Near-inertial Oscillations Research Articles

Current Patterns on the West Florida Shelf from Joint Self-Organizing Map Analyses of HF Radar and ADCP Data

Abstract To assess the spatial structures and temporal evolutions of distinct physical processes on the West Florida Shelf, patterns of ocean current variability are extracted from a joint HF radar and ADCP dataset acquired from August to September 2003 using Self-Organizing Map (SOM) analyses. Three separate ocean–atmosphere frequency bands are considered: semidiurnal, diurnal, and subtidal. The currents in the semidiurnal band are relatively homogeneous in space, barotropic, clockwise polarized, and have a neap-spring modulation consistent with semidiurnal tides. The currents in the diurnal band are less homogeneous, more baroclinic, and clockwise polarized, consistent with a combination of diurnal tides and near-inertial oscillations. The currents in the subtidal frequency band are stronger and with more complex patterns consistent with wind and buoyancy forcing. The SOM is shown to be a useful technique for extracting ocean current patterns with dynamically distinctive spatial and temporal structures sampled by HF radar and supporting in situ measurements.

Equatorial wave attractors and inertial oscillations

Three different approximations to the axisymmetric small-disturbance dynamics of a uniformly rotating thin spherical shell are studied for the equatorial region assuming time-harmonic motion. The first is the standard β-plane model. The second is Stern's (Tellus, vol. 15, 1963, p. 246) homogeneous, equatorial β-plane model of inertial waves (that includes all Coriolis terms). The third is a version of Stern's equation extended to include uniform stratification. It is recalled that the boundary value problem (BVP) that governs the streamfunction of zonally symmetric waves in the meridional plane becomes separable only for special geometries. These separable BVPs allow us to make a connection between the streamfunction field and the underlying geometry of characteristics of the governing equation. In these cases characteristics are each seen to trace a purely periodic path. For most geometries, however, the BVP is non-separable and characteristics and therefore wave energy converge towards a limit cycle, referred to as an equatorial wave attractor. For Stern's model we compute exact solutions for wave attractor regimes. These solutions show that wave attractors correspond to singularities in the velocity field, indicating an infinite magnification of kinetic energy density along the attractor. The instability that arises occurs without the necessity of any ambient shear flow and is referred to as geometric instability.For application to ocean and atmosphere, Stern's model is extended to include uniform stratification. Owing to the stratification, characteristics are trapped near the equator by turning surfaces. Characteristics approach either equatorial wave attractors, or point attractors situated at the intersections of turning surfaces and the bottom. At these locations, trapped inertia–gravity waves are perceived as near-inertial oscillations. It is shown that trapping of inertia–gravity waves occurs for any monochromatic frequency within the allowed range, while equatorial wave attractors exist in a denumerable, infinite set of finite-sized continuous frequency intervals. It is also shown that the separable Stern equation, obtained as an approximate equation for waves in a homogeneous fluid confined to the equatorial part of a spherical shell, gives an exact description for buoyancy waves in uniformly but radially stratified fluids in such shells.

Modification of the loop current warm core eddy by Hurricane Gilbert (1988)

Numerical investigation of Hurricane Gilbert (1988) effect on the Loop Current warm core eddy (WCE) in the Gulf of Mexico is performed using the Modular Ocean Model version 2 (MOM2). Results show that the storm-induced maximum sea surface temperature (SST) decrease in Gilbert’s wake is over 2.5°C, as compared with the 3.5°C cooling in the absence of the WCE. The near-inertial oscillation in the wake reduces significantly in an along-track direction with the presence of the WCE. This effect is also reflected between the mixed layer and the thermocline, where the current directions are reversed with the upper layer. After two inertial periods (IP), the current reversal is much less obvious. In addition, it is demonstrated that Hurricane Gilbert wind stress increases the current speed of the WCE by approximate 133%. With the forcing of Gilbert, the simulated translation direction and speed of the WCE towards the Mexican coast are closer to the observed (42% more accurate in distance and 78% more accurate in direction) compared with the simulation without the Gilbert forcing. The simulated ocean response to Gilbert generally agrees with the recent observations in Hurricane Fabian.

