Peter B. Rhines

Bio: Peter B. Rhines is an academic researcher from University of Cambridge. The author has contributed to research in topics: Mixed layer & Turbulence. The author has an hindex of 2, co-authored 2 publications receiving 613 citations.

The deepening of the wind-Mixed layer

Abstract: A simple model is given that describes the response of the upper ocean to an imposed wind stress. The stress drives both mean and turbulent flow near the surface, which is taken to mix thoroughly a layer of depth h, and to erode the stably stratified fluid below. A marginal stability criterion based on a Froude number is used to close the problem, and it is suggested that the mean momentum has a strong role in the mixing process. The initial deepening is predicted to obey where u. is the friction velocity of the imposed stress, N the ambient buoyancy frequency, and t the time. After one-half inertial period the deepening is arrested by rotadeon at a depth h = 22/4 u.{(Nf)+ where f is the Coriolis frequency. The flow is then a “mixed Ekman” layer, with strong inertial oscillations superimposed on it. Three quarters of the mean energy of the deepening layer is found to be kinetic, and only one-quarter potential. Heating and cooling are included in the model, but stress dominates for time-scales of ...

Observations of the energy-containing oceanic Eddies, and theoretical models of waves and turbulence

Abstract: Two of the best available observed frequency spectra of energy-containing oceanic motions are summarized. Without provoking any simple explanation, they affirm that an efficient, homogeneous cascade of energy to small scales isnot occurring. The way is left open for interpretation as a mixture of geostrophic turbulence and waves.

A Description of the Advanced Research WRF Version 3

Abstract: The Technical Note series provides an outlet for a variety of NCAR manuscripts that contribute in specialized ways to the body of scientific knowledge but which are not suitable for journal, monograph, or book publication. Reports in this series are issued by the NCAR Scientific Divisions ; copies may be obtained on request from the Publications Office of NCAR. Designation symbols for the series include: Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization

Abstract: If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing

Abstract: Measurements made from R/P Flip using rapid profiling conductivity, temperature, and depth probes and vector-measuring current meters provide a new and detailed look at the diurnal cycle of the upper ocean. A diurnal cycle occurs when solar heating warms and stabilizes the upper ocean. This limits the downward penetration of turbulent wind mixing so that air-sea fluxes of heat and momentum are surface trapped during midday. The central problem is to learn how the trapping depth D T (mean depth value of the diurnal temperature and velocity response) is set by the competi_ng effects of wind mixing and surface heating. In this data set the diurnal range of surface temperature T s was observed to vary from 0.05 < s < 0.4oC, with most of the day-to-day variability attributable to variations of wind stress r. Wind mixing causes a pronounced asymmetry of the T s response by limiting the warming phase to only about half of the period that the surface heat flux Q is positive. The associated wind-driven current, the diurnal ........

Waves and turbulence on a beta-plane

Abstract: Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber kβ = (β/2U)½ independent of the initial conditions other than U, the r.m.s. particle speed, and β, the northward gradient of the Coriolis frequency.The conversion of turbulence into waves yields, in addition, more narrowly peaked wavenumber spectra and less fine-structure in the spatial maps, while smoothly distributing the energy about physical space.The theory is discussed, using known integral constraints and similarity solutions, model equations, weak-interaction wave theory (which provides the terminus for the cascade) and other linearized instability theory. Computer experiments with both finite-difference and spectral codes are reported. The central quantity is the cascade rate, defined as \[ T = 2\int_0^{\infty} kF(k)dk/U^3\langle k\rangle , \] where F is the nonlinear transfer spectrum and 〈k〉 the mean wavenumber of the energy spectrum. (In unforced inviscid flow T is simply U−1d〈k〉−1/dt, or the rate at which the dominant scale expands in time t.) T is shown to have a mean value of 3·0 × 10−2 for pure two-dimensional turbulence, but this decreases by a factor of five at the transition to wave motion. We infer from weak-interaction theory even smaller values for k [Lt ] kβ.After passing through a state of propagating waves, the homogeneous cascade tends towards a flow of alternating zonal jets which, we suggest, are almost perfectly steady. When the energy is intermittent in space, however, model equations show that the cascade is halted simply by the spreading of energy about space, and then the end state of a zonal flow is probably not achieved.The geophysical application is that the cascade of pure turbulence to large scales is defeated by wave propagation, helping to explain why the energy-containing eddies in the ocean and atmosphere, though significantly nonlinear, fail to reach the size of their respective domains, and are much smaller. For typical ocean flows, . In addition the cascade generates, by itself, zonal flow (or more generally, flow along geostrophic contours).

Open-ocean convection: Observations, theory, and models

Abstract: We review what is known about the convective process in the open ocean, in which the properties of large volumes of water are changed by intermittent, deep-reaching convection, triggered by winter storms. Observational, laboratory, and modeling studies reveal a fascinating and complex interplay of convective and geostrophic scales, the large-scale circulation of the ocean, and the prevailing meteorology. Two aspects make ocean convection interesting from a theoretical point of view. First, the timescales of the convective process in the ocean are sufficiently long that it may be modified by the Earth's rotation; second, the convective process is localized in space so that vertical buoyancy transfer by upright convection can give way to slantwise transfer by baroclinic instability. Moreover, the convective and geostrophic scales are not very disparate from one another. Detailed observations of the process in the Labrador, Greenland, and Mediterranean Seas are described, which were made possible by new observing technology. When interpreted in terms of underlying dynamics and theory and the context provided by laboratory and numerical experiments of rotating convection, great progress in our description and understanding of the processes at work is being made.