Free Kelvin Research Articles

Negative storm surges in the Río de la Plata Estuary: mechanisms, variability, trends and linkage with the Continental Shelf dynamics

Negative storm surge (NSS) events frequently affect the Río de la Plata Estuary (RdP), limiting the access to major ports and waterways and emptying the freshwater intakes of one of the most socially developed basins of the Southwestern Atlantic Continental Shelf (SWACS). It is important to re-examine this issue, as the available studies are outdated, there are some contradictions in the literature and a regional framework of the adjacent shelf dynamics is not yet available. In this work (i) nonlinear statistical analyses were applied to review and update the climatological description of NSS in the RdP; and, then, (ii) an ocean numerical model was employed to describe and understand the surge dynamics framed into the larger scale dynamics of the atmospherically forced SWACS. An analysis of 87 years of hourly residual sea level observations (RSL) reveals that the number of yearly NSS events time series presents (i) a statistically significant multidecadal non-linear trend or envelope and (ii) two significant pseudo-cycles centred at 3.5 and 11.5 years that explain a large fraction of the interannual variability embedded in the multidecadal modulation.Numerical simulations results show that the surges (both negative and positive) that are generated in the SWACS and reach the RdP result from the passage of atmospheric planetary waves over Patagonia which produce winds with a significant alongshore (N-S) component. These winds force an Ekman transport either offshore or onshore at the coast, generating a negative or positive sea level anomaly, which will be larger as the atmospheric system is slower and more persistent. When synoptic atmospheric systems migrate away from the coast on their northeastward propagation, the forced sea level anomalies propagate along the coast to the north as free Kelvin waves, eventually reaching the estuary; thus the forcing for surges at the RdP can be remote. In this sense, despite the large gulfs and bays, the response of the Patagonian coast is similar to that of a linear coastline oriented in a north–south direction. In addition to remotely forced surges, locally forced events occur in the RdP as a result of the estuarine geometry and its resonant response to winds with a component longitudinal to the estuary axis (NW-SE), which could be forced by other atmospheric configurations besides Rossby waves, such as cyclogenesis of the Argentine Littoral.

Waves on the equatorial β-plane in the presence of a uniform zonal flow: Beyond the Doppler shift

Analytical and numerical solutions of the eigenvalue equation associated with zonally propagating waves of the linearized rotating shallow water equations are derived in a channel on the equatorial β-plane in the presence of a uniform mean zonal flow. The meridionally varying mean height field is in geostrophic balance with the prescribed mean zonal flow. In addition to the trivial Doppler shift of the free waves' phase speeds, the mean state causes the dispersion curves of each of the free Rossby and Poincaré waves to nearly coalesce in pairs of modes when the zonal wavenumber increases. For large zonal wavenumber or large mean flow, the latitudinal variation of the waves' amplitudes differs from that of free waves, i.e., Hermite functions (in wide channels) and harmonic functions (in narrow channels) do not describe the amplitude structure. For large mean speed and for large zonal wavenumber, the eigenvalue problem loses its Sturm–Liouville structure and the eigenfunctions have multiple extrema between successive zeros of the function itself. In contrast to free Kelvin waves, in the presence of a mean flow the meridional velocity component of these waves does not vanish identically. For zonal winds of order 20 m s−1 and for gravity wave speed of order 25 m s−1, conditions relevant to Earth's stratosphere, the phase speed with mean wind can be twice that of the classical theory with no mean zonal wind.

Inertial mode interactions in a rotating tilted cylindrical annulus with free surface

Laboratory experiments are performed in a partly filled and tilted rotating annulus, which is analog to the classical precession experiments. With the presence of a forcing Kelvin mode, two types of instability are observed under a resonant condition: a parametric triadic resonance, in which two free Kelvin modes form a triad with the forced Kelvin mode, and a shear-type instability, which is related to the nonzero mean flow.

Rapidly rotating precessing cylinder flows: forced triadic resonances

Rapidly rotating cylinder flows subjected to low-amplitude precessional forcing are studied numerically over a range of cylinder and precessional rotation rates. For sufficiently small rotation rates, viscous effects lead to a forced overturning flow that is steady in the precession (table) frame of reference. Increasing the rotation rates, this forced flow loses stability in a Hopf bifurcation, which can be either supercritical or subcritical, and may preserve or break the symmetry of the system, depending on the parameter regime studied. Regardless of these details of the Hopf bifurcation, it is found that the Hopf instability is associated with a slightly detuned triadic resonance between the forced overturning flow and two free Kelvin modes (inviscid eigenmodes of the rotating cylinder). Further increases in rotation rates lead to a sequence of secondary instabilities which also follow a generic pattern irrespective of the parameter regime investigated. The relationship between this sequence of instabilities and the resultant nonlinear dynamics with the experimentally observed phenomenon of resonant collapse is discussed.

