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Steven J. Lentz
and
John H. Trowbridge

Abstract

Moored temperature and shipboard CTD observations from a northern California coastal upwelling region reveal variable bottom mixed-layer heights that are typically 5–15 m, but occasionally exceed 50 m. Observations from Oregon, northern California, and Peru, indicate that in coastal upwelling regions, maximum bottom mixed-layer heights tend to increase with water depth over the shelf, but rarely exceed half the water depth. Over the northern California shelf the bottom mixed-layer height is shown to depend on the stratification, the current magnitude, and the current direction. The dependence on current direction tends to dominate the response, with thicker bottom mixed layers during poleward flows and thinner bottom mixed layers during equatorward flows. This asymmetric response to poleward and equatorward currents is consistent with model results which indicate that the asymmetric response is due to the up- or downslope Ekman transport of buoyancy along the bottom.

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Malcolm E. Scully
,
John H. Trowbridge
, and
Alexander W. Fisher

Abstract

Measurements just beneath the ocean surface demonstrate that the primary mechanism by which energy from breaking waves is transmitted into the water column is through the work done by the covariance of turbulent pressure and velocity fluctuations. The convergence in the vertical transport of turbulent kinetic energy (TKE) balances the dissipation rate of TKE at first order and is nearly an order of magnitude greater than the sum of the integrated Eulerian and Stokes shear production. The measured TKE transport is consistent with a simple conceptual model that assumes roughly half of the surface flux of TKE by wave breaking is transmitted to depths greater than the significant wave height. During conditions when breaking waves are inferred, the direction of momentum flux is more aligned with the direction of wave propagation than with the wind direction. Both the energy and momentum fluxes occur at frequencies much lower than the wave band, consistent with the time scales associated with wave breaking. The largest instantaneous values of momentum flux are associated with strong downward vertical velocity perturbations, in contrast to the pressure work, which is associated with strong drops in pressure and upward vertical velocity perturbations.

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W. Rockwell Geyer
,
John H. Trowbridge
, and
Melissa M. Bowen

Abstract

Measurements of velocity, density, and pressure gradient in the lower Hudson River estuary were used to quantify the dominant terms in the momentum equation and to characterize their variations at tidal and spring–neap timescales. The vertical momentum flux (assumed to be due mainly to turbulent shear stress) was estimated indirectly, based on the residual from the acceleration and pressure gradient terms. The indirect estimates of stress compared favorably to bottom stress estimates using a quadratic drag law, supporting the hypothesis that the tidal momentum equation involves a local balance between tidal acceleration, pressure gradient, and stress divergence.

Estimates of eddy viscosity indicated that there was significant tidal asymmetry, with flood tide values exceeding ebb values by a factor of 2. As a consequence of the asymmetry, the vertical structure of the tidally averaged stress bore no resemblance to the tidally averaged shear. In spite of the asymmetry of vertical mixing, the tidally averaged, estuarine circulation was found to depend simply on the intensity of bottom turbulence, which could be parameterized by a Rayleigh drag formulation based on the tidal velocity magnitude and the tidally averaged near-bottom flow. This seemingly paradoxical result indicates that the estuarine circulation can be modeled without detailed knowledge of the effective eddy viscosity, only requiring an estimate of the bottom drag coefficient, the tidal forcing conditions, and the baroclinic pressure gradient. A notable characteristic of this solution is an inverse dependence of the estuarine circulation on the amplitude of the tides.

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Malcolm E. Scully
,
W. Rocky Geyer
, and
John H. Trowbridge

