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David Walsh

Abstract

A simple model is used to study the behavior of a lens-shaped eddy in a background flow with uniform horizontal and vertical shear. The primary motivation for the work is to understand the influence of large-scale shear on Mediterranean salt lenses in the Canary Basin. The model eddy is represented by an isolated three-dimensional patch characterized by anomalous potential vorticity, and its evolution is governed by stratified, f-plane quasigeostrophic dynamics. Guided by the available observations, the potential vorticity field is chosen to be horizontally piecewise constant and is a linear function of depth within the lens. This produces a flow field characterized by a depth-dependent solid body rotation within the core of the eddy, with speeds decreasing monotonically outside the core, in good agreement with observations. A family of linearized solutions is discussed, representing a lens-shaped eddy with a large trapped fluid region, which is deformed due to interactions with external shear. The lens may propagate through the surrounding waters in the presence of external vertical shear, providing a possible explanation for the observed translation of Mediterranean sail lenses. These results generalize those of Hogg and Stommel to encompass three-dimension stratified dynamics, with a realistic, nonsingular representation of the potential vorticity field. The analysis predicts the form of the steady boundary deformation, the precession rate of boundary perturbations in the absence of external flow, and the propagation speed of the eddy as a function of external shear and core baroclinicity. It is found that there is a maximum differential rotation rate within the core beyond which no small amplitude solutions exist. General integral expressions are derived relating the propagation speed to the eddy potential vorticity and the external shear.

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David Walsh
and
Barry Ruddick

Abstract

The nonlinear behavior of thermohaline intrusions on a wide front is investigated using a one-dimensional numerical model. The model is used to follow the evolution of a field of intrusions from infinitesimal amplitude to a large-amplitude state characterized by inversions in temperature and salinity. It is thus possible to extend the analytical studies of Toole and Georgi and others to large amplitude, allowing for the effects of amplitude-dependent diffusivities, and for the appearance of stably stratified, diffusively stratified, and statically unstable regions in the water column as the intrusions grow.

The model runs are initialized with infinitesimal disturbances that grow exponentially in time until inversions in temperature and salinity occur. After inversions appear, the intrusions evolve toward an equilibrium state in which friction balances buoyancy forces, for both finger- and diffusive-sense basic-state stratifications. These equilibrium states are characterized by statically unstable “convecting” layers between layers of finger- and diffusively stratified fluid—the convecting layers appear when intrusions reach large amplitude and help to slow their growth. Equilibration seems to be insensitive to the specific functional forms chosen for the double-diffusive diffusivities and viscosities. The necessary condition for equilibration is that the TS flux ratio adjusts as the intrusions grow, and (within the context of the present model) turbulent mixing provides the mechanism for this adjustment.

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David Walsh
and
Barry Ruddick

Abstract

The influence of nonconstant diffusivity and viscosity on double-diffusive interleaving is examined using a simple model. The analysis allows a prediction of the slope, vertical wavenumber, and growth rate of the fastest-growing interleaving mode for specified background gradients of salinity and temperature. Allowing the salt diffusivity to be a function of the density ratio Rp leads to a larger growth rate and a lower vertical wavenumber than in the constant diffusivity case considered by Toole and Georgi, while the cross-front slope of the intrusions is essentially unaffected. The nonconstant viscosity included in the model formulation is found to have no effect on the form of the solutions. The larger vertical scales and growth rates predicted by the model can be traced to an enhanced “effective diffusivity” resulting from the diffusivity gradients associated with the growing intrusions. A transformation is found that converts the system with generalized diffusivities examined here to the simpler system considered by Toole and Georgi.

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David Walsh
and
Barry Ruddick

Abstract

The influence of turbulent mixing on double-diffusively driven thermohaline interleaving is investigated. The problem is formulated using a turbulence-modified flux ratio to link the fluxes of T and S; the addition of turbulence changes the way in which the effective flux ratio varies with the density ratio R ρ . Formulation of the problem maps onto past interleaving studies, except that the flux ratio is a function of R ρ in the present work. Posing the problem in this way allows the effects of turbulence and intrinsic variations in the salt-finger flux ratio to be studied within the same theoretical framework.

Turbulence modifies the slope, wavelength, and growth rate of the fastest-growing intrusions, decreasing the range of slopes and wavenumbers that can grow. However, analysis shows that growing solutions exist for any finite value of the turbulent diffusivity Kt , suggesting that double-diffusively driven intrusions can exist in the ocean even when double-diffusive fluxes are much weaker than turbulent fluxes.

