the upper ocean stratification

Ocean Science ◽  
2012 ◽  
Vol 8 (6) ◽  
pp. 931-943 ◽  
Author(s):  
I. Bashmachnikov ◽  
X. Carton
Keyword(s):  
Potential Vorticity ◽  
Initial Period ◽  
Relative Vorticity ◽  
Sea Surface ◽  
Upper Ocean ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Ocean Stratification ◽  
Surface Signature ◽  
Mediterranean Water

Abstract. Meddies, intra-thermocline eddies of Mediterranean water, can often be detected at the sea surface as positive sea-level anomalies. Here we study the surface signature of several meddies tracked with RAFOS floats and AVISO altimetry. While pushing its way through the water column, a meddy raises isopycnals above. As a consequence of potential vorticity conservation, negative relative vorticity is generated in the upper layer. During the initial period of meddy acceleration after meddy formation or after a stagnation stage, a cyclonic signal is also generated at the sea-surface, but mostly the anticyclonic surface signal follows the meddy. Based on geostrophy and potential vorticity balance, we present theoretical estimates of the intensity of the surface signature. It appears to be proportional to the meddy core radius and to the Coriolis parameter, and inversely proportional to the core depth and buoyancy frequency. This indicates that surface signature of a meddy may be strongly reduced by the upper ocean stratification. Using climatic distribution of the stratification intensity, we claim that the southernmost limit for detection in altimetry of small meddies (with radii on the order of 10–15 km) should lie in the subtropics (35–45° N), while large meddies (with radii of 25–30 km) could be detected as far south as the northern tropics (25–35° N). Those results agree with observations.

Suppression of Baroclinic Instabilities in Buoyancy-Driven Flow over Sloping Bathymetry

2017 ◽  
Vol 47 (1) ◽  
pp. 49-68 ◽  
Author(s):  
Robert D. Hetland
Keyword(s):  
Growth Rate ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Buoyancy Frequency ◽  
Bottom Slope ◽  
Coriolis Parameter ◽  
Plume Front ◽  
Instability Theory ◽  
Instability Growth ◽  
Flow Configurations

AbstractBaroclinic instabilities are ubiquitous in many types of geostrophic flow; however, they are seldom observed in river plumes despite strong lateral density gradients within the plume front. Supported by results from a realistic numerical simulation of the Mississippi–Atchafalaya River plume, idealized numerical simulations of buoyancy-driven flow are used to investigate baroclinic instabilities in buoyancy-driven flow over a sloping bottom. The parameter space is defined by the slope Burger number S = Nf−1α, where N is the buoyancy frequency, f is the Coriolis parameter, and α is the bottom slope, and the Richardson number Ri = N2f2M−4, where M2 = |∇Hb| is the magnitude of the lateral buoyancy gradients. Instabilities only form in a subset of the simulations, with the criterion that SH ≡ SRi−1/2 = Uf−1W−1 = M2f−2α 0.2, where U is a horizontal velocity scale and SH is a new parameter named the horizontal slope Burger number. Suppression of instability formation for certain flow conditions contrasts linear stability theory, which predicts that all flow configurations will be subject to instabilities. The instability growth rate estimated in the nonlinear 3D model is proportional to ωImaxS−1/2, where ωImax is the dimensional growth rate predicted by linear instability theory, indicating that bottom slope inhibits instability growth beyond that predicted by linear theory. The constraint SH 0.2 implies a relationship between the inertial radius Li = Uf−1 and the plume width W. Instabilities may not form when 5Li > W; that is, the plume is too narrow for the eddies to fit.

scholarly journals Dependence of Model Energy Spectra on Vertical Resolution

2016 ◽  
Vol 144 (4) ◽  
pp. 1407-1421 ◽  
Author(s):  
Michael L. Waite
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Vertical Mixing ◽  
Energy Spectra ◽  
Small Scale ◽  
Rossby Number ◽  
Vertical Resolution ◽  
Wide Range ◽  
Qualitative Shape ◽  
Vertical Grid

