Roland A. de Szoeke

The Speed of Observed and Theoretical Long Extratropical Planetary Waves

Planetary or Rossby waves are the predominant way in which the ocean adjusts on long (year to decade) timescales. The motion of long planetary waves is westward, at speeds

Satellite Microwave SST Observations of Transequatorial Tropical Instability Waves

1c m s 2 1. Until recently, very few experimental investigations of such waves were possible because of scarce data. The advent of satellite altimetry has changed the situation considerably. Curiously, the speeds of planetary waves observed by TOPEX/Poseidon are mainly faster than those given by standard linear theory. This paper examines why this should be. It is argued that the major changes to the unperturbed wave speed will be caused by the presence of baroclinic east‐ west mean flows, which modify the potential vorticity gradient. Long linear perturbations to such flow satisfy a simple eigenvalue problem (related directly to standard quasigeostrophic theory). Solutions are mostly real, though a few are complex. In simple situations approximate solutions can be obtained analytically. Using archive data, the global problem is treated. Phase speeds similar to those observed are found in most areas, although in the Southern Hemisphere an underestimate of speed by the theory remains. Thus, the presence of baroclinic mean flow is sufficient to account for the majority of the observed speeds. It is shown that phase speed changes are produced mainly by (vertical) mode-2 east‐west velocities, with mode-1 having little or no effect. Inclusion of the mean barotropic flow from a global eddy-admitting model makes only a small modification to the fit with observations; whether the fit is improved is equivocal.

The advective flux of heat by mean geostrophic motions in the Southern Ocean

The Pathfinder AVHRR data in Plate I were provided by PODAAC at the Jet Propulsion Laboratory (JPL). This work was supported by NASA/JPL contract 1206715, NASA TRMM contract NAS5-9919 and NASAs Earth Science Information Partnership through contract SUB1998-101 from the University of Alabama at Huntsville.

Microstructure fluxes across density surfaces

A method that is independent of choice of reference level is advanced for calculating, from standard hydrographic data, advective oceanic heat flux by mean geostrophic motions. The method depends on the ability to choose a path of constant vertically averaged potential temperature (reference temperature). It was applied to a collection of historical hydrographic data from the Southern Ocean. A circumpolar path with reference temperature 1.3°C that closely follows the mean position of the Antarctic Polar Front was chosen. The advective geostrophic heat flux across this path was calculated to be 0±23×1013 W. The standard error (and bias, which was found to be small) of this calculation was estimated from a statistical model of correlation of ocean variability that seems appropriate to the way the data are sampled in space and time. The wind-driven Ekman heat flux was calculated at −15×1013 W, that is, equatorward. To balance Gordons estimate of sea to air heat transfer of 30×1013 W south of the Polar Front, a compensating poleward flux of +45±30×1013 W is postulated. Eddy heat flux seems a prime candidate for accomplishing this flux.

The Duality between the Boussinesq and Non-Boussinesq Hydrostatic Equations of Motion

Abstract When averaging the equations of motion, thermodynamics, and scalar conservation over turbulent fluctuations, we perform the process in several stages. First, an average is taken over the microscopic scales of turbulence, including the centimeter-scale band in which the dissipation of kinetic energy and temperature or density variance occurs. The eddy-correlation fluxes that arise in this stage are called microstructure fluxes. Next, the equations are transformed into coordinates relative to the microscopically averaged isopycnals. Finally, an average is taken, relative to these isopycnals, over macroscopic scales of eddy variability, which may include the mesoscale band of planetary motions. Average transport terms, analogous to conventional Reynolds transports in fixed-depth averages, arise also from the macroscopic eddies. This is not so for density, for which no counterparts of macroscopic Reynolds transports exist on constant density surfaces. Only microstructure flux divergence, which is syn...

The Modification of Long Planetary Waves by Homogeneous Potential Vorticity Layers

Abstract The hydrostatic equations of motion for ocean circulation, written in terms of pressure as the vertical coordinate, and without making the Boussinesq approximation in the continuity equation, correspond very closely with the hydrostatic Boussinesq equations written in terms of depth as the vertical coordinate. Two mathematical equivalences between these non-Boussinesq and Boussinesq equation sets are demonstrated: first, for motions over a level bottom; second, for general motions with a rigid lid. A third non-Boussinesq equation set, for general motions with a free surface, is derived and is shown to possess a similar duality with the Boussinesq set after making due allowance for exchange of the roles of bottom pressure and sea surface height in the boundary conditions, a reversal of the direction of integration of the hydrostatic equation, and substitution of specific volume for density in the hydrostatic equation. The crucial simplification in these equations of motion comes from the hydrostat...

