Coriolis Parameter Research Articles

Potential Vorticity and Instability in the Pacific Equatorial Undercurrent West of the Galápagos Archipelago

Abstract The Galápagos Archipelago lies on the equator in the path of the eastward flowing Pacific Equatorial Undercurrent (EUC). When the EUC reaches the archipelago, it upwells and bifurcates into a north and south branch around the archipelago at a latitude determined by topography. Since the Coriolis parameter (f) equals zero at the equator, strong velocity gradients associated with the EUC can result in Ertel potential vorticity (Q) having sign opposite that of planetary vorticity near the equator. Observations collected by underwater gliders deployed just west of the Galápagos Archipelago during 2013–16 are used to estimate Q and to diagnose associated instabilities that may impact the Galápagos Cold Pool. Estimates of Q are qualitatively conserved along streamlines, consistent with the 2.5-layer, inertial model of the EUC by Pedlosky. The Q with sign opposite of f is advected south of the Galápagos Archipelago when the EUC core is located south of the bifurcation latitude. The horizontal gradient of Q suggests that the region between 2°S and 2°N above 100 m is barotropically unstable, while limited regions are baroclinically unstable. Conditions conducive to symmetric instability are observed between the EUC core and the equator and within the southern branch of the undercurrent. Using 2-month and 3-yr averages, e-folding time scales are 2–11 days, suggesting that symmetric instability can persist on those time scales. Significance Statement The Pacific Ocean contains fast-moving currents near the equator and below the surface that result in instabilities and mixing. The Galápagos Archipelago lies directly in the path of the eastward-flowing Pacific Equatorial Undercurrent. There are few observations of what happens to the current when it reaches the Galápagos Archipelago, so theories and models of the instabilities and mixing resulting from these strong currents have not been well verified. The Repeat Observations by Gliders in the Equatorial Region (ROGER) project deployed autonomous underwater gliders to observe the current system in this region. The results show that a range of instabilities may be responsible for the cold sea surface temperature of the Galápagos Cold Pool and the generation of tropical instability waves.

Tropical Cyclone Size Is Strongly Limited by the Rhines Scale: Experiments with a Barotropic Model

Abstract Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradient β. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect of β varies with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on a β plane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradient β and initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex to β. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is well described by the vortex Rhines time scale, which is defined as the overturning time scale of the circulation at the vortex Rhines scale and is shown to be directly related to the Rossby wave group velocity. The relationship between our idealized results and the real Earth is discussed. Results may generalize to other eddy circulations, such as the extratropical cyclone. Significance Statement Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general.

On the extension of streamwise turbulence intensity profile beyond the atmospheric surface layer under neutral to unstable stratifications

Turbulence intensity (TI) is a key factor that affects both the energy production and the performance of individual wind turbines and wind farms. In particular, accurate energy production estimation from wind sources requires a reliable TI model at turbine hub height. Modern multi-megawatt wind turbines operate at heights well above the atmospheric surface layer (ASL). However, most existing analytical TI models are merely valid in the ASL or under neutral atmospheric conditions. Therefore, this paper aims to derive an analytical expression for streamwise TI under neutral to unstable stratifications, which can reasonably model TI at heights beyond the ASL. To this end, the Monin-Obukhov similarity theory, Townsend's attached eddy hypothesis, and a modification proposed in the literature to the eddy population density of Townsend for unstable conditions are utilized. The proposed models are validated against datasets from four tall meteorological towers in Denmark, Sweden, and China. The sites constitute a considerable difference in Coriolis parameter and surface roughness. Results show that the proposed models reasonably follow the measured velocity variance and TI data under neutral to unstable conditions in the ASL and beyond.

Updated parameterization of internal tidal mixing in the deep ocean based on laboratory rotating tank experiments

The Coriolis effect plays an important role in the generation and dissipation of internal tides. In this study, the effects of the Coriolis parameter on internal tides generated by tidal current flowing over rough subsurface topography were investigated in the laboratory. The results show that the variation in the internal tidal local dissipation rate with variation in the Coriolis parameter in the deep layer follows a Gaussian distribution. The strongest dissipation occurs near the critical latitude where the local Coriolis parameter is half of the tidal frequency. A modified internal tidal mixing parameterization was developed by introducing a correction function related to the Coriolis effect on internal tidal local dissipation in the deep ocean, based on the original version developed by St. Laurent et al. (2002). The new parameterization was then implemented in a parallel ocean model. The results indicate that the deep global meridional overturning circulation (GMOC) is strengthened in the low and middle latitudes and the Southern Ocean by the change, compared with the original parameterization.