Abstract Many high-resolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a power-law slope of −3 at large horizontal scales that shallows to approximately −5/3 in the mesoscale. This paper investigates the possible dependence of model energy spectra on the vertical grid resolution. Idealized simulations forced by relaxation to a baroclinically unstable jet are performed for a wide range of vertical grid spacings Δz. Energy spectra are converged for Δz 200 m but are very sensitive to resolution with 500 m ≤ Δz ≤ 2 km. The nature of this sensitivity depends on the vertical mixing scheme. With no vertical mixing or with weak, stability-dependent mixing, the mesoscale spectra are artificially amplified by low resolution: they are shallower and extend to larger scales than in the converged simulations. By contrast, vertical hyperviscosity with fixed grid-scale damping rate has the opposite effect: underresolved spectra are spuriously steepened. High-resolution spectra are converged except for the stability-dependent mixing case, which are damped by excessive mixing due to enhanced shear over a wide range of horizontal scales. It is shown that converged spectra require resolution of all vertical scales associated with the resolved horizontal structures: these include quasigeostrophic scales for large-scale motions with small Rossby number and the buoyancy scale for small-scale motions at large Rossby number. It is speculated that some model energy spectra may be contaminated by low vertical resolution, and it is recommended that vertical-resolution sensitivity tests always be performed.

Role of Vertical Resolution in Numerical Models Towards the Intensification, Structure and Track of Tropical Cyclones

2010 ◽  
Vol 33 (4) ◽  
pp. 338-355 ◽  
Author(s):  
D. V. Bhaskar Rao ◽  
D. Hari Prasad ◽  
D. Srinivas ◽  
Y. Anjaneyulu
Keyword(s):  
Tropical Cyclones ◽  
Numerical Models ◽  
Vertical Resolution

Measurements of diapycnal diffusivities in stratified fluids

2001 ◽  
Vol 442 ◽  
pp. 267-291 ◽  
Author(s):  
MICHAEL E. BARRY ◽  
GREGORY N. IVEY ◽  
KRAIG B. WINTERS ◽  
JÖRG IMBERGER
Keyword(s):  
Root Mean Square ◽  
Buoyancy Frequency ◽  
Data Sets ◽  
Laboratory System ◽  
Mean Square ◽  
Wide Range ◽  
Vertical Grid ◽  
Order Of Magnitude ◽  
Set Up ◽  
Rate Of Dissipation

Linearly stratified salt solutions of different Prandtl number were subjected to turbulent stirring by a horizontally oscillating vertical grid in a closed laboratory system. The experimental set-up allowed the independent direct measurement of a root mean square turbulent lengthscale Lt, turbulent diffusivity for mass Kρ, rate of dissipation of turbulent kinetic energy ε, buoyancy frequency N and viscosity v, as time and volume averaged quantities. The behaviour of both Lt and Kρ was characterized over a wide range of the turbulence intensity measure, ε/vN2, and two regimes were identified.In the more energetic of these regimes (Regime E, where 300 < ε/vN2 < 105), Lt was found to be a function of v, κ and N, whilst Kρ was a function of v, κ and (ε/vN2)1/3. From these expressions for Lt and Kρ, a scaling relation for the root mean square turbulent velocity scale Ut was derived, and this relationship showed good agreement with direct measurements from other data sets.In the weaker turbulence regime (Regime W, where 10 < ε/vN2 < 300) Kρ was a function of v, κ and ε/vN2.For 10 < ε/vN2 < 1000, our directly measured diffusivities, Kρ, are approximately a factor of 2 different to the diffusivity predicted by the model of Osborn (1980). For ε/vN2 > 1000, our measured diffusivities diverge from the model prediction. For example, at ε/vN2 ≈ 104 there is at least an order of magnitude difference between the measured and predicted diffusivities.

scholarly journals Harmonized dataset of ozone profiles from satellite limb and occultation measurements

