Combined wavelet and principal component analysis (WEof) of a scale-oriented model of coastal ocean gravity waves

Coastal ocean numerical modeling is basically the representation of the dynamics of the coastal ocean in a chosen range of length scales and over an associated frequency band, including the modeling of both coherent processes and associated transient processes. The ocean dynamical features can be individually identified by combining wavelet analysis for time and frequency localization and principal component analysis to “decorrelate” physically consistent structures. In the present paper, the so-called WEof analysis is applied for the extraction of external gravity waves and internal gravity wave lower modes in a simple case of a flat bottom, constant Brunt-Väisälä ocean. It is shown that, with some well known restrictive assumptions, WEof analysis is an efficient candidate for the recognition of frequency localized dynamical processes.     

The influence of the coast on the dynamics of upwelling fronts: Part II. Numerical simulations

We investigated the dynamics of upwelling fronts near a coast. This work was first motivated by laboratory experiments [Bouruet-Aubertot, Linden, Dyn. Atmos. Oceans, 2002] in which the front is produced by the adjustment of a buoyant fluid initially confined within a bottomless cylinder. It was shown that cyclonic eddies consisting of coastal waters are enhanced when the front is unstable near the coast (the outer vertical boundary). The purpose of this paper is to provide further insights into this process. We reproduced the experimental configuration using a three-dimensional model of the primitive equations. We first show that for coastal fronts more potential energy, in terms of the maximum available potential energy, is released than for open-ocean fronts. Therefore, waves of larger amplitude are generated during the adjustment and the mean flow that establishes has a higher kinetic energy in the former case. Then as baroclinic instability starts and wave crests reach the boundary, cyclonic eddies are enhanced as in the laboratory experiments and in a similar way. However, in contrast to the laboratory experiments, offshore advection of cyclonic eddies can occur in two stages, depending on the spatial organization of the baroclinic wave. When the baroclinic wave consists of the sum of different modes and is thus highly asymmetric, the offshore advection of cyclonic eddies occurs just after their enhancement at the boundary, as in the laboratory experiments. By contrast, when a single-mode baroclinic wave develops, neighboring cyclonic eddies first merge before being advected offshore. Very different behavior is observed for open-ocean fronts. First a mixed baroclinic–barotropic instability grows. Then the eddies transfer their energy to the mean flow and the barotropic and baroclinic instabilities start again. An excellent agreement is obtained with the main result obtained in the laboratory experiments: the ratio between growth rates of surface cyclonic and anticyclonic vorticity increases as the instability develops nearer to the coast.     

Vorticity waves in a shallow basin

Observed oscillatory current patterns in the southern basin of Lake Michigan, with a distinctive peak in the energy spectrum at a period of about 90 h, are simulated using a linear potential vorticity conservation model. Solutions of the forced vorticity equation in a paraboloidal basin show rotational, oscillatory motions tuned to the low-frequency topographic modes that are very similar to the observed flow patterns. Topography-controlled vorticity waves are excited most effectively by wind episodes with frequency nearly in resonance with the topographic modes. Bottom resistance has no significant effect on the frequency equation; it simply decays the waves slowly in the open lake and more quickly near the coast. Flow patterns of both the gravest free vorticity wave and the corresponding forced wave consist of two opposite circulation cells separated by a null streamline through the center of the basin and rotating cyclonically near the free wave and atmospheric forcing frequencies, respectively. Interactions between the forced and free waves result in an apparent rotational pattern with a frequency the median of the two. A combination of elliptic—paraboloidal basin and shorter period forced modes can approximate the observed Lake Michigan response. Doppler shift, due to the persistence of cyclonic vorticity in the flow field, is also determined to be a factor in shifting the elliptical basin mode to a higher frequency.     

On leaky modes on a buoyancy interface

When the fluid below a buoyancy interface such as the seasonal thermocline in the ocean is stably stratified as it is often, energy radiation by internal waves into regions deep below is possible. In this paper, the dispersion relation for a sharp thermocline separating a well-mixed layer from a weakly but stably stratified fluid below is derived and examined for such energy leakage into the fluid below. It is found that the interfacial waves running along such a buoyancy interface leak their energy to radiating internal waves and are rapidly attenuated, if their frequency is less than the buoyancy frequency of the fluid below. The implications the leaky nature of the modes have on resonant excitation of internal waves in the ocean by atmospheric pressure fluctuations and turbulence in the mixed layer are also examined. It is found that efficient resonant build up of interfacial waves is possible only for nonleaky modes and even then their growth rate is modified slightly by the presence of stratified fluid below the interface.     