Isopycnal and diapycnal mixing parameterization schemes for submesoscale processes induced by mesoscale eddies

With continuous and rapid improvements in computing power, the ability of ocean numerical models to resolve mesoscale process gradually increased. Consequently, traditional mesoscale parameterization schemes are potentially no longer suitable, requiring new schemes for submesoscale processes (SMPs). Mesoscale eddies are widely distributed in the global ocean, and their interiors and edges are often accompanied by SMPs. As such, it is the aim of this study to parameterize these processes and provide a new SMP parameterization scheme for mesoscale eddy-resolving models. Submesoscale phenomena accompanying mesoscale eddies are simulated using the Coastal and Regional Ocean Community (CROCO) model at a horizontal resolution of 500 m. Based on the flux-gradient relationship, each component of the eddy diffusivity tensor is then diagnosed by using the Moore-Penrose pseudo-inverse method. The least-square fitting is then used to obtain a new parameterization scheme. The eddy diffusivity tensor is found to be a function of horizontal front strength, stratification, eddy depth, Coriolis parameter and Richardson number.

Effect of rotation on mixing efficiency in homogeneous stratified turbulence using unforced direct numerical simulations

Diapycnal (irreversible) mixing is analyzed using thirty direct numerical simulations (at \(1024^3\) resolution) of homogeneous rotating stratified turbulence (RST) in the absence of imposed shear or forcing. The influence of varied rotation and stratification rates on the energetics (in particular the dissipation rates of kinetic and potential energies) is presented. Data is also analyzed within a new parametric framework, using the turbulent Froude and Rossby numbers \(Fr_t = \epsilon /Nk\), \(Ro_t = \epsilon / f k\), where k is the turbulent kinetic energy, \(\epsilon\) its rate of dissipation, N the buoyancy frequency and f the Coriolis parameter. This framework is used to illustrate relative magnitudes of the stratification and rotation in geophysical flows and provide a useful tool for explicating the relationship between \(Fr_t\) and \(Ro_t\) as relevant dynamic parameters in the geophysical setting. Results indicate that unforced rotation does not impact the magnitude of the irreversible mixing coefficient (\(\Gamma =\epsilon _P/\epsilon\)) when compared to results without rotation, where \(\epsilon _P\) is the rate of potential energy dissipation. Moreover, it is shown that the recent scaling laws for mixing efficiency in stably stratified turbulence in the absence of rotation, as exemplified in Garanaik & Venayagamoorthy (J. Fluid Mech. 867, 2019, pp. 323-333), are applicable as well for homogeneous and decaying RST. Results also highlight the ambiguity of the ratio N/f as a control parameter for the classification of small-scale RST, and thus for evaluating diapycnal mixing.

Bathymetry Based Modeling of Subaxial Magma Flows Under the Mid-Atlantic Ridge, 0 to 30° N

Fracture patterns of the Mid-Atlantic Ridge (MAR) provide evidence of tectonic forces related to divergence and magma upwelling at the ridge axis. In this study, we focus on the MAR from 0 to 30° N, where the N-S ridge exhibits slow spreading rates (2-4 cm/yr) and pronounced axial topography. Ridge segments and transform faults identified in bathymetry data were analyzed for strike orientation and axial depth profiles. Azimuths of transform faults and ridge segments exhibit increasing clockwise rotation with latitude, and all have left lateral displacement. Bathymetric sampling along ridge segments occurred at 9 km intervals with 20 km sampling radii, producing axial lithostatic pressure gradients. One-dimensional magma flows parallel to the ridge axis at 10 and 50 km depths were modeled using Darcy’s law based on published parameters and calculated gradients. Subaxial magma velocities of up to 4 cm/yr were predicted for horizontal flow at depth and are comparable in magnitude to upwelling rates in published literature. Average flow magnitudes (n = 422) within the melt generation region are predicted at 0.8 and 0.2 cm/yr for 10 and 50 km depths respectively. Flow velocities up to five times higher are expected with this model in the high-porosity boundary layer below the solidus. The Coriolis parameter would affect the movement of the flows predicted by our model and may be linked to rotational patterns observed at the MAR. Future research of magma migration below divergent margins would benefit from incorporating axial lithostatic load variations as a driver of flow.

