Geophysical Boundary Layers Research Articles

Asymptotic analysis for the homogeneous model of wind‐driven oceanic circulation in the small viscosity limit

In this paper, we study the asymptotic expansion for the homogeneous model of wind‐driven oceanic circulation with the nonslip boundary condition when both of the beta‐plane parameter and the Reynolds number go to infinity. By asymptotic analysis under certain constraints on wind tensor, we derive a formal expansion including the geophysical boundary layer in the large beta‐plane parameter and high Reynolds number limit, from which one sees that the external force, wind tensor, has an important effect on the behavior of the boundary layers. Moreover, when the external force and initial data satisfy certain constraints, to exclude the appearance of strong boundary layers, we construct approximate solutions with steady boundary layers to the homogeneous model of wind‐driven oceanic circulation in the large beta‐plane parameter and high Reynolds number limit. By using an energy method, we obtain the ‐stability of small perturbation around this approximate solutions, which verifies the validity of the asymptotic expansion of weak boundary layers in the large beta‐plane parameter and high Reynolds number limit.

Models of Climate, Geophysical Boundary Layers, and the Active Land Layer: In Memory of V. N. Lykosov

Models of Climate, Geophysical Boundary Layers, and the Active Land Layer: In Memory of V. N. Lykosov

Well-posedness and Blowup of the Geophysical Boundary Layer Problem

The proposal of this paper is to study the local existence of analytic solutions, and blowup of solutions in a finite time for the geophysical boundary layer problem. In contrast with the classical Prandtl boundary layer equation, the geophysical boundary layer equation has an additional integral term arising from the Coriolis force. Under the assumption that the initial velocity and outer flow velocity are analytic in the horizontal variable, we obtain the local well-posedness of the geophysical boundary layer problem by using energy method in the weighted Chemin-Lerner spaces. Moreover, when the initial velocity and outer flow velocity satisfy certain condition on a transversal plane, for any smooth solution decaying exponentially in the normal variable to the geophysical boundary layer problem, it is proved that its $$W^{1,\infty }-$$ norm blows up in a finite time. Comparing with the blowup result obtained in Kukavica et al. (Adv Math 307:288–311, 2017) for the classical Prandtl equation, we find that the integral term in the geophysical boundary layer equation triggers the formulation of singularities earlier.

Dissipation of Turbulent Kinetic Energy in the Oscillating Bottom Boundary Layer of a Large Shallow Lake

AbstractMixing rates and biogeochemical fluxes are commonly estimated from the rate of dissipation of turbulent kinetic energy ε as measured with a single instrument and processing method. However, differences in measurements of ε between instruments/methods often vary by one order of magnitude. In an effort to identify error in computing ε, we have applied four common methods to data from the bottom boundary layer of Lake Erie. We applied the second-order structure function method (SFM) to velocity measurements from an acoustic Doppler current profiler, using both canonical and anisotropy-adjusted Kolmogorov constants, and compared the results with those computed from the law of the wall, Batchelor fitting to temperature gradient microstructure, and inertial subrange fitting to acoustic Doppler velocimeter data. The ε from anisotropy-adjusted constants in SFM increased by a factor of 6 or more at 0.2 m above the bed and showed a better agreement with microstructure and inertial method estimations. The maximum difference between SFM ε, computed using adjusted and canonical constants, and microstructure values was 25% and 50%, respectively. This difference was 30% and 55%, respectively, for those from inertial subrange fitting at times of high-intensity turbulence (Reynolds number at 1 m above the bed of more than 2 × 104). Comparison of the SFM ε to those from law of the wall was often poor, with errors as large as one order of magnitude. From the considerable improvement in ε estimates near the bed, anisotropy-adjusted Kolmogorov constants should be applied to compute dissipation in geophysical boundary layers.

An analytic solution for barotropic flow along a variable slope topography

AbstractAn analytic solution is derived for the generic oceanographic situation of a barotropic current flowing along sloping topography. It is shown that the shallow water equations can be reduced to a heat‐like equation in which βeffect is balanced by Ekman dissipation. For constant topography, the system is found to admit a well‐known similarity solution and this solution is generalized to the case of variable topography. Several properties of the solution are explored, and an example is given for flow along the northern Gulf of Mexico slope, between the De Soto Canyon and the Mississippi Canyon. This “Topographic β‐plume” solution may serve as a model for further research concerning the influence exerted by geophysical boundary layers on the interior flow via their structure and stability.