Growing interfacially coupled oscillations of the ocean–atmosphere

A stability analysis of the coupled ocean–atmosphere is presented which shows that the potential energy (PE) of the upper layer of the ocean is available to generate coupled growing planetary waves. An independent analysis suggests that the growth of these waves would be maintained in the presence of oceanic friction. The growing waves are a consequence of relaxing the rigid lid approximation on the ocean, thus allowing an upward transfer of energy across the sea surface. Using a two and a half layer model consisting of an atmospheric planetary boundary layer, coupled with a two layer ocean comprising an active upper layer and a lower layer in which the velocity perturbation is vanishingly small, it is shown that coupled unstable waves are generated, which extract PE from the main thermocline. The instability analysis is an extension of earlier work [Tellus 44A (1992) 67], which considered the coupled instability of an atmospheric planetary boundary layer coupled with an oceanic mixed layer, in which unstable waves were generated which extract PE from the seasonal thermocline. The unstable wave is an atmospheric divergent barotropic Rossby wave, which is steered by the zonal wind velocity, and has a wavelength of about 6000 km, and propagates eastward at the speed of the deep ocean current. It is argued that this instability, which has a multidecadal growth time constant, may be generated in the Southern Ocean, and that its properties are similar to observations of the Antarctic Circumpolar Wave (ACW).     

Nonlinear kinetic energy interactions and their contributions to the growth and decay of atmospheric waves in the lower troposphere during summer monsoon, 1979

Summary Lower tropospheric (1000–500) hPa kinetic energy (KE), temporal variations of KE and nonlinear KE transfer of rotational and divergent flows and energy conversion between them, partitioning further into stationary and transient components in the Fourier spectral domain and the mechanism for the evolution of significant transient waves for the month July 1979 in the latitudinal belt 10° S–30° N are studied.Divergent zonal and eddy KE show their maxima at the lowest level 1000 hPa. Lower tropospheric monsoon motion provides a non-divergent level close to 850 hPa. The daily flow patterns bear little resemblence to the climatology over tropics at 500 hPa. Although the transient mode of synoptic scale waves is stronger than that of planetary scale waves they are comparable. Analysis of energetics over global tropics can get signature of transient activities embedded in the large scale system. Summer momentum flux in the lower troposphere is essentially associated with stationary planetary and transient synoptic scale waves. Waves 1, 3 and 6 are the most preferred transient waves. Divergent to rotational KE conversion is the most dominating mechanism for the maintenance of planetary and synoptic scale waves. All categories of waves contribute towards the maintenance of zonal flows. The primary source of energy for transient synoptic scale waves is the transient divergent rotational KE transfer whereas the interaction between zonal stationary and transient wave is likely to be secondary source. Transient KE and all transient interactions, stationary KE and all stationary interactions are found to be strongest at 500 hPa and 850 hPa respectively. Growth and decay of transient waves 1 and 3 are mainly controlled by divergent-rotational KE conversions whereas those of transient wave 6 are controlled by KE transfer due to zonal-wave interaction.With 13 Figures     

Secondary instability and three-dimensionalization in a laboratory accelerating shear layer with varying density differences

We investigate the processes by which an accelerating stratified shear flow undergoes the transition to turbulence in a sequence of experiments in a tilted tank. We observe that the processes by which the flow undergoes breakdown are both complex and diverse, and suggest that the ratio, D, of the depth of the shear layer to the total tank depth and/or the (nondimensional) total density difference are important parameters in the determination of the dominant structures. In general, inherently three-dimensional, and relatively large-scale, flow structures strongly suppress simple subharmonic vortex pairing, and appear to dominate totally the transition to turbulence. In certain circumstances, the primary instabilities of the flow, namely Kelvin-Helmholtz billows, are able to develop in a quasi-two-dimensional manner before interaction between neighbouring billows becomes significant. In these circumstances, narrow secondary streamwise ‘tubes’ of vorticity are observed between neighbouring billows. Alternatively subharmonic, quasi-two-dimensional vortex mergings may be observed; these are not just simple pairings, but also three vortices are observed to merge into a single secondary billow, or two merge and the other persists, as predicted theoretically by Klaassen and Peltier (J. Fluid Mech., 202: 367–402, 1989). Three-dimensional vortex merging (knotting) of initially quasi-two-dimensional billows is also observed. Such knots are observed not only as pairwise transitions, as discussed by Thorpe (Geophys. Astrophys. Fluid Dyn., 34: 175–199, 1985), but also single billows are observed to knot with both adjacent neighbours simultaneously. Also, billows are observed to bow during merging events. However, particularly at larger density differences, higher Reynolds number and when the depth ratio, D, is sufficiently small, billow-billow interactions are apparent essentially immediately upon instability onset. Although the structures which develop resemble secondary tubes, these structures appear to be a primary instability of the flow, analogous to an instability observed by other researchers in both forced and unforced homogeneous shear layers.     

