Myrl C. Hendershott

The equilibrium statistical mechanics of simple quasi-geostrophic models

We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography and variable rotation rate. In the one-layer case without topography we recover the equilibrium energy spectrum given by Kraichnan (1967). In the two-layer case, we find that the internal radius of deformation constitutes an important dividing scale: at scales of motion larger than the radius of deformation the equilibrium flow is nearly barotropic, while at smaller scales the stream functions in the two layers are statistically uncorrelated. The equilibrium lower-layer flow is positively correlated with bottom topography (anticyclonic flow over seamounts) and the correlation extends to the upper layer at scales larger than the radius of deformation. We suggest that some of the statistical trends observed in non-equilibrium flows may be looked on as manifestations of the tendency for turbulent interactions to maximize the entropy of the system.

Stochastic closure for nonlinear Rossby waves

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for twodimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

Co-oscillating tides in long, narrow bays; the Taylor problem revisited

Abstract In a small, rectangular, mid-latitude bay too narrow and too deep for Poincare modes to propagates semidiurnal tidal energy, the co-oscillating semidiurnal tide must be primarily a superposition of oppositely travelling Kelvin waves. We generalize Taylors (1921) study of the reflection of Kelvin waves at the head of such a bay, now allowing the boundary at the head to absorb a variable portion of the power flux incident upon it. In a bay of uniform depth, the resulting displacement of amphidromic points away from the central axis of the bay becomes a unique measure of the total energy loss at the head of the bay. This displacement explains the marked difference between semidiurnal tides in the Adriatic Sea and in the Gulf of California; a Kelvin wave fit to these tides yields both the tidal energy incident at the mouth of each basin and the tidal energy dissipated within each basin.

The winter circulation of the Adriatic Sea

Abstract The winter circulation of the northern Adriatic Sea is examined in the light of 1965–1966 Bannock data. A vertically integrated numerical model of the flow is used to study the relative importance of evaporation, wind stress, coastal river runoff, and exchange with the Southern Adriatic Sea for the wintertime fields of vertically integrated mass transport and density. A strong and sudden outbreak of cold, dry central Asian air over the Adriatic Sea during January, 1966, resulted in such rapid evaporation rates that water columns evidently overturned continuously. Changes in the density and temperature in the interior of the basin were dominated by surface heat fluxes. Initially sea temperatures were high and evaporation was rapid but as it continued, sea temperatures fell and the rate of evaporation decreased. Model calculations suggest that the strong horizontal density gradient set up by evaporation and coastal inflow of fresh water is an important source of the large scale wintertime circulation. This circulation, counterclockwise in the northern Adriatic Sea with a net transport of about 0·4 × 10 6 m 3 s −1 , is closed upon itself in most of the model solutions because of the relief of the ocean bottom. Mass exchange with the Southern Adriatic Sea appears to be of secondary importance for this circulation.

M2, S2, K1 models of the global ocean tide on an elastic earth

Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipa‐tionless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplaces Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and K1. The resulting representations of the global tide are stable over at least a ±5% variation in the mean depth of the model basin, and they conserve mass. The paper presents maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each constituent.

Statistical aspects of surface drifter observations of circulation in the Santa Barbara Channel

Argos-tracked drifters are used to study the near-surface circulation in the Santa Barbara Channel. The mean consists of a cyclonic cell in the western Santa Barbara Channel with weaker flow in the eastern Channel. Drifter mean velocities agree well with record means from near-surface current meters. At the eastern entrance to the channel, drifter velocities are biased toward outflow (eastward velocity) conditions. Drifter variability at synoptic and seasonal scales shows a tendency for upwelling and eastward flow in spring, a strong cyclonic circulation in summer, poleward relaxation in fall, and weak, variable circulation in winter. Drifter estimates of eddy stress divergence indicate advective terms play a secondary role in the mean surface momentum balance. Lagrangian time and space scales are about 1 day and under 10 km, respectively. The mismatch between Lagrangian and Eulerian timescales indicates advective terms are important to the fluctuating circulation.

Near‐surface trajectories off central and southern California

The near-surface circulation in the Santa Barbara Channel and off the coast of central and southern California is described based on 20 releases of drifters drogued 1 m beneath the surface from 12 sites within the channel at bimonthly intervals. This description includes small-scale features of the circulation which are not part of descriptions based on moored observations or of the statistics of the drifter releases. The eventual fate of drifters at long time intervals compared to the residence time in the channel (about 7 days) is also included. In the channel the trajectories document a persistent cyclonic circulation with a typical recirculation period between 3 and 5 days. In the spring, currents near the mainland are weaker than near the Channel Islands, and the overall flow is toward the southeast. Trajectories document the possibility for water parcels to leave the channel through the interisland passes. In the late fall and winter a poleward flow with velocities often exceeding 0.5 m s−1 is confined within 20 km of the mainland. Between these two seasons the cyclonic tendency is enhanced, although most of the drifters eventually migrate westward. The trajectories of drifters released at the same time from sites only 20 km apart can be remarkably different. Once the drifters migrate out of the channel, their trajectories can be grouped into a few patterns. In spring and summer, drifters tend to remain in the Southern California Bight. Their trajectories often remain close over extended periods, as if they were caught in convergence zones. In fall the drifters often are caught in a poleward current.