Evaluation of Electromagnetic Fields Induced by Wake of an Undersea-Moving Slender Body

This paper presents the procedure for evaluating the electromagnetic field induced by the wake of an undersea-moving slender body. The slender body is considered equivalent to a pair of Havelock point sources that can generate wake flow fields. The electric current generated in the seawater is calculated by means of the moving conductive seawater that cuts the earth’s magnetic field. The electromagnetic fields in the air and in the seawater are then determined by solving the Maxwell equations with appropriate boundary conditions. The induced electromagnetic fields include two parts: One is the attenuating oscillation that can be ascribed to the free surface Kelvin wake, and the other is the bipolar pulse that can be ascribed to the localized volume wake. Near the sea surface, the magnitude of the former is typically a few hundred pico-tesla, while that of the latter could be greater by ten times.

The statistical structure of synoptic variability ocean currents at the continental slope of the Laptev Sea and features of their generation by anemobaric forces

Based on vector-algebraic analysis of random processes, we study the statistical structure of the synoptic variability of currents measured by an ADCP in the upper mixed layer in the central part of the continental slope of the Laptev Sea in 2006–2007. The results of statistical analysis show that in some cases the synoptic currents in the surface layer of the sea are signs of wind drift currents. This is indicated by the high correlation between the tangential friction of wind and currents, as well as the reversal of the depth of current vectors and the major axes of the ellipses of the mean-square deviation of the Ekman spiral. Due to the large variability of wind flows and stratification of water masses, the penetration depth of these currents is small and varies from 6 to 30 m, with pronounced seasonal variation. In deeper layers, no relationship between the currents and anemobaric forces is traced. It is concluded that the fluctuations of synoptic scale currents in the area of the continental slope of the Laptev Sea represent a superposition of Ekman drift currents and movements associated with free baroclinic Kelvin waves. These currents are the dominant contributor in the upper 30-m layer of the ocean, while waves play a key role in deeper waters.

Triadic instability of a non-resonant precessing fluid cylinder

Flows forced by a precessional motion can exhibit instabilities of crucial importance, whether they concern the fuel of a flying object or the liquid core of a telluric planet. So far, stability analyses of these flows have focused on the special case of a resonant forcing. Here, we address the instability of the flow inside a precessing cylinder in the general case. We first show that the base flow forced by the cylinder precession is a superposition of a vertical or horizontal shear flow and an infinite sum of forced modes. We then perform a linear stability analysis of this base flow by considering its triadic resonance with two free Kelvin modes. Finally, we derive the amplitude equations of the free Kelvin modes and obtain an expression of the instability threshold and growth rate.

Triadic resonances in nonlinear simulations of a fluid flow in a precessing cylinder

We present results from three-dimensional nonlinear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which—in cylindrical geometry—form so-called Kelvin modes. For a precession ratio (Poincaré number) considered by us, the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of Po. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin modes are triggered by nonlinear interactions and may constitute a triadic resonance with the fundamental forced mode when the height of the container matches their axial wave lengths. Our simulations reveal triadic resonances at aspect ratios close to those predicted by the linear theory except around the primary resonance of the forced mode. In that regime we still identify various free Kelvin modes, however, all of them exhibit a retrograde drift around the symmetry axis of the cylinder and none of them can be assigned to a triadic resonance. The amplitudes of the free Kelvin modes always remain below the forced mode but may reach up to 6% of the of the container’s angular velocity. The properties of the free Kelvin modes, namely their amplitude and their frequency, will be used in future simulations of the magnetic induction equation to investigate their ability to provide for dynamo action.

Resonance of long waves generated by storms obliquely crossing shelf topography in a rotating ocean

The oceanic forced wave beneath a moving atmospheric disturbance is amplified by Proudman resonance. When modified by the Earth's rotation this classical resonance only occurs if the disturbance time scale is smaller than the inertial period. With or without Coriolis effects, free transients generated by storm forced waves obliquely crossing step changes in water depth at particular angles are shown to resonate by exciting a range of long barotropic free waves. Rotationally influenced slow atmospherically forced waves crossing a vertical coast at a critical angle lead to a form of subcritical resonance, which occurs only when the component of the disturbances' phase velocities along the coast matches that of a free Kelvin wave (KW). In a rotating ocean, transients generated by disturbances crossing a step at a particular angle are shown to excite a free double Kelvin wave (DKW). This new type of resonance only occurs for sufficiently large steps and disturbances with time scale greater than the inertial period. A storm crossing a step shelf can result in the excitation of an infinite set of edge waves, a single KW, a unique DKW and a first-mode continental shelf wave, depending on the topography and the disturbance time scale, translation speed and incident angle. The study of resonances and wave mode excitations generated by storms crossing a coast or a continental shelf may contribute to understanding how a particular combination of the storm characteristics can result in destructive coastal events with time scales encompassing the typical meteotsunami period band (tens of minutes) and storm surges with periods of several hours or days.