Impacts of upscale heat and momentum transfer by moist Kelvin waves on the Madden–Julian oscillation: a theoretical model study

The Madden–Julian oscillation (MJO) is observed to interact with moist Kelvin waves. To understand the role of this interaction, a simple scale-interaction model is built, which describes the MJO modulation of moist Kelvin waves and the feedback from moist Kelvin waves through upscale eddy heat and momentum transfer. The backward-tilted moist Kelvin waves produce eddy momentum transfer (EMT) characterized by the lower-tropospheric westerly winds and eddy heat transfer (EHT) that warms the mid-troposphere. The EHT tends to induce the lower-tropospheric easterly winds and low pressure, which is located in front of the “westerly wind burst” induced by the EMT. Adding the eddy forcing to a neutral MJO skeleton model, we show that the EHT provides an instability source for the MJO by warming up the mid-troposphere, and the EMT offers an additional instability source by enhancing the lower-tropospheric westerly winds. The eddy forcing selects eastward propagation for the unstable mode, because it generates positive/negative eddy available potential energy for the eastward/westward modes by changing their thermal and dynamical structures. The present results show that moist Kelvin waves can provide a positive feedback to the MJO only when they are located within (or near) the convective complex (center) of the MJO. The EHT and EMT feedback works positively in the front and rear part of the MJO, respectively. These theoretical results suggest the potential importance of moist Kelvin waves in sustaining the MJO and encourage further observations to document the relationship between moist Kelvin waves and the MJO.     

One-dimensional baroclinically unstable waves on the Gulf Stream potential vorticity gradient near Cape Hatteras

Application of linear baroclinic instability theory to the observed distributions of velocity, stratification, and potential vorticity in the Gulf Stream near 74° W is successful in predicting the time and length scales of the most rapidly growing disturbances. A continuously-stratified, one-dimensional model with realistic bottom slope predicts propagation speeds of 10–50 cm s⁻¹ associated with two regimes of rapid temporal growth centered at periods of 28 days and 5–7 days. This prediction is consistent with observations of the propagation and growth of Gulf Stream meanders derived from inverted echo sounder measurements in this region. The instability model also predicts that for realistic bottom slopes the baroclinic energy transfer should be weakly negative (eddy-to-mean) in deep water, but for low-frequency waves should change to significant positive (mean-to-eddy) transfer above depths of 1500 m, consistent with observations.     

Role of Triad Kinetic Energy Interactions for Maintenance of Upper Tropospheric Low Frequency Waves during Summer Monsoon 1988

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Resonance of baroclinic waves in the tropical oceans: The Indian Ocean and the far western Pacific

The Indian Ocean has a particularity, its width is close to half the wavelength of a Rossby wave of biannual frequency, this coincidence having been capitalized on by several authors to give the observations a physical basis. The purpose of this article is to show that this is not the case since the resonance of tropical baroclinic waves occurs in all three oceans. This is because the westward-propagating Rossby wave is retroflexed at the western boundary to form off-equatorial Rossby waves dragged by countercurrents before receding and turning back as a Kelvin wave. Thus a quasi-stationary baroclinic wave is formed, whose mean period is tuned to the forcing period. Two independent basin modes resonantly forced are highlighted – 1) a nearly symmetric zonal 1/2-yr period Quasi-Stationary Wave (QSW) that is resonantly forced by the biannual monsoon. It is formed from first baroclinic mode equatorial-trapped Rossby and Kelvin waves and off-equatorial Rossby waves at the western antinode. This QSW controls the Equatorial Counter Current at the node. The Indian Ocean Dipole (IOD) results from a subharmonic mode locking resulting from the coupling of this QSW and the 2nd, 3rd and 4th baroclinic modes - 2) a 1-yr period QSW formed from an off-equatorial baroclinic Rossby wave, which is induced from the southernmost current of the Indonesian Throughflow through the Timor passage, propagating in the southern and northern hemispheres: the drivers are south-easterlies in the southern hemisphere and monsoon wind in the northern hemisphere.     