An analytic model of the tropical cyclone outer size

There are simple conceptual models of tropical cyclone intensification and potential intensity. However, such a framework has been lacking to describe the evolution of the outer circulation. An analytic growth model of the tropical cyclone outer size is derived from the angular momentum equation. The growth model fits a full-physics idealized tropical cyclone simulation. The lifecycle composite of the best-track outer size growth shows a strong super-linear nature, which supports an exponential growth as predicted by the growth model. The climatology of outer size growth measured by the radius of gale-force wind in the North Atlantic and Eastern Pacific during the period 2004–2017, can be understood in terms of four growth factors of the model: the initial size, the growth duration, the mean growth latitude, and the mean top-of-boundary-layer effective local inflow angle. All four variables are significantly different between the two basins. The observed lifetime maximum size follows a lognormal distribution, which is in line with the law of the proportionate effect of this exponential growth model. The growth model fits the observed outer size well in global basins. The time constant of the exponential size growth is approximately equal to the product of the Coriolis parameter and the mean effective inflow angle above the boundary layer. Further sensitivity experiments with the growth model suggest that the interannual variability of the global lifetime maximum size is largely driven by the variation of growth duration.

Rotating convective MHD flow over a vertical moving plate in the presence of heat source, radiation, chemical reaction and Hall effects

The steady MHD rotating flow and heat mass transfer over a semi-infinite vertical plate moving with a constant velocity in the presence of a heat source, thermal radiation, first-order chemical reaction and Hall effect are studied. The methodology proposed to predict the velocity, temperature and concentration evolutions is based on similarity transformation and finite difference method. The simulation has been carried out for different pertinent parameters of problem. The main results are that the velocity fields are considerably affected by the velocity ratio and coriolis parameters. Except the axial w-velocity that increases only near the plate with the velocity ratio parameter, all the velocities decrease as the velocity ratio and Coriolis parameters increase, whereas the temperature and the concentration profiles increase. Also, the fluid velocity and temperature increase when the heat source and radiation parameters increase but the concentration decreases.

Internal Lee Waves Generated by Shear Flow Over Small‐Scale Topography

AbstractWhen the bottom current flows over a small‐scale topographic feature (with characteristic horizontal scale of 0.1–10.0 km), it generates internal lee waves. These lee waves furnish the energy cascade from mesoscale to dissipative scale, resulting in enhanced turbulent mixing. The existing lee wave theory and parameterization are mostly based on uniform background flow. We improve the linear lee wave theory by considering shear background flow and viscous and diffusive effects, which are ubiquitous in the ocean. In particular, the introduction of vertical viscous and diffusive terms effectively improves the problem of critical layer (where the wave frequency is close to the Coriolis frequency) for linear lee waves under weakly dissipative limit. Then, the influences of different types of shear flow on the frequency, vertical wavelength, group velocity, energy flux, energy density, energy dissipation and irreversible mixing of lee waves are explored through both theory and numerical simulation. A bottom‐up decreasing background flow can enhance energy dissipation and irreversible mixing below the critical layer. However, in the real ocean, the dissipation and mixing caused by a decreasing background flow may be weaker than that caused by an increasing background flow in a depth integrated sense, especially when considering a bounded domain. Additionally, the theory of wave action conservation in the absence of dissipation, which is commonly used as a criterion in research of internal waves propagating in varying background fields, is extended to a “modified” wave action equation considering dissipation, which may potentially improve the lee wave parameterization in the future.

Impact of Anticyclonic Eddy on Nonlinear Wave‐Wave Interaction in the Southern South China Sea During Late Summer 2020

AbstractNonlinear wave‐wave interaction (WWI) in the southern South China Sea (SCS) has rarely been investigated due to sparse field observation. By analyzing datasets recorded by two adjacent moorings, we find active nonlinear WWI among diurnal internal tides (D1 ITs), near‐inertial waves (NIWs), and D1‐f waves in this area. Although the blue shift of NIWs can provide part of the energy for D1‐f waves, the bulk of D1‐f energy was generated from the nonlinear WWI. Driven by the summer monsoon, a dipole of mesoscale eddies was formed off the central Vietnam coast and intruded into the study area. The anticyclonic eddy of the dipole reduced the local effective Coriolis frequency by providing negative vorticity and suppressed the nonlinear WWI locally. During the intrusion period, D1‐f waves almost vanished suggesting the important role of mesoscale eddy on adjusting the nonlinear WWI in the SCS.