Precessional instability of a fluid cylinder

In this paper, the instability of a fluid inside a precessing cylinder is addressed theoretically and experimentally. The precessional motion forces Kelvin modes in the cylinder, which can become resonant for given precessional frequencies and cylinder aspect ratios. When the Reynolds number is large enough, these forced resonant Kelvin modes eventually become unstable. A linear stability analysis based on a triadic resonance between a forced Kelvin mode and two additional free Kelvin modes is carried out. This analysis allows us to predict the spatial structure of the instability and its threshold. These predictions are compared to the vorticity field measured by particle image velocimetry with an excellent agreement. When the Reynolds number is further increased, nonlinear effects appear. A weakly nonlinear theory is developed semi-empirically by introducing a geostrophic mode, which is triggered by the nonlinear interaction of a free Kelvin mode with itself in the presence of viscosity. Amplitude equations are obtained coupling the forced Kelvin mode, the two free Kelvin modes and the geostrophic mode. They show that the instability saturates to a fixed point just above threshold. Increasing the Reynolds number leads to a transition from a steady saturated regime to an intermittent flow in good agreement with experiments. Surprisingly, this weakly nonlinear model still gives a correct estimate of the mean flow inside the cylinder even far from the threshold when the flow is turbulent.

Seasonal Propagation of Sea Level along the Equator in the Atlantic

Abstract In the equatorial Atlantic the sea surface height (SSH) anomaly field is dominated by an annual signal propagating eastward. This signal has been previously interpreted in terms of propagating waves. In this article it is argued that this propagating signal is not a free equatorial Kelvin wave because the phase velocity observed is too small compared to first, second, or third baroclinic mode Kelvin waves, and is not the result of an equatorial forced wave because the zonal wind stress does not show a similar propagation. Rather, it is suggested that the eastward propagation in SSH is due to the sum of two independent modes of variability: one mainly driven by the wind stress curl off the equator, and the other driven by the zonal wind stress along the equator. These two modes are uncorrelated in time and space and therefore can be conveniently separated by an empirical orthogonal function analysis of the equatorial Atlantic sea surface height. The first mode explains 74% of the variance, is one-signed in longitude, and is interpreted as the variability of the warm water volume above the thermocline. The second mode explains 24% of the variance, consists of an east–west tilt along the equator, and is driven by variations of the zonal equatorial wind stress.

Instability of a fluid inside a precessing cylinder

In this letter, we report experimental results on the stability of a fluid inside a precessing and resonant cylinder. Above a critical Reynolds number, the Kelvin mode forced by precession triggers an instability which saturates at intermediate Re and which leads to a turbulent flow at high Reynolds numbers. Particle image velocimetry measurements in two different sections of the cylinder have revealed the three-dimensional structure of this instability. It is composed of two free Kelvin modes whose wavenumbers and frequencies respect the conditions for a triadic resonance with the forced Kelvin mode, as is obtained for the elliptical instability. Moreover, an experimental diagram of stability has been established by varying both the precessing angle and the Reynolds number. It shows a good agreement with a scaling analysis based on a triadic resonance mechanism.

On the fluctuations and vertical structure of the shelf circulation off Walvis Bay, Namibia