Nonlinear energy and enstrophy transfers in a realistically stratified ocean

We discuss the nonlinear transfers possible in a quasigeostrophic fluid with a basic stratification taken from oceanic data. The energy and enstrophy conservation laws imply a cascade of energy to larger total scale (including both the horizontal scale, defined as wavelength/2π, and the deformation radius of the vertical mode). The triplet interactions among components with various horizontal scales and vertical structures, represented by the vertical mode numbers, are considered in detail for exchanges involving the barotropic and first three baroclinic modes. The initial transfer rates from one component into the other two are estimated and the most rapid transfers described as a function of the initial scale and mode number. These results suggest that barotropic motions will cascade to larger-scale barotropic motions, first baroclinic small-scale motions will transfer to first baroclinic larger scales, and first baroclinic large-scale motions will cascade to barotropic and first baroclinic motions at the deformation scale. Second and third mode motions prefer to transfer energy into small-scale (second or third mode deformation radius) first and third baroclinic mode motions.We also show the relationship of these triplet interactions to Rossby wave instabilities and resonant triads. For the latter motions, the weakness of the nonlinearity adds additional constraints which impty that the motions will tend to become zonal.     

The effect of barotropic shear on baroclinic instability Part I: Normal mode problem

The effect of barotropic shear in the basic flow on baroclinic instability is investigated using a linear multilevel quasi-geostrophic β-plane channel model and a nonlinear spherical primitive equation model. Barotropic shear has a profound effect on baroclinic instability. It reduces the growth rates of normal modes by severely restricting their structure, confirming earlier results with a two-layer model. Dissipation, in the form of Ekman pumping and Newtonian cooling, does not change the main characteristics of the effect of the shear on normal mode instability.Barotropic shear in the basic state, characterized by large shear vorticity with small horizontal curvature, also effects the nonlinear development of baroclinic waves. The shear limits the energy conversion from the zonal available potential energy to eddy energy, reducing the maximum eddy kinetic energy level reached by baroclinic waves. Barotropic shear, which controls the level of eddy activity, is a major factor which should be considered when parameterizing the eddy temperature and momentum fluxes induced by baroclinic waves in a climate model.     

Experimental study of nonlinear wave—wave interaction and white-cap dissipation of wind-generated waves

An experimental scheme was designed to obtain laboratory-scale verification of Hasselmann's nonlinear wave—wave interaction and white-cap dissipation theories. Water wave height and fluctuating air pressure were measured simultaneously in a fixed reference frame as a function of fetch in the Stanford Wind, Water-Wave Research Facility under the conditions of a steady wind and a stationary wave spectrum. All the data were obtained 5 mm above the highest point of the wind waves for five stations (3 m apart on average) and at three wind speeds (7.1, 8.0 and 8.9 m/sec). The wave height and fluctuating pressure were measured by a capacitance wave-height gauge and a crystal pressure transducer, respectively.Based on the experimental results, Hasselmann's nonlinear wave—wave interaction theory appears to be valid. Barnett's approximate parametric equation for calculating the energy transfer of nonlinear wave—wave interaction and Hasselmann's white-capping dissipation model were also verified and appeared to be applicable in the relatively low and intermediate frequency region of a wave spectrum for a normalized fetch range of 100–500. Based on the results of an overall energy balance in a gravity wind-wave spectrum, the nonlinear wave—wave interaction mechanism is shown to play a dominant role in the energy transfer processes after the wave spectrum is generated.     

The global energy cycle of stationary and transient atmospheric waves: Results from ECMWF analyses

