The Okubo-Weiss criterion in hydrodynamic flows:Geometric aspects and further extension

The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

Oceanic response to cyclone moving in different directions over Indian Seas using IRG model

The IITM Reduced Gravity (IRG) ocean model is employed to investigate the influence of tropical cyclone moving in different directions in Indian Seas. Some of the observed storm tracks in the Arabian Sea and Bay of Bengal are considered which have northward and westward movement. Sensitivity study is carried out for initial position of the storm at (90° E, 10° N) and moving in different directions. For westward moving cyclones the right bias in the model upper-layer thickness deviation (ULTD) field disappears. In an another experiment of westward moving cyclone originating at different latitudes, the ocean response is found to be sensitive to the Coriolis parameter (f). The surface currents as well as ULTD reduce, as f increases. The amplitude and the wavelength of inertia gravity wave increase with decrease in f, in the wake of the cyclone. This study helps to determine the upwelling region arising due to movement of the cyclone.

Dynamics of tilted atmospheric vortices under asymmetric diabatic heating

Päschke et al. (J Fluid Mech, 2012) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, inter alia, that an azimuthal Fourier mode 1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of the tilt and the heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order unity in the limit. Formally, this restricts the applicability of the theory to rather weak vortices. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to low hurricane strengths. An extended discussion of the asymptotics as regards their physical interpretation and their implications for the overall vortex dynamics is also provided in this context. The paper’s second contribution is a series of three-dimensional numerical simulations examining the effect of different orientations of dipolar diabatic heating on idealized tropical cyclones. Comparisons with numerical solutions of the asymptotic equations yield evidence that supports the original theoretical predictions of Päschke et al. In addition, the influence of asymmetric diabatic heating on the time evolution of the vortex centerline is further analyzed, and a steering mechanism that depends on the orientation of the heating dipole is revealed. Finally, the steering mechanism is traced back to the correlation of dipolar perturbations of potential temperature, induced by the vortex tilt, and vertical velocity, for which diabatic heating not necessarily needs to be responsible, but which may have other origins.

Tropical Cyclone Intensification Simulated in the Ooyama-type Three-layer Model with a Multilevel Boundary Layer

The first successful simulation of tropical cyclone (TC) intensification was achieved with a three-layer model, often named the Ooyama-type three-layer model, which consists of a slab boundary layer and two shallow water layers above. Later studies showed that the use of a slab boundary layer would produce unrealistic boundary layer wind structure and too strong eyewall updraft at the top of TC boundary layer and thus simulate unrealistically rapid intensification compared to the use of a height-parameterized boundary layer. To fully consider the highly height-dependent boundary layer dynamics in the Ooyama-type three-layer model, this study replaced the slab boundary layer with a multilevel boundary layer in the Ooyama-type model and used it to conduct simulations of TC intensification and also compared the simulation with that from the model version with a slab boundary layer. Results show that compared with the simulation with a slab boundary layer, the use of a multilevel boundary layer can greatly improve simulations of the boundary-layer wind structure and the strength and radial location of eyewall updraft, and thus more realistic intensification rate due to better treatments of the surface layer processes and the nonlinear advection terms in the boundary layer. Sensitivity of the simulated TCs to the model configuration and to both horizontal and vertical mixing lengths, sea surface temperature, the Coriolis parameter, and the initial TC vortex structure are also examined. The results demonstrate that this new model can reproduce various sensitivities comparable to those found in previous studies using fully physics models.

The influence of front strength on the development and equilibration of symmetric instability. Part 1. Growth and saturation

Submesoscale fronts with large horizontal buoyancy gradients and $O(1)$ Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) – a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. Here, we use a weakly nonlinear stability analysis to study SI in an idealised frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance. We find that the structure and energetics of SI strongly depend on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Vertically bounded non-hydrostatic SI modes can grow by extracting potential or kinetic energy from the balanced front and the relative importance of these energy reservoirs depends on the front strength and vertical stratification. We describe two limiting behaviours as ‘slantwise convection’ and ‘slantwise inertial instability’ where the largest energy source is the buoyancy flux and geostrophic shear production, respectively. The growing linear SI modes eventually break down through a secondary shear instability, and in the process transport considerable geostrophic momentum. The resulting breakdown of thermal wind balance generates vertically sheared inertial oscillations and we estimate the amplitude of these oscillations from the stability analysis. We finally discuss broader implications of these results in the context of current parameterisations of SI.