Remotely sensing the surface dynamics of the Adriatic Sea

Abstract A set of images of the Adriatic Sea, collected by the Coastal Zone Color Scanner on board the satellite Nimbus-7, has been processed to obtain maps of the diffuse attenuation coefficient for visible radiation and of apparent temperature. Using the spatial variations of these properties as tracers of motion in the surface layer, a correlation between image patterns and water mass movements has been attempted. The majority of the large-scale features observed in the processed images has been directly related to known aspects of the surface circulation in the Adriatic Sea. Some small-scale phenomena, however, could not be explained in these terms and will require more detailed observations.

Adriatic seiche decay and energy loss to the Mediterranean

Abstract A salient feature of sea level records from the Adriatic Sea is the frequent occurrence of energetic seiches of period about 21 h. Once excited by a sudden wind event, such seiches often persist for days. They lose energy either to friction within the Adriatic, or by radiation through Otranto Strait into the Mediterranean. The free decay time of the dominant (lowest mode) seiche was determined from envelopes of handpassed sea level residuals from three locations (Bakar, Split and Dubrovnik) along the Croatian coast during twelve seiche episodes between 1963 and 1986 by taking into consideration only time intervals when the envelopes decreased exponentially in time, when the modelled effects of along-basin winds were smaller than the error of estimation of decay time from the envelopes and when across-basin winds were small. The free decay time thus obtained was 3.2±0.5 d. This value is consonant with the observed width of the spectral peak. The decay caused by both bottom friction and radiation was included in a one dimensional variable cross section shallow water model of the Adriatic. Bottom friction is parameterized by the coefficient k appearing in the linearized bottom stress term ρ0u (where u is the along-basin velocity and ρ0 the fluid density). The coefficient k is constrained by values obtained from linearization of the quadratic bottom stress law using estimates of near bottom currents associated with the seiche, with wind driven currents, with tides and with wind waves. Radiation is parameterized by the coefficient f appearing in the open strait boundary condition ζ =auh/c (where ζ is sea level, h is depth and c is phase speed). This parameterization of radiation provides results comparable to allowing the Adriatic to radiate into an unbounded half plane ocean. Repeated runs of the model delineate the dependence of model free seiche decay time on k and a, and these plus the estimates of k allow estimation of a. The principle conclusions of this work are as follows. 1. (1) Exponential decay of seiche amplitude with time does not necessarily guarantee that the observed decay is free of wind influence. 2. (2) Winds blowing across the Adriatic may be of comparable importance to winds blowing along the Adriatic in influencing apparent decay of seiches; across-basin winds are probably coupled to the longitudinal seiche on account of the strong along-basin variability of across-basin winds forced by Croatian coastal orography. 3. (3) The free decay time of the 21.2 h Adriatic seiche is 3.2±0.5 d. 4. (4) A one dimensional shallow water model of the seiche damped by bottom stress represented by Godins (1988) approximation to the quadratic bottom friction law ρ0CDu|u| using the commonly accepted drag coefficient CD = 0.0015 and quantitative estimates of bottom currents associated with wind driven currents, tides and wind waves, as well as with the seiche itself with no radiation gives a damping time of 9.46 d; radiation sufficient to give the observed damping time must then account for 66% of the energy loss per period. But independent estimates of bottom friction for Adriatic wind driven currents and inertial oscillations, as well as comparisons between quadratic law bottom stress and directly measured bottom stress, all suggest that the quadratic law with CD=0.0015 substantially underestimates the bottom stress. Based on these studies, a more appropriate value of the drag coefficient is at least CD=0. In this case, bottom friction with no radiation leads to a damping time of 4.73 d, radiation sufficient to give the observed damping time then accounts for 32% of the energy loss per period.

The Fortnightly and Monthly Tides: Resonant Rossby Waves or Nearly Equilibrium Gravity Waves?

Abstract The fortnightly and monthly tides are discussed in the light of recent sea level observations and numerical modeling results. Within the tide gauge network of the low-latitude Pacific, the fortnightly tide is shown to possess a large-scale phase lag of roughly 10–40 degrees. Although the nonequilibrium part of the fortnightly tide is traditionally thought to be dominated by Rossby wave dynamics, it is shown, via global shallow-water modeling studies, that this large-scale phase lag is explicable in terms of remotely forced gravity waves whose origin is mainly in the Arctic Ocean. Although future observations outside the low-latitude region of the Pacific may eventually reveal Rossby wave excitation, the fortnightly tidal signal in the tide gauge network at hand appears to reveal at most only weak excitation of Rossby waves compared to the phase lag due to remotely forced gravity waves. The observed monthly tide appears to be only slightly closer to equilibrium than the fortnightly tide. The reaso...