Rapid Variability in the Japan/East Sea: Basin Oscillations, Internal Tides, and Near-Inertial Oscillations

Abstract : Many processes contribute to the variations of currents, sea surface height (SSH), and thermocline depth in marginal seas. Energetic examples range broadly over time scales from slow mesoscale and interannual variations to rapid basin oscillations, internal tides, and near-inertial oscillations. Our measurement array in the Japan/East Sea (JES) offered a special opportunity to study these processes simultaneously, revealing important interconnections among them. The PIES (pressure- guage-equipped inverted echo sounder) experiment in the Ulleung Basin of the southwestern JES was originally designed to investigate the dynamics of meandering currents and eddies in the upper and deep ocean. For those purposes, we low-pass filtered the measurements to examine mesoscale variability. The companion papers by Watt et al.(this issue) and Mitchell et al. (2OO5a) describe the mesoscale circulation patterns, including evolution and propagation of warm and cold eddies. The acoustic-echo-time records also included energetic short period signals. which dominated the bottom pressure record. Within the JES the barotropic (or surface) tidal amplitudes are so small (< 10cm, compared to I m typically in mid-ocean) that these energetic short-period signals stood out and demanded our attention. We present here an overview of three aspects of short-period variability (less than about 10 days) observed in the JES, even though short-period phenomena were originally outside our main objective.

Normal modes of an incompressible and stratified fluid model including the vertical and horizontal components of coriolis force

Numerical solutions of the normal modes of a linearized Boussinesq fluid model are studied with respect to the variable static stability in height z, the Brunt-Väisälä frequency N(z). The model includes both the vertical and horizontal components of Coriolis force. Our aim is to explore the characteristics of the little-known class of normal modes, referred to as the ‘boundary-induced inertial (BII)’ modes, in addition to the traditional inertio-gravity (IG) modes. Two kinds of finite-difference schemes are used to set up the eigenvalue-eigenvector matrix problem for crosscheck.Numerical results of the characteristics of IG and BII modes are presented for the case of an exponential form of N(z), together with the cases of constant N, whose exact solutions are used to check the performance of the numerical models. Because the frequencies of BII modes are close to the inertial frequency, which is a singular point of the model, the eigenfunctions of BII modes become highly oscillatory in z for a large value of N. It is shown that, under a realistic profile of N(z) in the oceans, the BII modes can appear complementary to the IG modes throughout the domain, suggesting that the joint consideration of both the IG and BII modes is necessary to understand the near-inertial oscillations in the seas.

Ballooning of River-Plume Bulge and Its Stabilization by Tidal Currents

Abstract When freshwater debouches into an adjacent ocean, an anticyclonic eddy (bulge) is formed in front of the river mouth. It is well known that a bulge growing offshore (ballooning) hardly reaches a steady state in the absence of either ambient currents or wind forcing. This study provides a physical interpretation for the ballooning of river-plume bulges by conducting numerical experiments in which a river plume is induced by a coastal freshwater source. Part of the freshwater released to the model ocean undergoes inertial instability. Near-inertial oscillations are predominant when disturbances are not forced in ambient waters of the river plume. These isotropic disturbances are amplified by inertial instability, so that unstabilized freshwater can move in arbitrary directions. Thus, unstabilized freshwater does not need to move toward the coastal boundary current on the right-hand side of the river mouth. Freshwater unstabilized for a long time can stay in the bulge for a long time. Unstabilized freshwater accumulates gradually in the bulge, and so ballooning occurs. When the direction of disturbances is prescribed in ambient waters, unstabilized freshwater is forced to move in the same direction. Thereby, the motion of unstabilized freshwater is restricted in the alongshore direction when background disturbances are induced by alongshore tidal currents. It is therefore concluded that tidal currents play a role in stabilizing the offshore growth of river-plume bulges in coastal and shelf waters.

Mixing in seasonally stratified shelf seas: a shifting paradigm

Although continental shelf seas make up a relatively small fraction (ca 7%) of the world ocean's surface, they are thought to contribute significantly (20-50% of the total) to the open-ocean carbon dioxide storage through processes collectively known as the shelf sea pump. The global significance of these processes is determined by the vertical mixing, which drives the net CO(2) drawdown (which can occur only in stratified water). In this paper, we focus on identifying the processes that are responsible for mixing across the thermocline in seasonally stratified shelf seas. We present evidence that shear instability and internal wave breaking are largely responsible for thermocline mixing, a clear development from the first-order paradigm for the water column structure in continental shelf seas. The levels of dissipation observed are quantitatively consistent with the observed dissipation rates of the internal tide and near-inertial oscillations. It is perhaps because these processes make such a small contribution to the total energy dissipated in shelf seas that they are not well represented in current state-of-the-art numerical models of continental shelf seas. The results thus present a clear challenge to oceanographic models.