Summary The role of stationary (monthly mean) and transient (departure from monthly mean) waves within the atmospheric energy cycle is examined using global analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) for the period 1980–1987. Only January and July averages are considered.It is confirmed that planetary stationary waves are basically baroclinic. Their contribution to the globally averaged energy cycle of the atmosphere is comparable to that of the transient waves. In January they contribute about 40% to the baroclinic conversion (CA) from zonal mean to eddy available potential energy. Local values for the northern hemisphere even show a predominant role of the stationary wave conversions over those originating from transient waves. Part of the available potential energy of stationary waves (A _SE) is converted to kinetic energy by warm air rising and cold air sinking. Nonlinear energy conversion, which can be interpreted as destruction of stationary temperature waves by transients, is the second sink forA _SE. The order of magnitude of these two processes is similar.Barotropic nonlinear conversions, though negligible in the global average, reveal large conversion rates between the mean positions of the polar and the subtropical jets. Their orientation is suggestive of a tendency to increase stationary wave kinetic energyK _SE at its local minimum between the jets at the expense of the synoptic scale transients.While all terms of the energy cycle related to stationary waves reveal a predominance of the planetary scale (zonal wave numbers 1–3) transient waves are governed by synoptic scale waves (zonal wave numbers 4–9) only with respect to the baroclinic and barotropic conversions: a significant amount of transient wave energy (50% for the global average ofA _TE) is due to planetary scale waves.With 15 Figures     

Microwave scatter and sea state estimation: Two-scale ocean wave models

The efficient estimation of ocean wave-structure parameters with a remote, narrow-beam, pulsed, microwave radar at intermediate incidence angles is discussed. The sea surface is described as the sum of random small- and large-scale structures (waves), the latter the sum of a sinusoid and a random field. It is shown that the small-scale structure is responsible for scattering and that the scatter depends parametrically on the large-scale structure. For the estimation problem it is assumed, reasonably, that the received signal is normally distributed: a relatively simple processor which will efficiently estimate parameters of the sinusoidal structure is illustrated and its performance discussed. A brief comparison is made with a normal incidence system with which the variance of the large-scale random roughness can be estimated.Research supported by NASA Grant NSG-5048.     

Turbulence Structure of Stable Boundary Layers with a Near-Linear Temperature Profile

By using a thermally stratified wind tunnel, we have successfullysimulated stably stratified boundary layers (SBL), in which the meantemperature increases upward almost linearly. We have investigated the flow structure and the effects of near-linearstable stratification on the transfer of momentum and heat. Thevertical profiles of turbulence quantities exhibit different behaviour in two distinct stability regimes of the SBLflows with weak and strong stability. For weak stability cases, theturbulent transfer of momentum and heat is basically similar to that for neutral turbulent boundary layers, although it is weakenedwith increasing stability. For strong stability cases, on the other hand,the time-mean transfer is almost zero over the whole boundary-layer depth.However, the instantaneous turbulent transfer frequently occurs in bothgradient and counter-gradient directions in the lower part of the boundary layer. This is due to the Kelvin–Helmholtz (K–H) shear instability and therolling up and breaking of K–H waves. Moreover, the internal gravity wavesare observed in the middle and upper parts of all stable boundary layers.     

Richardson number profiles through shear instability wave regions observed in the lower planetary boundary layer

Remote sensing of the lower planetary boundary layer in the vicinity of a meteorological tower on many occasions reveals the existence of shear instability (Kelvin-Helmholtz) waves. In general, such waves are found within shallow strata which are marked by strong thermal stability and large vertical wind shear. The independent and concurrent measurements of the vector wind and temperature, made on a 152-m high tower, allow the construction of wind and temperature profiles. From such measurements, the Richardson number profile is constructed as well as the instability regime according to Drazin's criterion. The results show that regions of shear-instability waves as depicted by the remote sensor (an acoustic sounder) agree well with Drazin's instability regime, and that within such regions the Richardson number is indeed 0.25.     

The reflection and diffraction of internal waves from the junction of a slit and a half-space, with application to submarine canyons

We consider the three-dimensional reflection and diffraction properties of internal waves in a continuously stratified rotating fluid which are incident on the junction of a vertical slit and a half-space. This geometry is a model for submarine canyons on continental slopes in the ocean, where various physical phenomena embodying reflection and diffraction effects have been observed. Three types of incident wave are considered: (1) Kelvin waves in the slit (canyon); (2) Kelvin waves on the slope; and (3) plane internal waves incident from the half-space (ocean). These are scattered into Kelvin and Poincaré waves in the slit, a Kelvin wave on the slope and Poincaré waves in the half-space. Most of the discussion is centered around case (1). Various properties of the wave field are calculated for ranges of the parameters c/cot θ, γα and ƒ/ω where cot θ is the topographic slope, c is the internal wave ray slope, α is the canyon half-width, γ is the down-slope wave-number, ƒ is the Coriolis parameter and ω is the wave frequency. Analytical results are obtained for small γα and some approximate results for larger values of γα. The results show that significant wave trapping may occur in oceanic situations, and that submarine canyons may act as source regions for internal Kelvin waves on the continental slope.