Abstract

Field observations of turbulent kinetic energy (TKE), dissipation rate ε, and turbulent length scale demonstrate the impact of both density stratification and nonlocal turbulent production on turbulent momentum flux. The data were collected in a highly stratified salt wedge estuary using the Mobile Array for Sensing Turbulence (MAST). Estimates of the dominant length scale of turbulent motions obtained from the vertical velocity spectra provide field confirmation of the theoretical limitation imposed by either the distance to the boundary or the Ozmidov scale, whichever is smaller. Under boundary-limited conditions, anisotropy generally increases with increasing shear and decreased distance to the boundary. Under Ozmidov-limited conditions, anisotropy increases rapidly when the gradient Richardson number exceeds 0.25. Both boundary-limited and Ozmidov-limited conditions demonstrate significant deviations from a local production–dissipation balance that are largely consistent with simple scaling relationships for the vertical divergence in TKE flux. Both the impact of stratification and deviation from equilibrium turbulence observed in the data are largely consistent with commonly used turbulence closure models that employ “nonequilibrium” stability functions. The data compare most favorably with the nonequilibrium version of the L. H. Kantha and C. A. Clayson stability functions. Not only is this approach more consistent with the observed critical gradient Richardson number of 0.25, but it also accounts for the large deviations from equilibrium turbulence in a manner consistent with the observations.

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Gregory P. Gerbi
,
John H. Trowbridge
,
Eugene A. Terray
,
Albert J. Plueddemann
, and
Tobias Kukulka

Abstract

Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.

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Tobias Kukulka
,
Albert J. Plueddemann
,
John H. Trowbridge
, and
Peter P. Sullivan

Abstract

Langmuir circulation (LC) is a turbulent upper-ocean process driven by wind and surface waves that contributes significantly to the transport of momentum, heat, and mass in the oceanic surface layer. The authors have previously performed a direct comparison of large-eddy simulations and observations of the upper-ocean response to a wind event with rapid mixed layer deepening. The evolution of simulated crosswind velocity variance and spatial scales, as well as mixed layer deepening, was only consistent with observations if LC effects are included in the model. Based on an analysis of these validated simulations, in this study the fundamental differences in mixing between purely shear-driven turbulence and turbulence with LC are identified. In the former case, turbulent kinetic energy (TKE) production due to shear instabilities is largest near the surface, gradually decreasing to zero near the base of the mixed layer. This stands in contrast to the LC case in which at middepth range TKE production can be dominated by Stokes drift shear. Furthermore, the Eulerian mean vertical shear peaks near the base of the mixed layer so that TKE production by mean shear flow is elevated there. LC transports horizontal momentum efficiently downward leading to an along-wind velocity jet below LC downwelling regions at the base of the mixed layer. Locally enhanced vertical shear instabilities as a result of this jet efficiently erode the thermocline. In turn, enhanced breaking internal waves inject cold deep water into the mixed layer, where LC currents transport temperature perturbation advectively. Thus, LC and locally generated shear instabilities work intimately together to facilitate strongly the mixed layer deepening process.

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Gregory P. Gerbi
,
John H. Trowbridge
,
James B. Edson
,
Albert J. Plueddemann
,
Eugene A. Terray
, and
Janet J. Fredericks

Abstract

This study makes direct measurements of turbulent fluxes in the mixed layer in order to close heat and momentum budgets across the air–sea interface and to assess the ability of rigid-boundary turbulence models to predict mean vertical gradients beneath the ocean’s wavy surface. Observations were made at 20 Hz at nominal depths of 2.2 and 1.7 m in ∼16 m of water. A new method is developed to estimate the fluxes and the length scales of dominant flux-carrying eddies from cospectra at frequencies below the wave band. The results are compared to independent estimates of those quantities, with good agreement between the two sets of estimates. The observed temperature gradients were smaller than predicted by standard rigid-boundary closure models, consistent with the suggestion that wave breaking and Langmuir circulation increase turbulent diffusivity in the upper ocean. Similarly, the Monin–Obukhov stability function ϕh was smaller in the authors’ measurements than the stability functions used in rigid-boundary applications of the Monin–Obukhov similarity theory. The dominant horizontal length scales of flux-carrying turbulent eddies were found to be consistent with observations in the bottom boundary layer of the atmosphere and from laboratory experiments in three ways: 1) in statically unstable conditions, the eddy sizes scaled linearly with distance to the boundary; 2) in statically stable conditions, length scales decreased with increasing downward buoyancy flux; and 3) downwind length scales were larger than crosswind length scales.

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