If the flux ratio is a decreasing function of R ρ (as suggested by some models of salt finger convection) a different instability occurs, which has unbounded growth rates in the high wavenumber limit (a “UV catastrophe”). In most cases, the instability can be suppressed by the addition of sufficiently strong turbulent mixing. The threshold for this instability depends upon variation of the T/S flux ratio with R ρ , and hence on the relative strengths of turbulent and double-diffusive mixing. The instability is shown to be nonintrusive in nature, as it does not rely upon lateral advection across a front; it is found to be closely related to the one-dimensional double-diffusive instability investigated by Huppert.

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Barry Ruddick
,
David Walsh
, and
Neil Oakey

Abstract

Microstructure data from the North Atlantic Tracer Release Experiment (NATRE) are presented, providing detailed profiles of the thermal variance χ in the upper 360 m of the Canary Basin for the fall and spring seasons. The Osborn–Cox model is used to compute the diffusivity K T . The diffusivity for the depth range 240–340 m is found to be 1.0(±0.04) × 10−5 m2 s−1 in the fall and 2.2(±0.1) × 10−5 m2 s−1 in the spring, in good agreement with dye-inferred diffusivities at similar depths. Measured turbulent kinetic energy (TKE) dissipation rates were found to be contaminated by hydrodynamic noise, so the Osborn dissipation method was not used to compute K ρ . However, data segments for which the TKE dissipation rate (ε) was large enough to be unaffected by noise were used to compute the “apparent mixing efficiency” Γ d . The computed Γ d values are used to investigate variations in apparent mixing efficiency with respect to density ratio (R ρ ) and turbulence Reynolds number [ε/(νN 2)], in an attempt to elucidate the underlying mechanisms of mixing in the NATRE region. Observed variations of Γ d are compared with existing theoretical models of mixing due to: salt fingers, a combination of salt fingers and turbulence, “conventional” high Reynolds number turbulence, and low Reynolds number buoyancy-modified turbulence. Significant variations of Γ d with respect to both R ρ and ε/(νN 2) are found. Although Monte Carlo tests show that some of the observed variations could be noise-induced, a substantial portion of the systematic variations the authors observed were not reproduced by Monte Carlo simulations. These trends are found to be statistically significant, and the authors conclude that they represent real variations in the apparent mixing efficiency. The authors find that Γ d is an increasing function of ε/(νN 2) and a decreasing function of R ρ ; these variations are not fully consistent with any of the available mixing models.

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David Walsh
,
Philip L. Richardson
, and
Jim Lynch

Abstract

SOFAR floats at different depths within two Mediterranean Water eddies (meddies) reveal that the meddy rotation axes tilt transversely with respect to the meddy translation direction. The rotation axis of one of the meddies (Meddy 1) was displaced by about 6 km over a depth of roughly 100 m; the axis of the second meddy (Meddy 2) was displaced by about 0.4 km over 100-m depth. These results are compared to a simple theoretical model that predicts the deformation and translation of a lens-shaped eddy embedded in large-scale external shear. Observed lateral deformations of the meddles are in good agreement with model predictions. The observed tilt of Meddy 1 is attributed to a combination of depth-varying rotation rate beneath the meddy core and the horizontal translation of the meddy; the tilt of Meddy 2 is attributed to a deformation of the meddy core by vertically sheared flow outside the meddy. The observed translation speed of the meddies with respect to nearby floats outside of the meddies is significantly larger than that predicted by the model.

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Neil F. Laird
,
John E. Walsh
, and
David A. R. Kristovich

Abstract

Idealized model simulations with an isolated elliptical lake and prescribed winter lake-effect environmental conditions were used to examine the influences of lake shape, wind speed, and wind direction on the mesoscale morphology. This study presents the first systematic examination of variations in lake shape and the interplay between these three parameters. The array of 21 model simulations produced cases containing each of the three classic lake-effect morphologies (i.e., vortices, shoreline bands, and widespread coverage), and, in some instances, the mesoscale circulations were composed of coexisting morphologies located over the lake, near the downwind shoreline, or inland from the downwind shore.

As with lake-effect circulations simulated over circular lakes, the ratio of wind speed (U) to maximum fetch distance (L) was found to be a valuable parameter for determining the morphology of a lake-effect circulation when variations of lake shape, wind speed, and wind direction were introduced. For a given elliptical lake and strong winds, a morphological transform from shoreline band toward widespread coverage accompanied changes in ambient flow direction from along to across the major lake axis. For simulations with weak winds over a lake with a large axis ratio, the morphology of the lake-effect circulation changed from vortex toward shoreline band with a change in wind direction from along to across the major lake axis. Weak winds across lakes with smaller axis ratios (i.e., 1:1 or 3:1) produced mesoscale vortices for each wind direction. Across the array of simulations, a shift in mesoscale lake-effect morphology from vortices to bands and bands toward widespread coverage was attended by an increase in U/L. Last, the elliptical-lake results suggest that the widths of the lake-effect morphological transition zones in U/L parameter space, conditions favorable for the coexistence of multiple morphologies, were greater than for circular lakes.