Wind-Forced Variability of the Zonal Overturning Circulation

AbstractThe mechanisms of wind-forced variability of the zonal overturning circulation (ZOC) are explored using an idealized shallow water numerical model, quasigeostrophic theory, and simple analytic conceptual models. Two wind-forcing scenarios are considered: midlatitude variability in the subtropical/subpolar gyres and large-scale variability spanning the equator. It is shown that the midlatitude ZOC exchanges water with the western boundary current and attains maximum amplitude on the same order of magnitude as the Ekman transport at a forcing period close to the basin-crossing time scale for baroclinic Rossby waves. Near the equator, large-scale wind variations force a ZOC that increases in amplitude with decreasing forcing period such that wind stress variability on annual time scales forces a ZOC ofO(50) Sv (1 Sv ≡ 106m3s−1). For both midlatitude and low-latitude variability the ZOC and its related heat transport are comparable to those of the meridional overturning circulation. The underlying physics of the ZOC relies on the influences of the variation of the Coriolis parameter with latitude on both the geostrophic flow and the baroclinic Rossby wave phase speed as the fluid adjusts to time-varying winds.Significance StatementThe purpose of this study is to better understand how large-scale winds at mid- and low latitudes move water eastward or westward, even in the deep ocean that is not in direct contact with the atmosphere. This is important because these currents can shift where heat is stored in the ocean and if it might be released into the atmosphere. It is shown that large-scale winds can drive rapid cross-basin transports of water masses, especially so at low latitudes. The present results provide a guide on what controls this motion and highlight the importance of large-scale ocean waves on the water movement and heat storage.

Polar vortex crystals: Emergence and structure

Vortex crystals are quasiregular arrays of like-signed vortices in solid-body rotation embedded within a uniform background of weaker vorticity. Vortex crystals are observed at the poles of Jupiter and in laboratory experiments with magnetized electron plasmas in axisymmetric geometries. We show that vortex crystals form from the free evolution of randomly excited two-dimensional turbulence on an idealized polar cap. Once formed, the crystals are long lived and survive until the end of the simulations (300 crystal-rotation periods). We identify a fundamental length scale, Lγ=(U/γ)1/3, characterizing the size of the crystal in terms of the mean-square velocity U of the fluid and the polar parameter γ=fp/a2p, with fp the Coriolis parameter at the pole and ap the polar radius of the planet.

Influence of Coriolis Parameter Variation on Langmuir Turbulence in the Ocean Upper Mixed Layer with Large Eddy Simulation

Influence of Coriolis Parameter Variation on Langmuir Turbulence in the Ocean Upper Mixed Layer with Large Eddy Simulation

High-resolution far-infrared synchrotron FTIR spectroscopy and analysis of the [formula omitted], [formula omitted] and [formula omitted] bands of trioxane

Ro–vibrational band spectra of the three ν20, ν7 and ν19 bands of 1, 3, 5-trioxane (H2CO)3 were recorded in the 50–650cm−1 range using a long path absorption cell coupled to a high resolution Fourier transform spectrometer and synchrotron radiation at the AILES beamline of the SOLEIL synchrotron. More than 16000 lines were assigned with a dRMS better than 0.17×10−3cm−1. Two different formalisms (tensorial and Watson) were used to derive accurate rotational and quartic parameters for the three bands and for the first time, a precise determination of Coriolis parameter and q+l−doubling constant for both ν20 and ν19 perpendicular bands was also obtained. Lastly, each set of spectroscopic parameters is compared and discussed between both formalisms.

The multiple kink solutions and interaction mechanism with help of the coupled Burgers' equation

This paper presents a study of the traditional approximation potential vorticity equation. A nonlinear forced Zakharov-Kuznetsov equation by using the perturbation expansion method and multiple temporal and spatial scales method is obtained. And the multiple kink solutions of the forced Zakharov-Kuznetsov equation are obtained and the one- and two-soliton solutions are given by making use of the simplest equation method, namely the coupled Burgers’ equation, which is of a low-order than obtained equation and the multiple kink solutions of the equation are already given by utilizing the simplified Hirota's method. The results show that the proposed method is a powerful mathematical method to solve the nonlinear evolution equation arising in various areas of nonlinear science. Based on the one- and two-soliton solutions, graphical figures are portrayed by taking definite values to parameters and the features of the variable parameters are discussed in detail. Some results are given about interaction of two-soliton solutions and we found the wave amplitude of the two-soliton is influenced with the Coriolis parameters. Meanwhile, the soliton of the model with the external source is also obtained.