Temporal variations of the current field on the shelf of the South East Atlantic off Walvis Bay were studied during austral summer and fall by moored current profiler and temperature-salinity recorder located on the shelf 20 nm off Walvis Bay, Namibia. Spatial and temporal variations of the wind field in the South East Atlantic were investigated by 3-day averaged wind fields measured by the QuikSCAT satellite. The local wind was provided by a time series of hourly wind vectors measured on a moored buoy off Swakopmund. The significant tidal motion on the shelf off Walvis Bay is composed of the anticlockwise rotating barotropic semidiurnal constituents M2 and S2. The tidal currents are described to a first order by a barotropic deep ocean Kelvin wave. The land-sea breeze forces anticlockwise rotating diurnal variations of the current in the surface mixed layer and an opposite directed current below the thermocline, which compensates the mass flux normal to the coast in the surface layer. Most of the energy of the current fluctuations were concentrated around the local inertial period of T i = 30.7 h . These fluctuations consisted of at least four significant anti-clockwise rotating vertical modes with amplitudes ranging between 10 and 20 cm/s. On a large scale the amplitudes of inertial motions correlate with the wind fluctuations but locally the motions consist of a superposition of locally wind forced inertial oscillations and inertial waves generated at larger distances as well near the surface as close to the bottom. The vertical structure of the inertial motion suggests that it could be a possible candidate for mixing in the bottom boundary layer by differential advection. Coastal trapped waves of horizontal mode number less that four were observed at periods of about 7 days. The mean cross shelf circulation consisted of a two cell structure. The upper cell was made of the Ekman offshore current and a compensating onshore current at intermediate depth below the thermocline. The lower cell consisted of an offshore current in the bottom layer below 80 m depth and was closed by the onshore current in the intermediate depth range. The cross shelf circulation controlled the fraction of ESACW on the shelf water mass. The long shelf circulation consisted in the surface mixed layer of an equatorward coastal jet driven by the local meridional wind stress and an almost barotropic poleward counter current appearing partly as free Kelvin wave emanating from the Angola-Benguela front and as coastal counter current forced by the local negative curl of the wind stress. The longshore current controlled the fraction of the SACW on the shelf water mass, which increased continuously between austral summer and fall.

An Intersection of Oceanic Waveguides: Variability in the Indonesian Throughflow Region

Abstract Temperature and sea level variability within the Indonesian seas and southeast Indian Ocean are described based on expendable bathythermograph deployments along volunteer merchant shipping lines under way since 1983. These data resolve variability at time scales ranging from the intraseasonal to the interannual. A lagged partial regression technique reveals that anomalies from a mean seasonal cycle of temperature and sea level for seasonal to interannual time scales can be largely understood in terms of free Kelvin and Rossby waves generated by remote zonal winds along the equator of the Indian and Pacific Oceans, with local wind forcing appearing to play a minor role. About 60%–90% of sea level variability and 70% of thermocline temperature variability can be accounted for in this way. Variations in zonal Pacific equatorial winds force a response along the Arafura/ Australia shelf break through Pacific equatorial Rossby waves exciting coastally trapped waves off the western tip of New Guinea, wh...

Initial Development of Tropical Precipitation Patterns in Response to a Local Warm SST Area: An Aqua-Planet Ensemble Study

For the purpose of examining the initial development of the atmospheric response to a warm SST anomaly placed at the equator, an ensemble switch-on experiment is conducted with an aqua-planet GCM. An ensemble average of the size of 128 significantly reduces the transient noises caused by both small scale convective activity and large scale intraseasonal variability.In the first three days after the switch-on of the SST anomaly, a convection center develops above the warm SST area. As a barotropic response to the heating of convection center, a global increase of surface pressure occurs outside the low pressure region around the warm SST area. The response after the emergence of the high pressure anomaly is consistent with Gill (1980); a warm Kelvin wave-like anomaly is emitted to the east of the convection center, while a warm Rossby wave-like anomaly is emitted to the west.The Kelvin wave-like signal propagates at a speed slower than that of free Kelvin wave expected from its vertical wavelength, suggesting that the signal is a “moist” Kelvin wave. Transient decrease of precipitation occurs at the moist Kelvin wave front; a decrease of convection associated with the downward motion at the wave front is consistent with its slow propagation. After several days, precipitation recovers and is even intensified because of the surface frictional convergence associated with the Kelvin wave-like equatorial low pressure anomaly. To the west of the warm SST area, on the other hand, precipitation decreases monotonically. The continuous reduction of precipitation is caused by the equatorial surface frictional divergence associated with the relatively high pressure anomaly at the equator of the Rossby wave structure.Finally, there appears a slow zonally symmetric response within the Hadley cell characterized with surface pressure rise in the tropics and westerly wind anomaly in the troposphere. The change of eddy zonal momentum transport, together with the transport toward the lower level by the Hadley circulation and the geostrophic adjustment to the resulting low level westerly acceleration, seems to be responsible for the response.