Seasonal/Spatial Variations of the Near-Inertial Oscillations in the Deep Water of the Japan Sea

A general description of the near-inertial oscillations in the deep water of the Japan Sea has been found by analyzing observed current data accumulated over a period of ten years. The near-inertial oscillations were dominant in the deep water, and those in the southern Japan Sea, the Tsushima current region, were more energetic than those in the northern area. Their temporal variations have an annual cycle with wintertime intensifications corresponding to the windy season over the Japan Sea. In the Yamato Basin, however, the power of the near-inertial oscillations was small during spring and large during summer, in addition to the above seasonal variations. The results of a slab model showed that the wind stress could account for part of the long periodic variations such as the annual cycle of the near-inertial oscillations in the deep water, but this is not expected to be their only source. Since the surface currents in the southern Japan Sea, especially in the Yamato Basin, vary significantly both temporally and spatially, the surface layer itself also could be responsible for the generation of the near-inertial oscillations in the deep water.

Doppler-Shifted Inertial Oscillations on a β Plane

Abstract On the spherical earth, and in the absence of a background flow, the poleward propagation of near-inertial oscillations is restricted by the turning latitude. A background flow, on the other hand, provides a way to increase the apparent frequency of near-inertial waves through Doppler shifting. In this note, it is shown that near-inertial oscillations can be advected to latitudes higher than their turning latitude. Associated with the poleward advection there is a squeezing of the meridional wavelength. A numerical model is used to verify this result. The squeezed inertial oscillations are vulnerable to nonlinear interactions, which could eventually lead to small-scale dissipation and mixing.

Near-Inertial Oscillations of Geophysical Surface Frontal Currents

Intrinsic oscillations of stable geophysical surface frontal currents of the unsteady, nonlinear, reduced-gravity shallow-water equations on an f plane are investigated analytically and numerically. For frictional (Rayleigh) currents characterized by linear horizontal velocity components and parabolic cross sections, the primitive equations are reduced to a set of coupled nonlinear ordinary differential equations. In the inviscid case, two periodic analytical solutions of the nonlinear problem describing 1) the inertially reversing horizontal displacement of a surface frontal current having a fixed parabolic cross section and 2) the cross-front pulsation of a coastal current emerging from a motionless surface frontal layer are presented. In a linear and in a weakly nonlinear context, analytical expressions for field oscillations and their frequency shift relative to the inertial frequency are presented. For the fully nonlinear problem, solutions referring to a surface frontal coastal current are obtained analytically and numerically. These solutions show that the currents oscillate always superinertially, the frequency and the amplitude of their oscillations depending on the magnitude of the initial disturbance and on the squared current Rossby number. In a linear framework, it is shown that disturbances superimposed on the surface frontal current are standing waves within the bounded region, the frequencies of which are inertial/superinertial for the first mode/higher modes. In the same frame, a zeroth mode, which could be interpreted as the superposition of an inertial wave on a background vorticity field, would formally yield subinertial frequencies. For surface frontal currents affected by Rayleigh friction, it is shown that the magnitude of the mean current decays according to a power law and that the oscillations decay faster, because this decay follows an exponential law. Implications of the intrinsic oscillations and of their rapid dissipation for the near-inertial motion in an active ambient ocean are discussed.