On the Effects Of Horizontal Variability of Wind Stress on the Dynamics of the Ocean Mixed Layer

A mechanism by which long planetary waves in the ocean may propagate significantly faster than the classical long baroclinic Rossby waves is investigated. The mechanism depends on the poleward thickening of intermediate density layers and the concomitant thinning of near-surface and deep layers. These features of the mass distribution are associated with the well-known homogenization of potential vorticity in intermediate density layers and with significantly elevated meridional potential vorticity gradients near the surface and somewhat at depth. The mechanism is explored in a simple three-layer model, in which the middle layer has zero potential vorticity gradient and is sandwiched between a surface layer with large potential vorticity gradient and a bottom layer with modest potential vorticity gradient. The effective phase speed of the planetary waves is merely the sum of the phase speeds of virtual baroclinic Rossby waves propagating on the individual layer interfaces as though the other interface were not there and as though there were no mean vertical shear. The mechanism is also examined for a continuous model with zero potential vorticity gradient throughout the interior and large virtual potential vorticity gradients near the surface and bottom. Planetary waves in these models can propagate westward up to twice as fast as baroclinic Rossby waves would through an ocean with the same vertical stratification, but no mean vertical shear. This explanation of the Rossby wave speedup complements a recent detailed theoretical calculation of planetary-wave phase speeds based on geostrophic velocity profiles from archived hydrographic data.

The Structure of Near-Inertial Waves during Ocean Storms

Abstract The one-dimensional bulk mixed-layer model of Niiler (1975) is extended to two (or three) dimensions to take account of horizontal variation in wind stress on mixed-layer dynamics. Both surface stirring (Kraus and Turner, 1967) and bulk shear (Pollard et al., 1973) entrainment mechanisms are included. The development of horizontal structure in the upper ocean an the subseasonal to seasonal time scale is the focus of interest. An asymptotic two-timing technique is employed to simplify the dynamical equations. Wind-driven advection can be important in establishing and concentrating horizontal gradients of the sea surface temperature. Wind stress curl-driven vertical velocity can be as important as entrainment velocity in determining the horizontal distribution of mixed-layer depth. Several illustrative calculations are discussed. A case with initially horizontally uniform temperature, 0.05°C m−1 initial vertical gradient, and wind stress of 1 dyn cm−2 and scale of 1000 km, shows horizontal temperat...

Internal Waves in the Upper Ocean During MILE

Abstract Current meter data from two sites were analyzed for near-inertial motions generated by storm during the ten-month period of the Ocean Storms Experiment in the northeast Pacific Ocean. The most striking feature of the inertial wave response to storms was the almost instantaneous generation of waves in the mixed layer, followed by a gradual propagation into the thermocline that often lasted many days after the initiation of the storm. The propagation of near-inertial waves generated by three storms in October, January, and March was studied by using group propagation theory based on the WKB approximation. It was found that wave frequencies were slightly superinertial, with inertial shifts 1%–3% in October and March and around 1% in January. The phase of near-inertial currents propagated upward below the mixed layer, confirming the downward radiation of energy by these waves. The average downward energy flux during the storm periods was between 0.5 and 2.8 mW m−2. The vertical wavelengths indicated ...

Equations of Motion Using Thermodynamic Coordinates

Abstract We describe the spectral analysis of temperature and velocity measurements made in the northeast Pacific as part of the Mixed Layer Experiment (MILE) and attempt to relate the observed fluctuations to internal-wave models of the upper ocean. From the inertial frequency to 1 cph there is good agreement between these upper-ocean data and typical deep-ocean observations as described by the WKB-scaled Garrett-Munk model. The largest deviations from the Garrett-Munk model occur in the vertical-displacement field at high frequency, 1–5 cph, where there is a spectral peak or shoulder and high vertical coherence. These high-frequency features in vertical displacement are successfully modeled using a few standing modes and un-correlated noise, though the velocity spectra are poorly modeled—probably because of contamination by mooring motion. There are significant temporal fluctuations of the high-frequency energy that are not correlated with the local winds but are perhaps associated with the advection of...