2013 ◽  
Vol 5 (2) ◽  
pp. 349-363 ◽  
Author(s):  
V. F. Sofieva ◽  
N. Rahpoe ◽  
J. Tamminen ◽  
E. Kyrölä ◽  
N. Kalakoski ◽  
...  
Keyword(s):  
European Space Agency ◽  
Original Data ◽  
Data Consistency ◽  
Vertical Resolution ◽  
Data Merging ◽  
Space Agency ◽  
Vertical Range ◽  
Uncertainty Estimates ◽  
Vertical Grid ◽  
User Friendly

Abstract. In this paper, we present a HARMonized dataset of OZone profiles (HARMOZ) based on limb and occultation measurements from Envisat (GOMOS, MIPAS and SCIAMACHY), Odin (OSIRIS, SMR) and SCISAT (ACE-FTS) satellite instruments. These measurements provide high-vertical-resolution ozone profiles covering the altitude range from the upper troposphere up to the mesosphere in years 2001–2012. HARMOZ has been created in the framework of the European Space Agency Climate Change Initiative project. The harmonized dataset consists of original retrieved ozone profiles from each instrument, which are screened for invalid data by the instrument teams. While the original ozone profiles are presented in different units and on different vertical grids, the harmonized dataset is given on a common pressure grid in netCDF (network common data form)-4 format. The pressure grid corresponds to vertical sampling of ~ 1 km below 20 km and 2–3 km above 20 km. The vertical range of the ozone profiles is specific for each instrument, thus all information contained in the original data is preserved. Provided altitude and temperature profiles allow the representation of ozone profiles in number density or mixing ratio on a pressure or altitude vertical grid. Geolocation, uncertainty estimates and vertical resolution are provided for each profile. For each instrument, optional parameters, which are related to the data quality, are also included. For convenience of users, tables of biases between each pair of instruments for each month, as well as bias uncertainties, are provided. These tables characterize the data consistency and can be used in various bias and drift analyses, which are needed, for instance, for combining several datasets to obtain a long-term climate dataset. This user-friendly dataset can be interesting and useful for various analyses and applications, such as data merging, data validation, assimilation and scientific research. The dataset is available at http://www.esa-ozone-cci.org/?q=node/161 or at doi:10.5270/esa-ozone_cci-limb_occultation_profiles-2001_2012-v_1-201308.

scholarly journals The universal aspect ratio of vortices in rotating stratified flows: experiments and observations

2012 ◽  
Vol 706 ◽  
pp. 34-45 ◽  
Author(s):  
Oriane Aubert ◽  
Michael Le Bars ◽  
Patrice Le Gal ◽  
Philip S. Marcus
Keyword(s):  
Aspect Ratio ◽  
Salt Water ◽  
Boussinesq Equations ◽  
Companion Paper ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Aspect Ratios ◽  
Horizontal Length ◽  
The Law ◽  
The Relationship

AbstractWe validate a new law for the aspect ratio $\ensuremath{\alpha} = H/ L$ of vortices in a rotating, stratified flow, where $H$ and $L$ are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter $f$ and buoyancy (or Brunt–Väisälä) frequency $\bar {N} $ of the background flow, but also on the buoyancy frequency ${N}_{c} $ within the vortex and on the Rossby number $\mathit{Ro}$ of the vortex, such that $\ensuremath{\alpha} = f \mathop{ [\mathit{Ro}(1+ \mathit{Ro})/ ({ N}_{c}^{2} \ensuremath{-} {\bar {N} }^{2} )] }\nolimits ^{1/ 2} $. This law for $\ensuremath{\alpha} $ is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly stratified salt water. In one set of experiments, the vortices viscously decay while obeying our law for $\ensuremath{\alpha} $, which decreases over time. In a second set of experiments, the vortices are sustained by a slow continuous injection. They evolve more slowly and have larger $\vert \mathit{Ro}\vert $ while still obeying our law for $\ensuremath{\alpha} $. The law for $\ensuremath{\alpha} $ is not only validated by our experiments, but is also shown to be consistent with observations of the aspect ratios of Atlantic meddies and Jupiter’s Great Red Spot and Oval BA. The relationship for $\ensuremath{\alpha} $ is derived and examined numerically in a companion paper by Hassanzadeh, Marcus & Le Gal (J. Fluid Mech., vol. 706, 2012, pp. 46–57).

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