Simple Hurricane Model: Asymmetry and Dynamics

In recent decades, the development of several products and hurricane-related models has attempted to predict the dynamic conditions of these systems and regions beyond they can impact. Thus, this article presents a parametric model to describe wind asymmetry in these systems. For this, the analysis of this model was applied in Hurricane Ike, which occurred in September 2008. In this model, the tangential wind field above the boundary layer was considered in balance with the thermal wind. It was possible to identify that as Hurricane Ike evolves, tangential velocity also evolves. Thus, there was a change in static, baroclinic, and inertial stability. An exponential radial reduction was included for maximum speed, and, therefore, the maximum winds always to the right of the hurricane displacement were identified. In addition, pumping near the surface had an influx into this system induced caused by drag between the air and the surface.

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.

The influence of front strength on the development and equilibration of symmetric instability. Part 2. Nonlinear evolution

In Part 1 (Wienkers, Thomas & Taylor, J. Fluid Mech., vol. 926, 2021, A6), we described the theory for linear growth and weakly nonlinear saturation of symmetric instability (SI) in the Eady model representing a broad frontal zone. There, we found that both the fraction of the balanced thermal wind mixed down by SI and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of SI we call ‘slantwise inertial instability’ by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in ‘slantwise convection.’ Here, we extend the theory from Part 1 using nonlinear numerical simulations to focus on the adjustment of the front following saturation of SI. We find that the details of adjustment and amplitude of the induced inertial oscillations depend on the front strength. While weak fronts develop narrow frontlets and excite small-amplitude vertically sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. The turbulent dissipation rate in these strong fronts is large, highly intermittent and intensifies during periods of weak stratification. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state, and in particular focus on the effect of varying the dimensionless front strength.

The modification of turbulent thermal wind balance by non-traditional effects

The meridional component of the earth's rotation is often neglected in geophysical contexts. This is referred to as the ‘traditional approximation’ and is justified by the typically small vertical velocity and aspect ratio of such problems. Ocean fronts are regions of strong horizontal buoyancy gradient and are associated with strong vertical transport of tracers and nutrients. Given these comparatively large vertical velocities, non-traditional rotation may play a role in governing frontal dynamics. Here the effects of non-traditional rotation on a front in turbulent thermal wind balance are considered using an asymptotic approach. Solutions are presented for a general horizontal buoyancy profile and examined in the simple case of a straight front. Non-traditional effects are found to depend strongly on the direction of the front and may lead to the generation of jets and the modification of the frontal circulation and vertical transport.

Short-term Hydro-Thermal-Wind-Solar Power Scheduling: A Case Study of Kanyakumari Region of India

In this paper, a multi-objective hydro-thermal-wind-solar power scheduling problem is established and optimized for the Kanyakumari (Tamil Nadu, India) for the 18th of September of 2020. Four contrary constraints are contemplated for this case study (i) fuel cost and employing cost of wind and solar power system, (ii) NOx emission, (iii) SO2 emission, and (iv) CO2 emission. An advanced hybrid simplex method named as-the -constrained simplex method (ACSM) is deployed to solve the offered problem. To formulate this technique three amendments in the usual simplex method (SM) are adopted (i) -level differentiation, (ii) mutations of the worst point, and (iii) the incorporation of multi-simplexes. The fidelity of the projected practice is trailed upon two test systems. The first test system is hinged upon twenty-four-hour power scheduling of a pure thermal power system. The values of total fuel cost and emissions (NOx, SO2, CO2) are attained as 346117.20 Rs, 59325.23 kg, 207672.70 kg, and 561369.20 kg, respectively. In the second test system, two thermal generators are reintegrated with renewable energy resources (RER) based power systems (hydro, wind, and solar system) for the same power demands. The hydro, wind, and solar data are probed with the Glimn-Kirchmayer model, Weibull Distribution Density Factor, and Normal Distribution model, respectively. For this real-time hydro-thermal-wind-solar power scheduling problem the values of fuel cost and emissions (Nox, SO2, CO2) are shortened to 119589.00 Rs, 24262.24 kg, 71753.80 kg, and 196748.20 kg, respectively for the specified interval. The outturns using ACSM are contrasted with the SM and evolutionary method (EM). The values of the operating cost of solar system, wind system, total system transmission losses, and computational time of test system-2 with ACSM, SM, and EM are evaluated as 620497.40 Rs, 1398340.00 Rs, 476.6948 MW & 15.6 seconds; 620559.45 Rs, 1398479.80 Rs, 476.7425 MW & 16.8 seconds; and 621117.68 Rs, 1399737.80 Rs, 477.1715 MW and 17.3 seconds, respectively. The solutions portray the sovereignty of ACSM over the other two methods in the entire process.