Evanescent acoustic-gravity waves in a rotating stratified atmosphere

In this work, we focused on the study of the influence of the rotation of the Earth’s atmosphere on the properties of evanescent acoustic-gravity waves, which we studied earlier in the absence of rotation. It is shown that evanescent acoustic-gravity waves (AGW) with a continuous spectrum can exist in an atmosphere rotating with an angular frequency Ω below the frequency 2 Ω (the Coriolis parameter). It is also shown that the rotation of the atmosphere also leads to a modification of the previously discovered continuous spectrum of evanescent AGWs with frequencies higher than the Coriolis parameter, which fills the entire “forbidden” region in the diagnostic diagram between freely propagating acoustic and internal gravity waves. It is concluded that the AGW spectrum in the diagnostic diagram consists of regions of acoustic and gravity waves, as well as two regions of evanescent waves, and is continuous. The found new spectrum expands the full spectrum of evanescent waves and indicates the need to search for evanescent waves at ultra-low frequencies. The result is obtained for high-latitude regions from a system of linear hydrodynamic equations for perturbations that take into account the rotation of the Earth’s atmosphere, by imposing an additional spatial relation on the components of the perturbed velocity vector of the elementary volume of the medium, which proposed by us for the first time. This made it possible to obtain an infinite number of solutions describing evanescent acoustic-gravity waves propagating in an isothermal atmosphere. The specified connection between the components of the perturbed velocity is characterized by the α parameter, which can only take real values. It has been established that the detected spectrum of evanescent acoustic-gravity waves can exist only at 0 < α < 1 , while the previously found spectrum of these waves, modified by taking into account the Earth’s rotation, is realized at arbitrary values of α . Analytical and numerical analysis of the obtained solutions is carried out. It is shown that these solutions, at certain values of the parameter α , pass into the previously studied evanescent modes.

The Okubo–Weiss criterion in hydrodynamic flows: geometric aspects and further extension

The Okubo (1970 Deep Sea Res. 17 445)–Weiss (1991 Physica D 48 273) 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 vorticity manifold. The Okubo–Weiss criterion is then reformulated in polar coordinates, and is validated for 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 β-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 formulate for 3D axisymmetric slows, and is validated via application to the round Landau–Squire Laminar jet flow.

Evidence of submesoscale coastal eddies inside Todos Santos Bay, Baja California, México

Submesoscale eddies (1-10 km diameter) were identified using surface velocity observations obtained from a high-frequency radar system (HFR) operated in Todos Santos Bay (TSB), Baja California, Mexico. Eddies were detected through a special case of the Okubo-Weiss parameter for divergent flows in the form of eigenvalues of the Jacobian matrix. The detection method, applied for a surface velocity grid, shows encouraging results in the recognition and tracking of submesoscale features in TSB. The detection method is rapid and efficient. Results show the formation and persistence of an eddy structure inside the Bay in December 6, 2010, displaying a trajectory from NE to SW until disappearing at the center of the Bay. The eddy is approximately 4 km in diameter with a frequency of ~0.1f (f is the Coriolis parameter). The real part of the Okubo-Weiss parameter ranged between −4×10−9 to −1×10−9 s−2, and outlined the eddy for approximately 9 hours. Although it is difficult to identify the origin of the detected submesoscale eddy, its appearance coincided with a drop in relative atmospheric humidity suggesting land-ocean Santa Ana winds as a possible generating mechanism.

Effects of an along-shelf current on the generation of internal tides near the critical latitude

The effects of along-shelf barotropic geostrophic currents on internal wave generation by the $K_1$ tide interacting with a shelf at near-critical latitudes are investigated. The horizontal shear of the background current results in a spatially varying effective Coriolis frequency which modifies the slope criticality and potentially creates blocking regions where freely propagating internal tides cannot exist. This paper is focused on the barotropic to baroclinic energy conversion rate, which is affected by a combination of three factors: slope criticality, size and location of the blocking region where the conversion rate is extremely small and the internal tide (IT) beam patterns. All of these are sensitive to the current parameters. In our parameter space, the current can increase the conversion rate up to 10 times.