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Neil F. Laird
,
David A. R. Kristovich
, and
John E. Walsh

Abstract

An array of 35 idealized mesoscale model simulations was used to examine environmental and surface forcing factors controlling the meso-β-scale circulation structure resulting from cold flow over an isolated axisymmetric body of water at the midlatitudes. Wind speed, lake–air temperature difference, ambient atmospheric stability, and fetch distance were varied across previously observed ranges. Simulated meso-β-scale lake-effect circulations occurred within three basic regimes (e.g., vortices, shoreline bands, widespread coverage), similar to observed morphological regimes. The current study found that the morphological regimes of lake-effect circulations can be predicted using the ratio of wind speed to maximum fetch distance (U/L). Lake-effect environmental conditions producing low values of U/L (i.e., approximately < 0.02 m s−1 km−1) resulted in a mesoscale vortex circulation. Conditions leading to U/L values between about 0.02 and 0.09 m s−1 km−1 resulted in the development of a shoreline band, and U/L values greater than approximately 0.09 m s−1 km−1 produced a widespread coverage event. It was found that transitions from one morphological regime to another are continuous and within transitional zones the structure of a circulation may contain structural features characteristic of more than one regime. Results show that 1) the U/L criterion effectively classifies the morphology independently of the lake–air temperature difference for the parameter value combinations examined and 2) the Froude number, suggested as a potential lake-effect forecasting tool in previous studies, does not permit the unique classification of lake-effect morphology.

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John T. Allen
,
David J. Karoly
, and
Kevin J. Walsh

Abstract

The influence of a warming climate on the occurrence of severe thunderstorms over Australia is, as yet, poorly understood. Based on methods used in the development of a climatology of observed severe thunderstorm environments over the continent, two climate models [Commonwealth Scientific and Industrial Research Organisation Mark, version 3.6 (CSIRO Mk3.6) and the Cubic-Conformal Atmospheric Model (CCAM)] have been used to produce simulated climatologies of ingredients and environments favorable to severe thunderstorms for the late twentieth century (1980–2000). A novel evaluation of these model climatologies against data from both the ECMWF Interim Re-Analysis (ERA-Interim) and reports of severe thunderstorms from observers is used to analyze the capability of the models to represent convective environments in the current climate. This evaluation examines the representation of thunderstorm-favorable environments in terms of their frequency, seasonal cycle, and spatial distribution, while presenting a framework for future evaluations of climate model convective parameters. Both models showed the capability to explain at least 75% of the spatial variance in both vertical wind shear and convective available potential energy (CAPE). CSIRO Mk3.6 struggled to either represent the diurnal cycle over a large portion of the continent or resolve the annual cycle, while in contrast CCAM showed a tendency to underestimate CAPE and 0–6-km bulk magnitude vertical wind shear (S06). While spatial resolution likely contributes to rendering of features such as coastal moisture and significant topography, the distribution of severe thunderstorm environments is found to have greater sensitivity to model biases. This highlights the need for a consistent approach to evaluating convective parameters and severe thunderstorm environments in present-day climate: an example of which is presented here.

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John T. Allen
,
David J. Karoly
, and
Kevin J. Walsh

Abstract

The influence of a warming climate on the occurrence of severe thunderstorm environments in Australia was explored using two global climate models: Commonwealth Scientific and Industrial Research Organisation Mark, version 3.6 (CSIRO Mk3.6), and the Cubic-Conformal Atmospheric Model (CCAM). These models have previously been evaluated and found to be capable of reproducing a useful climatology for the twentieth-century period (1980–2000). Analyzing the changes between the historical period and high warming climate scenarios for the period 2079–99 has allowed estimation of the potential convective future for the continent. Based on these simulations, significant increases to the frequency of severe thunderstorm environments will likely occur for northern and eastern Australia in a warmed climate. This change is a response to increasing convective available potential energy from higher continental moisture, particularly in proximity to warm sea surface temperatures. Despite decreases to the frequency of environments with high vertical wind shear, it appears unlikely that this will offset increases to thermodynamic energy. The change is most pronounced during the peak of the convective season, increasing its length and the frequency of severe thunderstorm environments therein, particularly over the eastern parts of the continent. The implications of this potential increase are significant, with the overall frequency of potential severe thunderstorm days per year likely to rise over the major population centers of the east coast by 14% for Brisbane, 22% for Melbourne, and 30% for Sydney. The limitations of this approach are then discussed in the context of ways to increase the confidence of predictions of future severe convection.

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