Tropical Pacific basin‐wide adjustment and oceanic waves

This study examines the basin‐wide adjustment process associated with El Niño‐Southern Oscillation (ENSO) in terms of oceanic waves using the Cane‐Zebiak model. The Rossby waves induce not only the meridional mass divergence in the ocean interior but also the incoming zonal mass flux at the western boundary, which generally overcompensates the interior meridional divergence. Therefore, the Rossby waves alone cannot make a negative feedback. However, the outgoing zonal mass flux associated with the reflected Kelvin wave at the western boundary reduces the incoming boundary mass flux associated with the Rossby waves, resulting in the tendency of equatorial basin‐wide heat content varying in phase with the meridional divergence. Also shown is that the nonequilibrium adjustment of the tropical Pacific Ocean is mainly due to the free Kelvin waves reflected at the western boundary.

Wave dynamics of super cloud clusters over the tropical region

A wave dynamics for the super cloud clusters associated with the tropical intraseasonal oscillation is constructed. Under the present framework, the basic state of super cloud clusters is considered to be a large-scale convergence of the zonal wind. This convergence is created by a nonlinear diabatic Kelvin wave front, which moves eastward slowly without change of shape. When interacting with free equatorial waves with n=−1, 0, 1 and 2, this basic flow will suppress those waves which move eastward except for free Kelvin waves, and permit westward propagating modes such as the mixed Rossby-gravity wave, the inertio-gravity waves with n=1 and 2 to appear in the large-scale convergent region. Among these waves, only fast modes, that is, inertio-gravity waves with n=1 and 2 are regarded to be responsible for the presence of cloud clusters which move westward within a super cloud cluster, while the multiplicity of the occurrences of super cloud clusters, which move eastward within the large-scale convergent region, is due to the superposition of free Kelvin wave upon these inertio-gravity waves.

Flow transition in a multilouvered fin array

The paper describes the detailed transition mechanism from steady to unsteady flow in a multilouvered fin geometry. The initial instability appears in the wake of the exit louver at a Reynolds number of 400 with a characteristic non-dimensional frequency (based on inflow velocity and louver pitch) of 0.84. Between a Reynolds number of 700 and 800, power spectra in the interior of the array indicate an increase in energy in the vicinity of the first harmonic of the initial exit wake instability. By a Reynolds number of 900, free shear layer or Kelvin–Helmholtz type instabilities develop on the leading edge shear layers of louvers near the exit. These instabilities have a characteristic non-dimensional frequency of 1.7. As the Reynolds number increases further, instabilities move upstream into the array. By a Reynolds number of 1300, most of the louvers exhibit unsteadiness, except for the entrance louver and the first two louvers following it. By this Reynolds number, the flow in the downstream half of the array exhibits a chaotic behavior.

Effects of a sloping thermocline and Rayleigh friction on equatorially trapped Kelvin waves

Based on the observed equatorial ocean dynamic characteristics, the effects of a sloping thermocline and Rayleigh friction on the equatorially trapped free Kelvin waves were theoretically studied with a linear one-and-one-half layer reduced gravity model, the multiple-scale method and a small parameter expansion technique. Assuming that main thermocline depth (MTD) variations are slow, i. e. the changes of MTD over one wavelength are smaller than that of the wave amplitude and that wave reflections are negligible, the authors showed by their analytical results that the wavelengths and amplitudes of Kelvin waves are significantly modified by the MTD variations and Rayleigh friction. The results also showed that for an eastward shallowing thermocline, the zonal velocity of the Kelvin waves varies with thermocline depth to the power −7/8. The eastward shallowing of the thermocline depth strengthens Kelvin wave entrapment at the equator. Rayleigh friction reduces the Kelvin wave's eastward velocity while the thermocline acts in the opposite way. The friction causes dispersion of the Kelvin wave, whose dissipation factor does not depend on its wavelength. The friction increases the lateral decay length and causes phase lines of Kelvin waves to slant westward in parabolic arcs.

Wind‐forced upwelling and internal Kelvin wave generation in Mackenzie Canyon, Beaufort Sea

Low‐frequency current, temperature, and salinity variations over the shelf break in the southeastern Beaufort Sea (Mackenzie Shelf) are examined to determine the response of seasonally ice‐free waters to wind forcing and the role of submarine canyons in upwelling events and shelf circulation. Upwelling events were found to be statistically correlated to northeasterly winds, which transport surface waters offshore and draw up water from deeper layers. The response to alongshore wind stress is significantly amplified in Mackenzie Canyon, where isopycnal displacements of over 400 m are observed. Such displacements are then observed to propagate eastward at a phase velocity near 0.6 m s−1. The canyon is thus a site of intense upwelling, while the collapse of displaced isopycnals subsequent to cessation of wind forcing creates a disturbance propagating northeast along shelf as a free internal Kelvin wave.