Estimates of gradient Richardson numbers from vertically smoothed data in the Gulf Stream region

Abstract

SUMMARY: We use several hydrographic and velocity sections crossing the Gulf Stream to examine how the gradient Richardson number, Ri, is modified due to both vertical smoothing of the hydrographic and/or velocity fields and the assumption of parallel or geostrophic flow. Vertical smoothing of the original (25 m interval) velocity field leads to a substantial increase in the Ri mean value, of the same order as the smoothing factor, while its standard deviation remains approximately constant. This contrasts with very minor changes in the distribution of the Ri values due to vertical smoothing of the density field over similar lengths. Mean geostrophic Ri values remain always above the actual unsmoothed Ri values, commonly one to two orders of magnitude larger, but the standard deviation is typically a factor of five larger in geostrophic than in actual Ri values. At high vertical wavenumbers (length scales below 3 m) the geostrophic shear only leads to near critical conditions in already rather mixed regions. At these scales, hence, the major contributor to shear mixing is likely to come from the interaction of the background flow with internal waves. At low vertical wavenumbers (scales above 25 m) the ageostrophic motions provide the main source for shear, with cross-stream movements having a minor but non-negligible contribution. These large-scale motions may be associated with local accelerations taking place during frontogenetic phases of meanders. -Hemos utilizado varias secciones hidrográficas y de velocidad, que atraviesan la Corriente del Golfo, con el fin de analizar como se modifica el número de gradiente de Richardson, Ri, debido tanto al suavizado vertical de los datos hidrográficos y de velocidad como a la aproximación de flujo geostrófico paralelo. El suavizado vertical de los datos originales de velocidad (intervalo de 25 m) conlleva un aumento substancial del valor medio de Ri, del mismo orden que el factor de suavizado, mientras que la desviación estándar permanece aproximadamente constante. Esto contrasta con los cambios muy pequeños en la distribución de los valores de Ri causados por el suavizado vertical del campo de densidades sobre distancias similares. Los valores medios geostróficos de Ri permanecen siempre por encima de los valores de Ri obtenidos mediante los datos originales de velocidad sin suavizar, típicamente uno o dos órdenes de magnitud mayores, mientras que la desviación estándar de los valores geostróficos usualmente es unas cinco veces mayor que la de los valores reales de Ri. En números de onda verticales altos (escalas de longitud por debajo de 3 m) la cizalla geostrófica solo ocasiona condiciones casi críticas in regiones que ya se encuentran bastante mezcladas. En estas escalas, por tanto, la mayor contribución a la mezcla por cizalla probablemente proviene de la interacción entre el flujo base y las ondas internas. En números de onda verticales bajos (escalas por arriba de 25 m) los movimientos geostróficos proporcionan la fuente principal de cizalla, teniendo los movimie...

High‐resolution comparison of sediment dynamics under different forcing conditions in the bottom boundary layer of a shallow, micro‐tidal estuary

“…The Ri was estimated using for BBL to examine the relative importance between stratification and shear instability (Figures 8c and 8d). Large values of Ri indicate a stable condition, while low values may indicate dynamic instability, with the transition taking place at a critical Richardson number of order of one [ van Gastel and Pelegrí , 2004]. The Ri showed a noticeable difference between winter 2008 and spring 2009.…”

Hydrographic conditions near the coast of northwestern Baja California: 1997–2004

“…This number serves as a criterion for the linear stability of the geostrophic flow, which is guaranteed for Ri g > 1 (reported critical values vary between 0.25 and 1.0 (Kundu, 1990;van Gastel & Pelegri, 2004)). Our values are generally higher than 1.5.…”

Ocean rheology

“…not being influenced by buoyancy) and approximately corresponds to the high wave number cutoff of the internal wave spectrum [20]. Following the previous considerations we have selected a Pegasus horizontal velocity data set [21,22], with vertical resolution δz = 25 m. This appears to be enough to resolve the major dynamical features of the flow [18], while remaining of the same order but above the Ozmidov scale. For our analysis we have used data from two positions in the North Atlantic that are dynamically very different.…”

“…The key point is the selection of δz such that is neither much larger than the relevant dynamical features nor below the size of internal waves, i.e. that it corresponds to a vertical wavelength capable of assessing the inertial transfer from large to small eddies [17,18]. In the stratified ocean this scale is the buoyancy (or Ozmidov) scale given by [19]:…”