Comments on “Second-order turbulence closure models for geophysical boundary layers: A review of recent work”

Comments on “Second-order turbulence closure models for geophysical boundary layers: A review of recent work”

Second-order turbulence closure models for geophysical boundary layers. A review of recent work

Recent contributions to second-order turbulence modelling are reviewed with an emphasis on models of the coastal ocean. Classical and recent turbulence models are reformulated using a unifying notation, making differences in model structure and model parameters more transparent. The essential characteristics of a number of models are compared. It is further demonstrated that the mathematical stability and realisability of the models is crucial for practical applications. The parameter constraints to insure stable computations are discussed. Model performance is evaluated for a number of idealised entrainment scenarios that are typical for shelf seas: entrainment in linearly stratified and two-layer fluids caused by (a) surface wind stress (b) bottom stress due to water motion driven by a barotropic pressure gradient (c) bottom stress due to water motion in a bottom jet. It is shown that the predicted entrainment velocities are in good agreement with available laboratory data, provided the models have been calibrated according to a theoretical constraint. In addition, model behaviour in free convection is re-analysed with the help of recent data from large eddy simulations (LES). It is shown that even the most simple models, which do not solve a differential equation for the turbulent kinetic energy (TKE), can approximately reproduce the entrainment depth, however, they fail completely in reproducing the correct budget of the TKE-balance. In contrast, second-order models solving transport equations for the TKE and a length scale determining variable are in reasonable agreement with the TKE-budgets from LES.

The improvement made by a modified TLM in 4DVAR with a geophysical boundary layer model

The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.

Turbulence: perspectives on flow and sediment transport

Outlines the fundamental principles of the measurement and analysis of turbulent flow and sediment transport. It reviews laboratory work over the last three decades on near-boundary flow structure, as well as providing more recent research dealing with the high frequency monitoring and modelling of sediment transport. The research sections address aspects of turbulence characteristics and sediment behaviour in fluvial, tidal, and aeolian boundary layers. The effects of roughness transitions are extensively discussed and some of the most popular instrumentation is reviewed. This book brings together contributions from twenty researchers worldwide providing both review material and some of the latest research into small-scale interactions of turbulence and sediment transport in geophysical boundary layers. (Editors)

Modeling the effects of buoyancy on the evolution of geophysical boundary layers

A simple modeling based on the Imperial College k‐ε turbulence description is shown to be capable of describing the highly anisotropic phenomena associated with the strong buoyancy effects encountered in upper ocean (and atmospheric boundary layer) environments. Both diurnal stratification and transition to buoyant mixing (from that driven by wind shear) are described in considerable detail, provided that the modeling of the turbulent Prandtl number and of the buoyant generation term in the ε model equation are evaluated in a suitably realistic and consistent way. The resulting model equations are suitable for simulating the evolution of the ensemble‐averaged properties of the oceanic mixed layer in response to a specified history of interfacial shear stress and heat flux. The model is tested by comparing the predicted mixed layer evolution with the dissipation rate measurements of Shay and Gregg.

Spectral and Pseudospectral Methods for Eigenvalue and Nonseparable Boundary Value Problems

It is shown that spectral and pseudospectral methods can lead to great savings in numerical efficiency-typically, at least a factor of four in storage and eight in operation count-in comparison with finite-difference methods for solving eigenvalue and nonseparable, noniterative boundary value problems at the cost of only a a slight amount of additional programming. The special problems or apparent problems that geophysical boundary layers, critical latitudes and critical levels and real data create for spectral algorithms are also discussed along with when and how these can be solved.

The influence of suspended cohesive sediments on boundary-layer structure and erosive activity of turbulent seawater flow

Velocity and suspension measurements in the logarithmic layer of hydraulically smooth turbulent tidal flow from the North Sea are reported. The data were not compatible with the assumption of Newtonian flow for the experimental seawater—clay suspension. Laboratory measurements were initiated with mud and seawater from the North Sea in which the boundary-layer structure of this two-phase flow was measured down into the viscous sublayer. The dilute seawater—clay suspension was a mixture of illite, kaolinite and chlorite minerals with concentrations less than 380 mg/l and exhibited turbulent drag reduction. By reviewing flow measurements of other authors it is suggested that turbulent drag reduction occurs on a geophysical scale if the flows transport cohesive sediments. It is proposed that drag reduction is caused by dynamic interaction between turbulent shear strain in the flow and deformation of aggregates. As a consequence, the values of the critical friction velocity u ∗ crit and of erosion rates must be reviewed for cohesive bottom materials. Normally they were obtained under the assumption of a Newtonian flow structure which is not applicable if the flow transports cohesive sediments. To detect the occurrence of drag reduction in geophysical boundary layers (hydraulically smooth), flow measurements must be performed down into the viscous sublayer. The adequate velocity sensors must have a diameter of ⩽1 mm.

“Bursting” phenomena in the sea

INTEREST in the structure of turbulent boundary layers and in particular mechanisms responsible for the transfer of turbulent energy and generation of Reynolds stress has recently been stimulated by a series of laboratory flow visualisation experiments1–5. These have indicated that Reynolds stress production is intermittent and associated with a sequence of motions known collectively as “bursting”3. Experimental evidence presented here suggests that similar motions can be readily identified in a geophysical boundary layer at length and time scales unattainable in the laboratory.