Spatial constraints in large-scale expansion of wind power plants

When wind turbines are arranged in clusters, their performance is mutually affected, and their energy generation is reduced relative to what it would be if they were widely separated. Land-area power densities of small wind farms can exceed 10 W/m2, and wakes are several rotor diameters in length. In contrast, large-scale wind farms have an upper-limit power density in the order of 1 W/m2 and wakes that can extend several tens of kilometers. Here, we address two important questions: 1) How large can a wind farm be before its generation reaches energy replenishment limits and 2) How far apart must large wind farms be spaced to avoid inter–wind-farm interference? We characterize controls on these spatial and temporal scales by running a set of idealized atmospheric simulations using the Weather and Research Forecasting model. Power generation and wind speed within and over the wind farm show that a timescale inversely proportional to the Coriolis parameter governs such transition, and the corresponding length scale is obtained by multiplying the timescale by the geostrophic wind speed. A geostrophic wind of 8 m/s and a Coriolis parameter of 1.05 × 10−4 rad/s (latitude of ∼46°) would give a transitional scale of about 30 km. Wind farms smaller than this result in greater power densities and shorter wakes. Larger wind farms result instead in power densities that asymptotically reach their minimum and wakes that reach their maximum extent.

Variability of near-inertial waves in the lower stratosphere from balloon observations and the ECMWF (re)analyses

<p>Near-inertial waves (NIWs) with intrinsic frequency close to the local Coriolis parameter <em>f</em> constitute a striking component of the kinetic energy spectrum in both the atmosphere and the ocean. However, contrary to the oceanic case, the strong and variable background atmospheric winds tend to shift the frequency of the waves (Doppler effect). As a consequence, atmospheric NIWs cannot generally be observed directly as a kinetic energy peak at ground-based frequency <em>f </em>but are instead diagnosed indirectly (e.g. using the polarisation and dispersion relations). This complication does not appear when analyzing quasi-lagrangian observations from superpressure balloons (SPB), which drift together with the flow and are thus exempt from Doppler shift. Past SPB observations in the lower stratosphere have revealed the magnitude of the kinetic energy peak associated with NIWs and it was recently shown that state-of-the-art reanalyses partly represent this feature.</p><p>In this presentation, we will investigate the variability of NIWs using ECMWF (re)analysis products (the operational analysis and ERA5) and balloon observations from recent CNES campaigns (2005, 2010 and 2019-2020) at various latitudes ranging from the equator to the pole (and hence different inertial frequencies). As in Podglajen et al. (2020), NIWs are extracted from the (re)analyses by computing Lagrangian trajectories using the analyzed wind and temperature fields. We will illustrate the remarkable realism of model NIWs, both statistically and for specific case studies. Then, we will characterize the geographic and seasonal variability of NIW properties. In light of those results, possible factors influencing the near-inertial energy peak (horizontal wave propagation, refraction near critical levels, tide interactions) and the parallel with the oceanic situation will be discussed, as well as the ability of the model and data assimilation system to simulate them.</p><p>Reference :</p><p>Podglajen, A., Hertzog, A., Plougonven, R., and Legras, B.: Lagrangian gravity wave spectra in the lower stratosphere of current (re)analyses, Atmos. Chem. Phys., 20, 9331–9350, https://doi.org/10.5194/acp-20-9331-2020, 2020.</p>