Wind-induced internal wave dynamics near the Adriatic shelf break

Current and temperature measurements from a thermistor chain and current meter mooring were analysed to describe the near-surface internal wave field close to the middle Adriatic shelf break. Wind speed and direction from the nearby meteorological station Lastovo were analysed too, being a possible internal waves generating force. Spectral properties of currents and temperatures in the surface mixed and thermocline layers indicate strong deviations from the Garrett and Munk (Geophysical Fluid Dynamics 2 (1972) 225; Journal of Geophysical Research 80 (1975) 291) deep ocean internal wave models. The frequency spectra were dominated by three energetic bands: at 0.060 cph (near-inertial frequency), 0.080 cph (M 2 tidal frequency) and between 3 and 4 cph. Near-inertial and high-frequency (3–4 cph) internal waves were generated by wind and/or surface wind waves. The frequency band 3–4 cph of high-frequency energetic waves does not correspond to the local Brunt–Väisälä frequency (30 cph), but to the thickest constant N layer below the thermocline—Sabinin (Izvestiya Academy of Sciences, USSR, Atmospheric and Oceanic Physics, English Edition 2 (1966) 872) “resonance layer”. Near-inertial oscillations represented a major contribution to the horizontal kinetic energy accounting for about 25% (10%) of the total surface (bottom) current variances. Vertically, the clockwise current vector rotations in the surface layer are out of phase by 180° compared with those below the thermocline. The level of surface near-inertial spectral peak was very high compared to the Garrett–Munk level, because of the proximity of wind generating force, while its bandwidth was typical for mid-latitudes.

The Processes of SST Cooling by Typhoon Passage and Case Study of Typhoon Rex with a Mixed layer Ocean Model.

The mechanisms by which sea surface temperatures (SSTs) decrease by passage of typhoons under various initial oceanic conditions and the atmospheric boundary conditions were investigated. A stronger wind stress, slower typhoon translation, excessive heat flux from the sea to the atmosphere, a thinner initial mixed layer, and a greater vertical gradient of the sea temperature in the thermocline layer, all have an effect on mixed layer temperature (MLT) cooling. MLT cooling occurs through intermingled processes by enhanced entrainment and upwelling. In contrast, horizontal advection produced by near-inertial oscillation has a slight effect on determining the distributions of MLTs. The depth in the mixed layer near the area along the typhoon track is determined by the magnitudes of the wind stresses and the translation speeds irrespective of the initial thickness of the mixed layer. In addition, under different wind stresses, translation speeds, and vertical profiles of sea temperatures, the MLT cooling is closely related to the ratio of maximum variation of depth by upwelling to the maximum thickness of the mixed layer. The ratio of maximum variation of depth by upwelling to the maximum thickness of the mixed layer under conditions of excessive heat fluxes, is the same as that under conditions of no heat flux. However, MLT cooling under conditions in which the maximum heat flux reaches 800W/m2 is 0.7°C greater than those in no heat flux. In this case, seawater cooling at the transition layer caused by entrainment influences MLT cooling. Numerical simulations were conducted to elucidate the 3°C SST cooling by Typhoon Rex that was observed by R/V Keifu Maru of the Japan Meteorological Agency (JMA). The SST variation obtained by numerical simulation captures the aspects of observational SSTs reported by R/V Keifu Maru, in that the SST rapidly decreases and the maximum SST cooling reaches about 3°C. This rapid SST cooling is mainly caused by the stronger wind stresses and slower translation speeds of Typhoon Rex. The ocean heat contents, based on the model-computed sea temperature, are closely related to the intensities of Typhoon Rex.

Horizontal dispersion of near-inertial oscillations in a turbulent mesoscale eddy field

We study the dispersion of wind-induced near-inertial oscillations (NIOs) in a fully turbulent baroclinic mesoscale eddy e eld characterized by a continuous wavenumber spectrum. The ine uence of the eddy e eld on the horizontal dispersion of the different NIO modes is analyzed using a vertical normal mode expansion. Previous studies have identie ed two dispersion regimes: trapping and strong dispersion. We examine the modes in physical and spectral space to assess which regime prevails. Numerical and analytical results show the prevalence of a trapping regime. For each NIO mode, there exists a critical horizontal wavenumber, k c, that separates large-scale NIO structures, where trapping dominates, from the much less energetic small-scale NIO structures, where strong dispersion dominates. The maximum efe ciency of dispersion for scales close to k c concentrates NIO kinetic energy at these scales. The wavenumber k c results from a balance between refraction and dispersion. This balance e rst occurs at the highest wavenumber. Thereafter, kc, which has dimensional expression kc 2 5 p/( ftRm 2 ), decreases with time at a rate inversely proportional to the radius of deformation, Rm, of the baroclinic NIO mode considered. As a consequence, at any given time, higher NIO baroclinic mode energy can mostly be found in small-scale negative vorticity structures, such as e laments near sharp vorticity fronts, whereas lower NIO mode energy is concentrated within the core of mesoscale anticyclonic vortices. For large times, a saturation mechanism stops the time-evolution of k c at a value close to the peak of the kinetic energy spectrum of the QG e ow e eld.