Seasonal variability of the Rossby radius deformation in the Hornsund fjord

<p>The Earth's rotation affects the water circulation in the Arctic fjords. It can be described by means of the baroclinic Rossby radius deformation (R<sub>1</sub>) expressed as the ratio of the internal wave velocity to the Coriolis parameter.</p><p>The influence of the rotational effects on the water‐mass distribution depends on the width of the fjord in relation to the baroclinic radius of deformation (Gilbert, 1983). Most often the Rossby radius deformation in the Arctic fjords is 2-3 times smaller than the width of the fjord entrance, which allows the rotation of water masses within such fjords (Cottier, 2010). Such a situation exists in the small, western fjord of Svalbard - Hornsund, where the rotation makes the Atlantic and the Arctic waters flow from the shelf into the fjord along the southern bank and flow out of the fjord along the northern bank. The impact of the Coriolis force on the Hornsund environment was observed in a sedimentary record from the last century (Pawłowska et al. 2017). Literature estimates indicate that Hornsund is a typical fjord with an internal baroclinic Rossby radius between 3.5 and 6 km (Cottier, 2005, Nilsen, 2008).</p><p>The spatial and seasonal variation of the R<sub>1</sub> in the Hornsund fjord was carried out based on data from the numerical model (Jakacki et al. 2017) for the period 2005-2010 and for the selected actual data collected during the AREX survey campaigns.  The analysis of the actual data and model data confirms the seasonal variability of the vertical water structure in the fjord, which leads to cyclic changes of the vertical <strong>Brunta-Vaisali </strong>frequency structure and consequently to seasonal variability of R<sub>1</sub>. In the Hornsund fjord seasonality strongly influences the Rossby radius, which reaches maximum values in summertime and minimum values in wintertime. Moreover, R<sub>1</sub> values can be different even at points close to each other.  The values of the baroclinic Rossby radius of deformation also differ depending on the adopted calculation method.<br><br>Calculations were carried out at the Academic Computer Centre in Gdańsk.</p><p> </p><p> </p>

Ekman-inertial instability

<p>We report on an instability arising in sub-surface, laterally sheared geostrophic flows. When the lateral shear of a horizontal flow in geostrophic balance has a sign opposite to the Coriolis parameter and exceeds it in magnitude, embedded perturbations are subjected to inertial instability, albeit modified by viscosity. When the perturbation arises from the surface of the fluid, the initial response is akin to a Stokes problem, with an initial flow aligned with the initial perturbation. The perturbation then grows quasi-inertially, rotation deflecting the velocity vector, which adopts a well-defined angle with the mean flow, and viscous stresses, transferring horizontal momentum downward. The combination of rotational and viscous effects in the dynamics of inertial instability prompts us to call this process “Ekman-inertial instability.” While the perturbation initially grows super-inertially, the growth rate then becomes sub-inertial, eventually tending back to the inertial value. The same process repeats downward as time progresses. Ekman-inertial transport aligns with the asymptotic orientation of the flow and grows exactly inertially with time once the initial disturbance has passed. Because of the strongly super-inertial initial growth rate, this instability might compete favourably against other instabilities arising in ocean fronts.</p>

Numerical investigation of inertia gravity-wave activity in the differentially heated rotating annulus: The impact of boundary conditions

<p>The differentially heated rotating annulus is a classic experiment used for the examination of circulation patterns and waves in the atmosphere. In particular, by choosing an atmosphere-like experimental setup that allows the buoyancy frequency to become larger than the Coriolis parameter, it provides a useful tool to study the generation mechanism of spontaneous gravity wave (GW) emission in jet-front systems. Recently, with the aim to gain better understanding about the conditions for the spontaneous generation of GWs, Rodda et al. (2020) compared experimental data with results from numerical simulations and found differences in the GW signal most likely due to the model's treatment of boundary conditions. The aim of the present study is to improve the consistency between the model and experiment and to investigate the effect of the lateral and upper boundary conditions on GW generation and propagation in an atmosphere-like configuration of the annulus. More precisely, we implement the corresponding lateral and surface heat fluxes, air-temperature variations, as well as evaporation at the upper boundary condition into the numerical model and examine the characteristics of the observed GW signals, which are identified by the horizontal divergence field. Our systematic analysis may serve as a basis for subsequent research on the spontaneous GW generation mechanism, following the overarching objective to develop a parameterization scheme for GWs emitted from jets and front.</p><p> </p><p><strong>References:</strong></p><p>Rodda, C., S. Hien, U. Achatz, and U. Harlander, 2020: A new atmospheric-like differentially heated rotating annulus configuration to study gravity wave emission from jets and fronts. Exp. Fluids <strong>61, </strong>2. https://doi.org/10.1007/s00348-019-2825-z</p>