Radiation of Mixed Layer Near-Inertial Oscillations into the Ocean Interior

The radiation from the mixed layer into the interior of the ocean of near-inertial oscillations in the presence of the beta effect is reconsidered as an initial-value problem. Making use of the fact that the mixed layer depth is much smaller than the total depth of the ocean, the solution is obtained in the limit of an ocean that is effectively infinitely deep. For a uniform initial condition, analytical results for the velocity, horizontal kinetic energy density, and fluxes are obtained. This is the canonical solution for the radiation of near-inertial oscillations in the vertical, which captures the basic mechanisms due to the beta effect, and leads to the formation of small scales in the vertical. By superposing events, an average vertical wavenumber spectrum is constructed. The predicted decay of near-inertial mixed layer energy in the presence of the beta effect occurs on a timescale similar to that observed.

Prognostic Modeling Studies of the Keweenaw Current in Lake Superior. Part II: Simulation

The Keweenaw Current, observed along the coast of the Keweenaw Peninsula in Lake Superior during July 1973, was simulated using a 3D, nonorthogonal coordinate transformation, primitive equation coastal ocean model. The model domain covered the entire lake with a high resolution of 250–600 m in the cross-shelf direction and 4–6 km in the alongshelf direction along the peninsula. The model was initialized using the monthly averaged temperature field observed in June 1973 and was run prognostically with synoptic wind forcing plus monthly averaged heat flux. Good agreement was found between model-predicted and observed currents at buoy stations near Eagle Harbor. Comparison of the model results with and without inclusion of heat flux suggested that combined wind and heat fluxes played a key role in the intensification of the Keweenaw Current during summer months. The model-predicted relatively strong near-inertial oscillations occurred episodically under conditions of a clockwise-rotating wind. These oscillations intensified at the surface, were weak near the coast, and increased significantly offshore.

Radiative damping of near-inertial oscillations in the mixed layer

An idealized model of the transmission of near-inertial waves from the mixed layer into the deeper ocean is studied in order to assess the combined effects of background geostrophic vorticity and the planetary vorticity gradient. The model geostrophic e ow is steady and barotropic with a streamfunc- tion c 5 2 C cos (2a y); the planetary vorticity gradient is modeled using the b -effect. After projection onto vertical modes, each modal amplitude satise es a Schrodinger-like wave equation (in y and t) in which b y 1 (c yy/2) plays the role of a potential. With realistic parameter values, this potential function has a periodically spaced set of minima inclined by the b -effect. The initial near-inertial excitation is horizontally uniform, but strong spatial modulations rapidly develop: at 20 days the near-inertial energy level is largest near the minima of the b y 1 (c yy/2) potential. Near the maxima of the b y 1 (c yy/2) potential, the mixed-layer near-inertial energy rapidly decreases, but, at these same horizontal locations, energy maxima appear immediately below the base of the mixed layer. The b -effect and the geostrophic vorticity act in concert to produce a rapid vertical transmission of near-inertial energy and shear. Because of this radiation damping, the energy density of the spatially averaged,near-inertial oscillations in the mixed layer falls to about 10% of the initial level after 15 days. However, at the minima of the b y 1 (c yy/2) potential, concentrations of near-inertial energy persist in the mixed layer for at least forty days.

Near-Inertial Oscillations of a Barotropic Vortex: Trapped Modes and Time Evolution

Abstract Amplified motions in vortices have been observed in Gulf Stream rings and over seamounts. This paper uses the near-inertial oscillation approximation to model near-inertial motions in the presence of a barotropic vortical background flow. The resulting trapped modes are calculated: there is always at least one such mode, but higher modes may exist and these are obtained. The characteristics of the trapped mode depend on the quantity Γ/f0R2n where Γ is the circulation (integrated vorticity) of the ring, f0 is the local Coriolis frequency, and Rn is the nth Rossby radius of deformation, which may be interpreted as a combined measure of the vertical length scale and stratification. Asymptotic expressions are presented for the frequency of the gravest radial mode for strong and weak vortices. The calculated frequencies are compared to previous results, and good agreement is obtained. The initial value problem is also studied: the contribution of the trapped modes to the evolution of the near-inertial...

Enhanced dispersion of near-inertial waves in an idealized geostrophic flow

This paper presents a simplified model of the process through which a geostrophic flow enhances the vertical propagation of near-inertial activity from the mixed layer into the deeper ocean. The geostrophic flow is idealized as steady and barotropic with a sinusoidal dependence on the north-south coordinate; the corresponding streamfunction takes the form ψ = -Ψcos(2αy). Near-inertial oscillations are considered in linear theory and disturbances are decomposed into horizontal and vertical normal modes. For this particular flow, the horizontal modes are given in terms of Mathieu functions. The initial-value problem can then be solved by projecting onto this set of normal modes. A detailed solution is presented for the case in which the mixed layer is set into motion as a slab. There is no initial horizontal structure in the model mixed layer; rather, horizontal structure, such as enhanced near-inertial energy in regions of negative vorticity, is impressed on the near-inertial fields by the pre-existing geostrophic flow. Many details of the solution, such as the rate at which near-inertial activity in the mixed layer decays, are controlled by the nondimensional number, Y = 4Ψf 0 /H 2 mix N 2 mix , where f 0 is the inertial frequency, H mix is the mixed-layer depth, and N mix is the buoyancy frequency immediately below the base of the mixed layer. When Y is large, near-inertial activity in the mixed layer decays on a time-scale H mix N mix /α 2 Ψ 3/2 f 0 1/2 . When Y is small, near-inertial activity in the mixed layer decays on a time-scale proportional to N 2 mix H 2 mix /α 2 Ψ 2 f 0 .

Propagation of near-inertial oscillations through a geostrophic flow

The method of multiple time scales is used to obtain an approximate description of the linear propagation of near-inertial oscillations (NIOs) through a three-dimensional geostrophic flow. This 'NIO equation' uses a complex field, M(x, y, z, t), related to the demodulated horizontal velocity by M z = exp (if 0 t)(u + iv), where f 0 is the inertial frequency. The three processes of wave dispersion, advection by geostrophic velocity and refraction (geostrophic vorticity slightly shifts the local inertial frequency) are all included in the formulation. The NIO equation has an energy conservation law, so that there is no transfer of energy between NIOs and the geostrophic flow in the approximation scheme. As an application, the NIO equation is used to examine propagation of waves through a field of smaller scale, geostrophic eddies. The spatially local ζ/2 frequency shift, identified by earlier WKB calculations (ζ is the vertical vorticity of the geostrophic eddies), is not expressed directly in the wave field: the large-scale NIO samples regions of both positive and negative ζ so that there is cancellation. Instead, the ζ/2 frequency shift is rectified to produce an average dispersive effect. The calculation predicts that an NIO with infinite horizontal scale has a frequency shift -Kf 0 m 2 /N 2 where K is average kinetic energy density of the geostrophic eddies, m the vertical wavenumber of the NIO, f 0 the inertial frequency and N the buoyancy frequency. Because of the dependence of the frequency shift on m 2 , there is an effective vertical dispersion, whose strength is proportional to the eddy kinetic energy. This process greatly increases the vertical propagation rate of synoptic scale NIOs.

東京湾における近慢性内部振動

Internal near-inertial oscillations were observed by moored measurements in summer of 1979 in Tokyo Bay. The characteristics of observed oscillations are as follows; 1) The maximum amplitude of oscillations reached to about 8 cm s-1 2) The observed period ranged from 16 to 20 hours, which are shorter than the inertia period in Tokyo Bay; 3) The phase difference of oscillations between the surface and bottom layers is about 180°; 4) The major axis of the oscillations in the northernmost area is directed along the coast. The observed oscillations are explained as the transverse internal seiche in a stratified flat-bottomed channel with straight walls. The characteristics of the observed oscillations are also confirmed by the numerical experiments using the multi-level model with realistic basin and with the time change of wind.